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Quality Control Assurance

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
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Introduction to Quality Control

and Total Quality System

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Evolution of Quality Control

• Egyptians demonstrated a commitment to quality in the

construction of pyramids
• Quality of Greek architecture of 5th century B.C was so
envied that it profoundly affected the subsequent
architectural constructions of Rome
• Middle ages and up to 1900: Operator Quality Control
– Production of goods and services were predominantly confined to
single person or a group
– Generally they are family owned business and hence responsibility
of maintaining quality was determined by individual who is
producing it

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Evolution of Quality
Control – contd..
• Middle ages and up to 1900 – contd..
– Volume of production was limited
– Controlling the quality of the product was thus
embedded in the philosophy of the worker because
pride in workmanship was widespread
– Sculptures, Goldsmith etc.
• Early 1900 to about 1920: Foreman Quality
control
– Industrial revolution resulted in concept of mass
production
– Resulted in principle of specialization of labour and
hence individual not responsible for producing whole
product
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Evolution of Quality
Control – contd..
• Early 1900 to about 1920 – contd..
– Lacked in sense of accomplishment in their work, but
become skilled at a particular accomplishment
– But people are grouped together, where a supervisor
who directed that operation had the task of ensuring
that quality was achieved
• 1920 to 1940 : Inspection quality control phase
– Products and process were complicated and also the
volume increased
– Resulting in increase in number of workers under a
foreman and hence prevents him from keeping close
watch

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Evolution of Quality
Control – contd..
• 1920 to 1940 : Contd..
– Hence inspectors were designated to check quality of
the product after certain operations comparing it with
standards. If any problem, checked product is reworked
or discarded
– Foundation of statistical aspects of quality control were
developed
– W.A Shewhart developed control charts in 1924
– H.F. Dodge and H.G. Romig was working on acceptance
sampling plan and its application was started in late
1920s
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Evolution of Quality
Control – contd..
• 1940 to 1960 : Statistical quality control
– Production requirements increased during World war II
and hence 100% inspection was not feasible
– ASQC was formed in 1946 and developed sampling
inspection plans for military purposes MIL-STD-105A
– E. Deming visited Japan and lectured on importance of
statistical quality control in 1950
– J.M. Juran visited Japan in 1954 and impressed upon the
strategic role that management plays in achieving quality
program
– In 1959, Inspection and Quality control handbook was
updated with multi-level continuos sampling plan as well
as topics in life testing and reliability

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Evolution of Quality
Control – contd..
• 1960 to 1970 : Total quality control
– Gradual involvement of other departments and
management personnel in quality control process
– Attitude of quality is responsibility of inspection
department started changing
– Concept of ‘zero defect’ which emphasized productivity
through worker involvement emerged
– Use of Quality circles was started in Japan, which is based
on participative style of management
• 1970 to present : Total quality control
Organization wide
– Involves participation of everyone in the company from
the operator to supervisor to manager to CEO

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Evolution of Quality
Control – contd..
• 1970 to present : contd..
– A quality system was evolved which is
• Agreed on companywide operating work structure
• Documented integrating technical and managerial procedures
• Guiding the coordinated actions of men, machine and
information of the company
• To assure customer quality satisfaction and economical cost of
quality
– Expanded use of Ishikawa diagram
– G.Taguchi introduced the concept of quality
improvement through design of experiments
– With more advertisements on comparing competitors
brought quality into limelight

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Evolution of Quality
Control – contd..
• 1970 to present : contd..
– Top management saw the need for the marriage of quality
philosophy to production in all phases from determination
of customer needs, product design and customer service
– Training program in SQC methods for all workers
– With the wide use of computers, lot of quality control
software came and hence the emphasis on vendor quality
control, product quality audit were placed
– In this phase, customer will reign supreme as the
determiner of acceptable level of quality
– Industries need to adjust to this or lose market share

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Quality - Definition

• Juran (1974): Fitness for use

• Crosby (1979): Conformance to requirements or specifications
• Garvin (1984)
– Divides the definition of quality into 5 categories
• Transcendent (always improving or uplifting)
• Product-based
• User-based
• Manufacturing-based
• Value-based
– 8 attributes can be used to define quality
• Performance Features Reliability
• Conformance Durability Serviceability
• Aesthetics Perceived Quality
• Mitra (2000)
– Is the fitness of the product or service for meeting or exceeding its
intended use as required by customer

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How to define quality?

• Defined using Quality Characteristics

• Quality characteristics
– Defined as the elements that define the
intended quality level of the product or service

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How to define quality? – contd..

• Diameter
• Length
• Pressure
• Wall Thickness

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How to define quality? – contd.

• Taste, Smell

• Price, Way of serving

etc.

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How to define quality? – contd.

Place B Place A

• Time
• Reliability

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How to define quality? – contd.

• Honesty
• Courtesy

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Quality characteristics

• Can be grouped under 4 categories

– Structural characteristics: Length, Viscosity, Strength
– Sensory characteristics: Taste, smell, etc.
– Time related characteristics: Warranty, reliability
– Ethical characteristics: Honesty, courtesy etc.
• Are of two types
– Variables
• Measurable and expressed on numerical scale,
• Eg., Diameter, Resistance etc.
– Attributes
• If a characteristic is said to be conforming or non conforming or
that cant be measured
– Variable can be attribute, but attribute cannot be variable
• It results in economical measurement and time saving 17
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Some Terminologies
• Nonconformity • Nonconforming unit
– A quality characteristic – A unit that has one or
that does not meet its more nonconformities
stipulated specifications such that the unit is
– Eg. Thickness of plate: 5 unable to meet the
+/- 0.1, but if it is 5.2,
then nonconformity intended standards and
is unable to function as
required
– Eg. A plate having both
thickness and length
failing to meet
specifications

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Some Terminologies
• Defect • Defective
– Associated with quality – Severity of one or more
characteristic that does not defects in a product may
meet certain standards cause it to be unacceptable
– According to ANSI (The
American National Standard
Institute), a defect is a
departure of quality
characteristic from its
intended level or state that
occurs with a severity
sufficient to cause an
associated product or
service not to satisfy
intended normal or
reasonable foreseeable
usage requirements

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Some Terminologies – contd..
• Standard / specification • Standard
– Refers to a precise statement that – A prescribed set of conditions
formalizes the requirements of or requirements of general or
the customer, it may relate to a
product, process or a service broad application, established
• Specification by authority or agreement, to
– A set of conditions and be satisfied by a material,
requirements of specific and product, process, procedure,
limited application that provide a
detailed description of the test method etc and/or the
procedure, process, material, physical, functional,
product or service for use performance or conformance
primarily in procurement and
manufacturing characteristic thereof
– Standards may be referenced in – A physical embodiment of a
specification
unit of measurement (a
caesium block clock)

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Aspect of Quality

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Aspects of Quality
• Quality of design
– Implies that the product or service must minimally possess to
satisfy the requirements of the customer
– Design must be simplest and least expensive too
– Influenced by such factors as the type of product, cost, profit policy,
demand, availability of parts and materials, product safety etc.
– Eg: Customer requirement for yield strength of a cable is
100kg/cm2
– The parameters that influence the yield strength would be selected
to minimally satisfy this requirement
– In practice, the product is over designed with a safety factor k =
1.25, so the cable will be designed for 125 kg/cm2
– Increase in designed quality level will lead to increase in cost at an
exponential rate

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Aspects of Quality – contd.

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Aspects of Quality – contd..

Cost • Quality of design – Effect

Cost or of increase
value – Value of product increases
at a decreasing rate, with
Value the rate of increase
approaching zero beyond a
certain quality level
– At the middle, it maximizes
the difference between
value and cost, given that
minimum requirement ‘A’
is met.

Quality of design or designed

quality level

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Aspects of Quality – contd.

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Aspects of Quality – contd..

• Quality of conformance
– Implies that the manufactured product or service
rendered must meet the standards selected in the
design phase
– With respect to manufacturing, it is concerned with the
degree to which quality is controlled from the
procurement of raw material to the shipment of
finished goods
– It consists of 3 broad areas:
• Defect Prevention: deals with means to prevent the occurrence
of defects and is usually achieved using SPC techniques
• Defect Finding: Done through inspection, test and statistical
analysis of data from the process
• Defect analysis and rectification
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Aspects of Quality – contd..

• Quality of performance
– Is concerned with how well the product functions or
service performs, when put to use
– It measures the degree to which the product or service
satisfies the customer
– It is a function of both quality of design and quality of
conformance
– If a product does not function well enough to meet the
expectation of a customer or standards, then
adjustment need to be done in the design or
conformance phase
• Relation between QOD, QOC, QOP

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Aspects of Quality – contd..

Quality of
conformance

Quality of Quality of
design performance

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Aspects of Quality – contd..

• Relation between QOD, QOC, QOP – contd..

– QOD has an impact on the QOC
– Eg. If length of a shaft is 20 +/- 0.2mm, then the tools,
equipment and operations should be able to achieve
this design specification , ie. QOC should be capable of
meeting QOD, if not QOD is affected
– This result in constant exchange of information between
QOC and QOD or design and manufacturing phases for a
feasible design to be achieved
– Only single line interaction between QOC and QOP,
because, if QOD is met in QOC phase, then the QOP will
always be good and hence no double line

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Quality Control

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Quality control

• It is defined as a system that is used to maintain a

desired level of quality in a product or service
• Can be achieved by planning, design, use of proper
equipment and procedures, inspection and taking
corrective action in case of deviation
• 3 main sub areas
– Off-line quality control
– Statistical process control
– Acceptance sampling plans

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Quality control – contd..

• Offline Quality Control

– Procedures dealing with measures to select and choose
controllable product and process parameters in such a
way that the deviation between the product or process
output and the standard will be minimized
– Design of products and processes within the constraints
of resources and environmental parameters, so that
output of production meet the standards
– Most of the product and process parameters are set
before production
– Examples: Experimental design, Taguchi methods

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Quality control – contd..

• Statistical Process Control

– Involves comparing the output of a process or service
with a standard and taking remedial action in case of a
discrepancy
– Also involves whether a process can produce a product
that meets desired specification
– Generally SPC are online control procedures
– The information is gathered about the product, process
or service while it is functional and when the output
differs from a norm, corrective action is taken during
operation

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Quality control – contd..

• Statistical Process Control – contd..

– It is most desirable to corrective action on a real time
basis, as it minimizes the
• No. of unacceptable items produced
• Time over which undesirable services rendered
– Prevailing theme of quality control is that “Quality has
to be designed into the product or service; it cannot be
inspected into it”
– Though offline quality control measures are taken, there
may be a need for online quality control, because
variation in the manufacturing stage of the product or
the delivery of a service is inevitable
– A combination of offline and online quality control
measures will lead to a desirable level of operation

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Quality control – contd..

• Acceptance sampling plans

– Deals with inspection of product or service
– Used when 100% inspection is not possible
– Requires a decision on how many items should a sample
contain?
– Sample is inspected
– Compared with acceptance number, i.e. no. of
nonconforming items allowed in a sample and if less,
the whole batch is accepted
– Acceptance criteria is based on meeting certain
stipulated conditions (such as the risk of rejecting a
good lot or accepting a bad lot)
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Quality Assurance

• Quality is not the responsibility of one person in the

organization
• Role and purpose of the quality assurance function is to
have a “System that ensures all procedures that have been
designed and planned are followed”
• Objective of quality assurance is to have in place a formal
system that continually survey the effectiveness of the
quality philosophy of the company
• Definition: “It refers to all those planned or systematic
actions necessary to provide confidence that a product or
service will satisfy given needs”
• Quality assurance is conducted by carrying out a AUDIT to
check whether the given procedures are followed or not

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Quality Improvement

Is a never ending process to reduce both the variability of process and the
production of nonconforming items
Process control deals with identification and elimination of special causes that
force a system to go out of control, while quality improvement relates to the
detection and elimination of common causes

• Common causes • Special causes

– Inherent to the system and are – Not inherent to the system
always present – Impact on the output is not
– Impact on the output may be uniform
uniform – Are controllable by the
– Needs the attention of operator
management – Are those for which an
– Accounts for at least 90% of the identifiable reason can be
quality problems determined like tool wear, poor
raw materials etc.
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Quality Improvement – contd..

• Supports the principle that no deviation from a

standard is acceptable, which is similar to the
principle of the loss function developed by Taguchi
• Methods for quality improvement are graphical
techniques like Pareto chart, fishbone diagrams,
Process capability, DOE etc.
• Three stages of quality improvement
– Commitment stage
– Consolidation stage
– Maturity stage

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Quality Improvement – contd..

• Three stages of quality improvement – contd..

– Commitment stage
• Management agrees to take QIP
• Formal plan and policy are developed and organization structure is put
into place
• 2 stages: Introduction and Initial implementation
• Introduction (3 to 6 months)
– Policy statement
– Plans for creating infrastructure to implement quality improvement
methods
• Initial implementation (6 months to 1 year)
– Problem identified
– Elimination of special causes
– Process is brought into statistical control
• Time depends on business climate, type of company, product or
process, resource availability, management perception

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Quality Improvement – contd..

• Three stages of quality improvement – contd..

– Consolidation stage
• Objective is to produce an item that conform to requirements
• Start a continual improvement in the efficiency and
productivity of the process
• Improving common causes is necessary, which improves
process capability
• Involves huge investment to reduce error
• Education and training are integral part
– Maturity stage
• Quality improvement and management are way of life
• Very few defects are produced and focus in on defect
prevention

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Examples of quality problems

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Examples of quality problems

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Quality Circle and Quality Improvement
Team
• Quality circle • Quality Improvement team
– Informal group – Formal group
– Participation is voluntary – Participation is mandatory
– People from same area or – People from different
dept. department
– Consists of operators, – Work towards improvement
supervisors and managers of product or process from
– Work towards improvement quality perspective
of product, process or their – Team gets dismantled after
personal well being completion of project
– Team never gets dismantled
– Productivity improvement
tool

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Total Quality System – contd..

• Elements of total quality system

(ANSI/ASQC STD Z1.15) – contd..
– Legal requirements – Product liability and user
safety
• Providing clear directions on usage of the product
• All advertising statements to be supported by
certified data
• Creation of warranty policy, and policy of
replacement, service etc. for the failure of products
– Sampling and other statistical techniques

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References

• Text book
• www.iisd.org
• YouTube video
https://www.youtube.com/watch?v=guJ4I3O
8DeU
https://www.youtube.com/watch?v=Jxn2sdZ
TLH0

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Thank You

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Quality Control Assurance &

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
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Design to Customer satisfaction

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Benefits of Quality Control
• Cannot be realized immediately, but on long-term
perspective
• Benefits
– System is continually evaluated and modified to meet the
changing needs of customers and hence a mechanism
exists to rapidly modify product or process
– QC improves productivity as it reduces the scrap and
rework
– QC reduces cost in the long run and helps productivity and
cost reduction go hand in hand
– Improved delivery dates, due to reduction in lead time for
producing parts and SubAssembly are reduced
– Helps to stay competitive
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Responsibility for Quality

• All department right from top management to

each worker should have responsibility
• For a high product quality, all these functions
should take responsibility
– Marketing and product planning
– Product design and development
– Manufacturing Engineering
– Purchasing
– Manufacturing
– Inspection and testing
– Packaging and storing
– Customer service

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Total Quality System
• Quality system is defined as the collective plans, activities
and events that are provided to ensure that a product,
process or service will satisfy customer needs
• System approach integrates the various functions and
responsibilities of different units and provides a
mechanism to ensure that org. goals are met through
proper coordination of other departments
• Elements of total quality system (ANSI/ASQC STD Z1.15)
– Policy, planning organization and administration
• A quality policy is developed inline with org. goals
• Quality manuals are created, which gives the detailed procedure and
costs
• ANSI-American National Standards Institute

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Total Quality System – contd..

• Elements of total quality system (ANSI/ASQC STD

Z1.15) – contd..
– Product design assurance, specification, development
and control
• Product design based on customer requirements
• Tolerances on product characteristics, based on manufacturing
capabilities is developed
• Procedures to check and control the product characteristics to
conform the design standards during production
– Control of purchased materials and component parts
• Procedures to evaluate the capability and performance of
vendors
• Setting of specifications for the incoming materials
• Inspection and checking procedure for incoming materials to be
followed
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Total Quality System – contd..

• Elements of total quality system (ANSI/ASQC STD

Z1.15) – contd..
– Production quality control
• Involves determining process specifications, selecting equipment,
training personnel, designing forms and charts, doing process
capability analysis etc.
• Having preventive maintenance and feed forward control, where
when changes are made in product or processes, the information is
conveyed to those who deal with subsequent operations, with
emphasis on concurrent control during the transformation process
• Developing product quality audits to detect departures from
specified standards
– User contact and field performance
• A system that exists to collect information from the consumer to
determine the level of performance of the product or service
• Developing policies for installation and servicing and determining
guidelines for compliance with these policies to provide customer
satisfaction

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Total Quality System – contd..
• Elements of total quality system
(ANSI/ASQC STD Z1.15) – contd..
– Corrective action
• Problems are to be detected, categorized and
systematically documented, similar to that of the
remedial actions
• Specific procedures for corrective action for entities like
materials, vendors, process, equipment should be
developed
– Employee selection, training and motivation
• Guidelines should be established to select people for
particular jobs and job manuals to train people
• Recognition of superior effort and use of motivational
program help reassure employees of the support of mgt.
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Total Quality System – contd..

• Elements of total quality system

(ANSI/ASQC STD Z1.15) – contd..
– Legal requirements – Product liability and user
safety
• Providing clear directions on usage of the product
• All advertising statements to be supported by
certified data
• Creation of warranty policy, and policy of
replacement, service etc. for the failure of products
– Sampling and other statistical techniques

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Quality Cost

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Quality Costs

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Quality Costs

• Measure of performance of the total quality system

• 4 major categories for quality costs are:
– Prevention costs
– Appraisal costs
– Internal failure costs
– External failure costs
• Prevention costs
– Incurred in planning, implementing and maintaining a quality
system
– Includes salaries, development cost for product design, process,
equipment design, info. System design, education and training, cost
of a quality audit
– Prevention costs increase with the introduction of a quality system
and may be a significant proportion of the total quality system
– It increases with time
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Quality Costs – contd..

• Appraisal costs
– Are those associated with measuring, evaluating or
auditing products, components, purchased materials to
determine the degree of conformance to the specified
standards
– It includes inspection and test of incoming material,
product inspection and testing, cost of calibrating and
maintaining measuring instruments etc.
– These costs occur during or after production, but before
the product is released to the customer
– It decreases with time

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Quality Costs – contd..

• Internal failure costs

– Incurred when products or services fail to meet quality
requirements prior to the transfer of ownership to the
customer
– Includes scrap & rework costs for the materials, labor
and overhead associated with production.
– Also includes cost of lost production time, downgrading
cost, re-inspection cost etc.
• External failure costs
– Incurred when the product does not perform
satisfactorily after ownership is transferred to customer
– Includes cost of adjustment, investigation, costs due to
receipt handling, repair and replacement of parts,
warranty charges etc.
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Quality Costs – Examples

• External quality cost

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Quality Costs – Examples

• Internal quality cost

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Quality Costs – Examples

• Prevention cost

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Quality Costs – Examples

• Appraisal cost

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Measuring Quality Costs

• Magnitude of quality cost cannot be considered

because conditions often change like no. of units
etc which affects the direct cost of labour and
materials and hence total costs
• 4 indices were developed as a measurement base
– Labour base index
• Is defined as the quality costs / direct labour hour
• Should be used for short periods, as during extended periods,
the impact of automation may be significant
• Mainly useful for line and middle management

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Measuring Quality Costs – contd..
• 4 indices – contd..
– Cost base index
• Quality costs / dollar of manufacturing costs
• Includes direct labour, material and overhead costs
• More stable than labour base index because its not affected by
price fluctuations or changes in level of automation
• Important for middle management
– Sales base index
• Quality costs / dollar of sales
• Used by top management
• Not a good measure for short-term, but for long-term strategic
decisions, because sales lag behind production and are
subjected to seasonal variations
• Changes in selling price also affect this index
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Measuring Quality Costs – contd..
• 4 indices – contd..
– Unit base index
• Quality costs / unit of production
• Used only when output from different production lines are
similar
• For dissimilar ones, the product lines have to be weighted and
standardized product measure computed
– For all these indices, a change in denominator causes
the value of the index to change, even if quality cost do
not change
– Cost of direct labour decreases due to productivity
improvement, labour base index decreases, and it
should not be treated as increased quality costs
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Effect of Quality on..

• Productivity
– Quality decreases productivity is a misconception
– Quality relies on “make it right first time”, which
increases productivity
– Quality reduces waste (less scrap and rework) and
hence valuable resources can be utilized for production
of defect free goods.
• Effect on cost
– Prevention and appraisal cost
• Increases with initial improvements in productivity and due to
adequate process control procedures are installed
• With time, a reduction in appraisal costs is observed
• These costs are called costs of conformance to quality
requirements

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Effect of Quality on..

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Effect of Quality on.. – contd..

• Effect on cost – contd..

– Internal and External cost
• With improved quality, these costs decrease, which usually
offset the increase in prevention and appraisal cost
• Reduction in rework an scrap results in increased time for
productive output and hence the profitability
• Effect on Market
– An improvement in quality lead to increased market
shares, improved competitive position and increased
profits
– Due to decrease in external failure costs and increase in
performance of product
– High price can be charged and due to efficient resource
utilization, a firm can reduce cost of product

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Management of Quality
• Achieved through functions of planning, organizing,
staffing, directing and controlling
• Eg. Product development
Management function Product phase Action to be taken

Plan Proposal - Develop quality policy

phase - Plan for quality
- Consider product liability / safety

Organize Design / - Develop an org. structure

planning - Design assurance
phase - Design change control
- Develop production quality planning

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Management of Quality – contd..
Management Product phase Action to be taken
function

Staff Pre production - Select employee

phase - Train employee
- Motivate employees

Direct Production phase - Monitor purchased materials

- Monitor process control
- Direct final inspection
- Direct handling inspection

Control Production and Post - Obtain quality info.

production - Get data on field performance
- Take corrective action
- Conduct SQC
- Manage quality cost
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Total Quality Environmental Management

• Social responsibility of the organization is to operate and

maintain safe and adequate environmental conditions
– Eg. Xerox uses only recyclable and recycled thermoplastics and
metals
• ISO 14000 standards promote this philosophy with the
objective of uniform environmental management
standards that do not create unnecessary trade barriers
• It involves
– management commitment to continuous improvement,
– compliance and pollution prevention,
– creating and implementing environmental policies,
– integrating environmental considerations in operating procedures,
– conducting audits of the environment management system etc.

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The objectives of Total Quality Environmental

Management are to:
• reduce waste and improve continuously,
• reduce resource depletion,
• reduce or eliminate environmental pollution,
• design products for minimal environmental impact in production, use and
disposal,
• control environmental impact of raw material sourcing,
• control environmental impact of new developments,
• promote environmental awareness among employees and
• promote environmental awareness within the community.

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Case study- BBC

• The BBC spends £700 million (nearly $1 billion) a year on

goods and services, with no fewer than 20,000 suppliers.
• It employs 24,000 people, who collectively travel 17 million
kilometres a year by road and 38 million by air.
• The BBC occupies more than 500 buildings in the UK.
• In London alone, it produced 4,600 tonnes of waste in
2001, 85% of which was landfilled.

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Environment impact group

• Waste
• Utilities (energy & water)
• Transport
• Supply chain and procurement
• Property

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Challenges

• BBC is the ongoing transition from analogue to

digital broadcasting.
• The latter has a higher electricity demand, which
makes it difficult to achieve a reduction in overall
greenhouse gas emissions.
• To make matter worse, both systems are being run
simultaneously until the changeover to digital is
complete.

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Action

Waste
• Complete a comprehensive audit of waste throughout the BBC,
concentrating on paper, tapes and toner cartridges;
• Recycle at least 25% of office waste by 2003, rising eventually to 55%.
Utilities
• Each building manager to select an energy efficiency initiative, to be
run as a pilot programme;
• Reduce carbon dioxide emissions by 1% in the next year
Transport and travel
• Reduce car travel at the London White City site by 20% over four years,
by encouraging public transport use, cycling, teleworking and walking;
• Target the business units which require the most intensive transport
use.

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Supply chain and procurement

• Conduct an environmental risk analysis on suppliers and products;
• Identify what the BBC spends most money on, and prioritise those areas for assessment;
• Set up partnerships with suppliers to improve environmental performance;
• Develop an assessment scheme that enables the BBC to identify environmentally active
suppliers;
• Update the BBC's purchasing policy to incorporate environmental objectives;
• Introduce awareness training for all staff who procure goods and services.
Property
• Run a site compliance programme to set a baseline for future improvements;
• Develop an environmental brief for building 'churn', the process of teams coming together in a
space over a fixed time period;
• Improve specification and tendering documentation;
• Include environmental considerations at financial approval stage;
• Implement the 'Considerate Constructors Scheme' on BBC contracts;
• Develop guidance notes for projects, construction and facilities management staff;
• Build all new buildings to BREEAM (Building Research Establishment Environmental
Assessment Method) 'Excellent' standards

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Trends in Quality

• Quality certification
• Quality as project
• Quality in role of strategy
• Quality and sustainability(people and QMS)

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References

• Text book
• www.iisd.org
• GEMI practice
• Curkovic, Sime, and Robert Sroufe. "Total
quality environmental management and
total cost assessment: An exploratory
study." International Journal of production
economics 105.2 (2007): 560-579.
• YouTube video
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Homework

• TQEM practice for your organization

• Identifying cost of poor quality
• Quality consciousness

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Chapter - 2

• Some philosophies and their

impact on Quality

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Some Quality Gurus

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Deming’s contribution
• He emphasized on the role of management
• His approach is not a quick fix, rather a plan of
action to achieve long term goals
• Heart of his philosophy is that management and
workers should speak a common language – the
language of statistics
• His 14 points will form a framework for action and
it needs to be installed for the program to be
successful
• He identified the key components for continuous
improvement / “System of profound knowledge”
– Knowledge of the system and the theory of
optimization
– Knowledge of the theory of variation
– Exposure to the theory of knowledge
– Knowledge of psychology
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Deming’s contribution – 88

contd..
• “System of profound knowledge” – contd..
– Knowledge of the system and the theory of
optimization
• Management needs to understand that optimization of
total system is the objective and not optimizing the sub
system to have sub-optimal total system
– Knowledge of theory of variation
• Management should understand special causes and
common causes in the variation of process
• Special causes can be controlled by operator or engineer
• Common causes should be reduced by management
only, which makes the system stable and in control

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Deming’s contribution – 89

contd..
• “System of profound knowledge” – contd..
– Exposure to the theory of knowledge
• Experience and intuition are not of value to
management unless they can be interpreted and
explained in the context of a theory
• A data-analysis oriented approach to problem solving is
needed to suggest remedial action based on results
– Knowledge of psychology
• It is required to understand the behaviour and
interactions of people, and also the interactions of
people with their work environment
• People are motivated by intrinsic and extrinsic factors
– Job satisfaction and motivation: Intrinsic
– Reward and Recognition: Extrinsic
• Management should create the right mix of these factors
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Thank You

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Quality Control Assurance

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
Deming’s contribution – 92

contd..
• “System of profound knowledge” – contd..
– Exposure to the theory of knowledge
• Experience and intuition are not of value to
management unless they can be interpreted and
explained in the context of a theory
• A data-analysis oriented approach to problem solving is
needed to suggest remedial action based on results
– Knowledge of psychology
• It is required to understand the behaviour and
interactions of people, and also the interactions of
people with their work environment
• People are motivated by intrinsic and extrinsic factors
– Job satisfaction and motivation: Intrinsic
– Reward and Recognition: Extrinsic
• Management should create the right mix of these factors
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Deming’s 14 points for
management
• Focus is on Management
• He expects a fundamental change in the style of
management and corporate culture
• Corporate culture should be in such a way that the
workers feel comfortable enough to recommend
changes
• Point 1: “Create and publish to all employees a
statement of the aims and purposes of the company”
– Management must demonstrate constantly their commitment
to this statement
– Emphasis is on long-term strategic plans and also on mission
statements that need to be understood by employers,
consumers, vendors and investors too.
– Can be achieved by
• Product Improvement cycle
• Constancy and consistency of purpose 3
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Deming’s 14 points for 94

management

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Deming’s 14 points for
management

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Deming’s 14 points – contd..
• Point 1 – contd..
– Product Improvement cycle (Figure)
• It integrates the phases of QOD, QOC, QOP
• All customer needs must be quantified
• Company must focus on the customer and not on the
competitor
– Constancy and consistency of purpose (Figure)
• Implies setting a course (say all dept. follow the quality
improvement) and keeping to it
• Allocates resources for long-term planning, employee
training and education, which ensures that it can
maintain a competitive position for years to come
• Should not look into short term profits
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Deming’s 14 points – contd..
• Point 1 – contd..
– Constancy and consistency of purpose – contd..
• Company should not deviate from long-term objectives
• i.e. it should accept that variability exists in any
operation and hence it should try to reduce
• Doing your best is not good enough, you have to know
what to do, then do your best
• Point 2
– Learn the new philosophy, top management and
everybody
• Quality consciousness must be everything to everyone
• Acceptable level of defect should be abandoned and one
should work towards reducing defects continuously and
also address the need of customer

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Deming’s 14 points – contd..
• Point 3
– Understand the purpose of inspection, for
improvement of processes and reduction of cost
• Inspection does not increase quality, it just separates out
acceptable and non acceptable items
• It does not address the root cause of problem
• Hence emphasis should be placed on defect prevention
rather than defect detection
– Drawbacks of mass inspection
• Even 100% inspection will not eliminate all the defectives if
more than one person is responsible for inspection
• Reason being that, it is only human to assume that others
will find what you have missed
• Also the inspector fatigue should be taken into account
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Deming’s 14 points – contd..
• Point 4
– End the practice of awarding business on the basis of price
tag alone
• Companies should review the bidders approaches to quality
control, and if possible should know what is the fraction of non
conforming items and the stability of process etc.
• Generally contract should be based on effective price per unit
• Eg. 16Rs. With 8% defective and 17Rs with 2% defective
– Principle of vendor selection
• While selecting a vendor, the total cost should be taken into
account
• Vendors and buyers should work as a team to choose methods
and materials to improve customer satisfaction
• It is desirable to have reduced no. of suppliers
• Having multiple suppliers results in mistrust between vendor
and buyer and hence no long-term relationships
• Price not quality is the driving factor
• Also results in variability in the incoming quality and hence
increased cost due to changes in setup, no volume discounts etc.

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Deming’s 14 points – contd..
• Point 5
– Improve constantly and
forever the system of
production and service
• Focus is on defect
prevention and
process improvement
which are carried out
by the use of statistical
methods
• Process improvement
should be based on
Deming’s cycle which
consists of 4 stages:
Plan Do Check and Act
(PDCA)
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Deming’s 14 points – contd..
• Point 5
– Plan
• Opportunities for
improvement are
recognised and
operationally defined
• Since customer
satisfaction is
important, degree of
difference between
customer needs
satisfaction and
process performance
are analysed
• Goal is to reduce the
difference and the
possible relationship
between the variables
in the process and
their effect are
hypothesized
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Deming’s 14 points – contd..
• Point 5 – contd..
– Do
• Cause of action
developed in
planning is put
into action
• If necessary trial
runs or prototype
are conducted
• Feedback is
obtained from
process and
customer
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Deming’s 14 points – contd..
• Point 5 – contd..
– Check
• Analysing the result
• Statistical methods
will be used
– Act
• Decision is made
regarding
implementation if the
results of the check
stage are positive and
if negative alternative
plans are developed

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Deming’s 14 points – contd..
• Point 5 – contd..
– Variability reduction
and loss function
• Deming’s philosophy calls
for abandoning the idea
that everything is fine if
specifications are met
• Based on this Taguchi
formalized loss function
in 1960
• i.e. It explains that
economic loss accrue
with any deviation from
the target value
• However the loss
increase in a non linear
relationship with larger
deviation from target
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Deming’s 14 points – contd..
• Point 6

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Deming’s 14 points – contd..
• Point 6
– Institute training
• Employee training is integral for individual performance in
the extended process setting
• When employees are hired, they should be carefully
instructed in the company’s goals and this helps them to
understand their responsibilities for meeting customer
needs
• A employee should know what is to be done and its
importance in the entire process, which will make them
take pride in their work
• It make them feel secure, have better morale and hence
improve their productivity
• Training should be ongoing
• According to Deming, it is necessary for all employee of the
organization to be trained in SQC tools
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Deming’s 14 points – contd..
• Point 7

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Deming’s 14 points – contd..
• Point 7
– Teach and institute leadership
• Supervisors are the vital links between
management and the workers
• To be effective leader, the supervisors
must think in terms of helping workers do
a better job and manage them
• Supervisors should be trained in SQC and
should create a atmosphere, which
improves employee morale, promotes
team work and help achieve the overall
annual goal of quality improvement
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Deming’s 14 points – contd..
• Point 8
– Drive out fear, create
trust. Create climate for
innovation
• Fear results in physical
or psychological
disorders, poor morale
and also results in lack of
job security and hence
reduces productivity
• An employee should feel
free to know about the
process, about his
responsibility and
should be able to suggest
something, which helps
in building trust and a
climate
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Deming’s 14 points – contd..
• Point 9
– Optimize toward the aims
and purposes of the
company, the efforts of
teams, group, staff areas
• Focus is to remove
organizational barriers –
both internal and external
• Internal barriers will result
in impeding the flow of
information /
communication between
the different level of
employees and also
between departments
• External barrier is the lack
of flow of information
between the customers,
investors and vendors,
which should be
eliminated
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Deming’s 14 points – contd..
• Point 10
– Eliminate
exhortations for the
workforce
• Never set a target
arbitrarily as it has
demoralizing effect
• Set the goal, which
should be feasible and
the management
should specify the way
to achieve it
• Goals should not be
intuitive or arbitrary,
but should be based
on information from
every level
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Deming’s 14 points – contd..

• Point 11
– Eliminate numerical
quotas for production.
Instead learn and
institute methods for
improvement
– Eliminate
management by
objectives. Instead
learn the capabilities
of processes and how
to improve them
• Work standards
should not be fixed,
because it is based on
quantity and not on
quality.
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Deming’s 14 points – contd..
• Point 11 – contd..
• Results in workers strive to meet the quota rather
than to produce acceptable goods, resulting in
inefficiency and increased costs
• Further it results in loss of pride in their work,
morale, motivation
• Generally, in work standards, allowance is made
for producing non conforming items, which is
against the philosophy of continuous
improvement
• Work standards fails to distinguish between
special causes and common causes, when
improvements in process are sought
• Common causes can be eliminated only by
management and if it can’t be eliminated if there
is no effort from management

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Deming’s 14 points – contd..
• Point 12
– Remove barriers
that rob people the
pride of
workmanship
• Quality is achieved in
all components of the
extended process,
when the employees
are satisfied and
motivated and when
they understand their
role in the context of
organization goals
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Deming’s 14 points – contd..
• Point 12 – contd..
– Factors that cause loss of pride
• Lack of treatment of employee with dignity
• Lack of communication of company’s mission to all
levels
• Assigning blame to the employees for not meeting
company goals though the output has problems due to
system
– Performance classification system
• Inconsistencies in performance evaluation and there
should not be categorization of employee from a similar
sample
• Teamwork should be given importance, when
conducting performance appraisal, those promoting
teamwork should be placed in higher category
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Deming’s 14 points – contd..

• Point 13

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Deming’s 14 points – contd..

• Point 13
– Encourage education and self improvement for
everyone
• Management must commit resources for education
and training as educated workforce can safeguard
improvement in quality and productivity and help
companies to remain competitive
• Point 6 is about training for new employee, while this
addresses the need for ongoing and continual
education, to adopt to the latest technology
• Advantages
– Increases motivation, as they feel that company is
spending for them and hence loyalty too increases
– Keeps the employees up to date on latest technologies
and promote teamwork
– Helps to adopt different jobs, as they grow in company
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Deming’s 14 points – contd..
• Point 14
– Take action to accomplish the transformation
• A structure must be created and maintained for the
dissemination of the concepts
• People must be trained in statistics at all levels of the
organization
• Companies should allow free flow of information among
different levels
Deming’s deadly diseases
– Management by visible figures only
– Lack of constancy of purpose
– Performance appraisal by numbers
– A short-term orientation / short term profits
– Mobility of management – short tenure of
management and managers should be avoided
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Crosby’s Philosophy

• He developed Quality Management Grid

• This grid has 5 stages of maturity and 6 measurement
categories
• Stages: Uncertainty, Awakening, Enlightenment, Wisdom,
Certainty
• Categories
– Management understanding and attitude
– Quality organization status
– Problem handling
– Cost of quality as a % of sales
– Quality improvement actions
– Summary of company quality posture
• Example: Problem handling
– Uncertainty: Fire fighting, yelling and accusation
– Awakening: Team setup to attack problem
– Enlightenment: Corrective action communicated in systematic
way
– Wisdom: Problem identified early on development stage 29
– Certainty: Problems is prevented BITS Pilani, Pilani Campus
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Crosby’s Philosophy – contd..

• 4 absolutes of quality management

– Definition: Quality means conformance
to requirements
– System for achievement of quality: The
rational approach is prevention of defects
– Performance standard: Only
performance standard is zero defects
– Measurement: Performance
measurement is the cost of quality
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Crosby’s Philosophy – contd..
• 14 step plan for
quality improvement
– Management
commitment
• Emphasis on defect
prevention should be
communicated
• Quality policy should
states that individual
performance
requirements must
match the customer
requirements

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Crosby’s Philosophy – contd..
• 14 step plan – contd.
– Quality improvement team
• Representation from each department or division
form the team
• Responsible for bringing suggestions to actions

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Crosby’s Philosophy – contd..
• 14 step plan for
quality improvement –
contd..
– Quality measurement
• Identifies the status of
quality
• Identifies area where
corrective action is
needed and quality
improvement efforts
should be directed
• Results should be
placed in highly
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Crosby’s Philosophy – contd..

• 14 step plan for quality improvement – contd..
– Cost of quality evaluation
• Indicates where corrective action and quality improvement
will result in savings for the company
• It establishes a measure of managements performance

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Crosby’s Philosophy – contd..

• 14 step plan for quality improvement – contd..
– Quality awareness
• Results about the cost of non quality should be shared with
all employees including service and administrative people

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Crosby’s Philosophy – contd..
• 14 step plan for quality improvement – contd..
– Corrective action
• Needs open communication and action discussion of
problems
• Discussions exposes other problem not identified before
and helps to determine procedures to eliminate them
• Attempts to resolve problem should be made as they arise

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Crosby’s Philosophy – contd..
• 14 step plan for
quality improvement
– contd..
– Adhoc committee for
the zero defects
program
• Concept of zero defect
to be communicated
for all employee
• Committee is
responsible for getting
top management
commitment

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Crosby’s Philosophy – contd..
• 14 step plan for
quality improvement
– contd..
– Supervisor training
• All levels of
management must be
aware about the steps
of quality
improvement
programs
• They should be
explaining the
program to
employees
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Crosby’s Philosophy – contd..
• 14 step plan for
quality improvement
– contd..
– Zero defects day
• Philosophy of zero
defects should be
established
companywide and
should originate on
one day
• Management should
foster this type of
quality culture and
should try to motivate
the people
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Crosby’s Philosophy – contd..
• 14 step plan for
quality
improvement –
contd..
– Goal setting
• Employees along
with their
supervisors should
set specific
measurable goals,
which creates a
attitude among
people to achieve it
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Crosby’s Philosophy – contd..
• 14 step plan for quality
improvement – contd..
– Error cause removal
• Employees are asked to
identify reasons that
prevent them meeting
zero defect goal – They
should not make
suggestion, but list the
problem
• A separate functional
group should come up
with procedures for
removing it
– Recognition
• Award programs should
be based on recognition
rather than money, who
have met or exceeded 41
their goals BITS Pilani, Pilani Campus
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Crosby’s Philosophy – contd..

• 14 step plan for quality improvement

– contd..
– Quality councils
• Chairpersons, team leaders and
professionals associated with quality
program meets and discusses, which create
new ideas for further improvement
– Do it over again
• Whole process of quality improvement is
continuos

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Thank You

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 134

Quality Control Assurance &

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
 135
Juran’s Philosophy

• He believes that management has to adopt a unified

approach to quality, where the focus is on needs of the
customer
• Quality is defined as “fitness for use”
• Deterrents of unified approach are
– Existence of multiple functions and they believe it to be unique
– Presence of hierarchical levels in the organization structure
which has varied background and have different level of
exposure to quality management
– A variety of product lien that differ in markets, its production
processes etc.
• Unified approach is called “Quality Trilogy”, which
includes
– Quality planning
– Quality control
– Quality improvement
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Juran’s Philosophy

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Juran’s Philosophy – contd..
• Quality planning
– Occurs at various levels of
organization, each having a
distinct goal
– Strategic quality
management, where broad
quality goals are set, and a
management chooses a
plan of action and allocates
resources to achieve the
goals
– Operational quality
management, where
departmental goals are set,
inline with strategic goals
– At worker level, clear
assignment of task to each
worker to contribute to
departmental goal
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Juran’s Philosophy – contd..
• Quality control
– Goal is to run the process
effectively, such that plans
are enacted
– Any deficiency in planning
process, results in process
operating at high level of
chronic waste
– If unusual symptoms are
sporadically detected,
quality control will try to
identify the cause behind
the variation and remedial
action taken to bring it back
to control
– Objective is to eliminate the
cause of sporadic spike and
bring process output to
zone of quality 5
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Juran’s Philosophy – contd..
• Quality improvement
– Deals with continuous
improvement of product
and process
– It requires an action on
upper and middle
management
– Deals with actions like
creating new designs,
changing methods or
procedures, new
equipment investment
etc.
– Results in reducing the
chronic waste and hence
the cost of quality

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Quality trilogy – in detail

• Quality planning
– Identify the customer – both external and internal,
which is similar to that of Deming’s extended process
– Determine the customer needs. This decides the long
term survival of customers
– Develop product features that respond to customer
needs
– Establish quality goals that meet the needs of
customers and suppliers like and do so at a minimum
cost. Total cost from an organization point of view
should be minimum
– Develop a process that can produce the needed
product features
– Prove process capability: To establish whether the
process is adequate for making a product that
conforms to design specifications 7
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Quality trilogy – in detail: Contd..
• Quality control
– Choose control subjects
• Identify the product characteristics that is to be controlled in
order to make the product conform to requirements
• Selection is done by identifying the characteristics that has more
impact on customer
– Choose units of measurement
– Establish measurement
• Procedures for taking measurements are defined
• Involves identifying what equipments to be use, how to use, who
will be responsible, how to make measurements an when to
calibrate, what training is needed etc.
– Establish standards of performance
• Should be based on customer requirements
– Measure actual performance
• Concerned with measurement of actual process output; to know
the operation level of process
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Quality trilogy – in detail: Contd..
• Quality control – contd..
– Interpret the difference
• Compare actual and standard and if the process is stable,
the difference may not be significant
– Take action on the difference
• Take remedial action for the difference
• It is management’s responsibility to suggest a remedial
cause of action
• Quality Improvement
– Prove the need for improvement
• Identify problems and convert it into dollar figures to
attract management attention
• Convince the management and involve the management to
make a change in the process
– Identify specific projects for improvement
• Prioritize the problems, based on Pareto analysis as only 9
limited resources will be available
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Quality trilogy – in detail:
143
Contd..
• Quality Improvement – contd..
– Organize to guide the projects
• Establish a clear organization structure
• Assign authority and responsibility at all levels of
management to facilitate this
• Establish precise responsibilities: guidance for overall
improvement program, guidance for each individual
project and diagnosis and analysis for each project
– Organize for diagnosis – for discovery of causes
• A “Diagnostic Arm”, a group of persons brought together
to determine the causes of the problem
• Organization need to enlist the right people to ensure
that the required tools and resources. This is done by
“Steering Arm”
– Find the causes
• Involves data gathering and analysis to determine the
causes
• Involves studying the symptoms, hypothesising the
causes and validating it 10
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Quality trilogy – in detail: Contd..
• Quality Improvement – contd..
– Provide remedies
• Diagnostic step is based on cause and effect relationship
• Remedies may be for problems that are controllable by
management and those that are controlled by operators
• It may involve change in methods or equipment, which may
require substantial financial investment
– Prove that the remedies are effective under operating
condition
• Check whether the process can be implemented and will it have
benefits
• Breakthrough process requires overcoming resistance to change
• Proposed procedure may require new equipment and operators
may have to be trained
• Management commitment is vital
– Provide control mechanisms to hold the gains
• Once remedial action implemented, it need to be sustained, 11
which needs a control system like audit in some departments
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3 philosophies compared
Criteria Deming Crosby Juran
Definition of - Deals with - “Conformance -“Fitness for
quality predictable to requirements use”
uniformity of - Emphasis on - explicitly
product customer needs related to
- Emphasis on use implicitly meeting the
of SQC - Emphasize on needs
- Quality of product zero defects, the
depends on quality requirement
of process should be met
Management - Highly - Focussed on - Scales
commitment emphasized creating quality management
- Points 1, 2 and 14 culture which commitment at
are aimed at needs all levels
management management
commitment 12
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3 philosophies compared –
contd..
Criteria Deming Crosby Juran
Strategic - Top management - Need for - Need for
approach to involves pursuing all quality quality council
quality 13 points in a improvement and also
system structured cycle team emphasized on
problem-solving
steering and
diagnostic arms
Measurement - Depends on - Quality is free
of quality deriving a dollar and it is that un-
value for the total quality that costs
cost of quality
Never ending - Follow Plan-Do- - Repeats the Believes in
process of Check-Act cycle and cycle of quality breakthrough
improvement repeats planning, control sequence 13
and improvement BITS Pilani, Pilani Campus
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3 philosophies compared –
contd..
Criteria Deming Crosby Juran
Education - Emphasizes on - Emphasizes on - His stress on
and training training of new quality culture, education is
employee and also where education implicit
re-training on is a part of it
continuous basis for
existing people

Eliminating - Categorized as - No such - Special causes

the cause of special and categorization create sporadic
problem common causes problem
- 85% of problem - Common
can be solved by causes create
management Chronic
problem
14
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3 philosophies compared –
contd..
Criteria Deming Crosby Juran
Goal - No numerical goals - Explains that - Recommends an
setting should be established a mutually annual quality
- Never ending quality understandable improvement
improvement process goal, which is program with
to be followed and measurable specified goals
hence no short-term - Goals should be
goals set according to
requirements of
customer
Structural - Bottom up approach: - Top down - Quality
plan Bring process to approach improvement
statistical control: - Change in through a project
lower level management by project method
- common cause culture - used for middle
removed by top mgt. management 15
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Chapter - 3

Quality Management –
Practices, Tools and Standards

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Management Commitment
• Should have strategic plans with long-
term focus
• Should satisfy the customer and
investor by delivering quality products
• Can be accomplished by having a
‘Quality Program’ like TQE, TQM or Six
Sigma etc.
• Eg. Ford Motor Company follow Total
Quality Excellence (TQE) program
18
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Total Quality Excellence
• (TQE)
A system that integrates
all aspects of the company
and its suppliers into
strategic decision making
on different functions of a
company
• It is based on Ford’s
vision of “being a low cost
producer of the highest
quality products and
services which provide
the best customer value”
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TQE – Concepts, Functional
Areas
• Key Concepts
– Quality should be defined by customer
– Quality is achieved through prevention
of problems and not detection
– Vendor-Vendee concept, (Internal and
External Customer)
– All employees, suppliers, dealers and
part of the company (Deming’s
extended process)
– Quality improvement is never ending
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TQE – Contd..
• Functional Areas includes
Engineering, Delivery and
Commercial Performance
• Embraces the system approach
• Relies on partnership between
manufacturer and supplier
– Ford developed ‘Q101 Preferred
Quality Award’ for suppliers
• Emphasize on Process control, Customer
feedback and Documentation including
management developed documentation
for design and change control 21
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Q 101 Ford’s Preferred Supplier
Award

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Basic concepts of TQM

•What are the Basic Concepts of TQM. Explain?

• A committed and involved management to provide
long term top-to-bottom organizational support
• An unwavering focus on the customer – both internal
and external
• Effective involvement and utilization of the entire
work force
• Continuous improvement of the business and
production process
• Treating suppliers as partners
• Establish performance measures for the process

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Old vs. TQM Approach

Quality Element Previous Approach TQM Approach

Definition Product-oriented Customer-oriented
Priorities 2nd to service and Equals of service and cost
cost
Decisions Short-term Long-term
Emphasis Detection Prevention
Errors Operations System
Responsibility Quality control Everyone
Problem Solving Managers Teams

Procurement Price Life-cycle

costs,partnership
Manager’s Role Plan, assign, control, Delegate, coach, facilitate
and enforce and mentor

24
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Total Quality Management
(TQM)
• Management Commitment
– Must exists at all levels of the company
– Creates policy at top level, implements at
middle level and quality mgt tools and
techniques are used at operation level
• Customer
– Satisfying customer needs is the driving
force
– Direct feedback using a data driven
approach is the best way to identify
customer needs
– Key principle is that are customers are
both internal and external
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TQM – Contd..
Customer surveys are used to find the
discrepancies between expectation and
satisfaction and taking measures to
eliminate is called ‘Gap Analysis’
• Process
– Vendors are part of the process
– Cross functional team, with authority to
solve problem and improve the process
– Use of technical tools and techniques and
management tools is necessary to improve
continuously 27
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TQM – Contd..

• People
– Involving employees in the decision making
process (Empowerment)
– Ownership and motivation are necessary to
make employee get a sense of pride
• Communication
– Open channel of communication
– Emphasis is on Information sharing between
departments
– Change from role of management of
coordination and control to that of coaching
and caring 28
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TQM – Contd..

• Culture
– Links the human element and the
company’s vision
– They are the beliefs, values, norms and
rules that prevail within an company
– Culture should embrace a ‘participative
style’ of management
• Vision
– Tells about what company wants to be
– It is general and outlines the scope and
purpose of organization
– Should be motivational and make people
work towards the goal 29
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TQM – Contd..
• Mission
– Derived from vision
– More focused and defines the areas of
concentration
– No mention about time frame
• Quality Policy
– Framed by senior management, it is the
company’s road map
– Indicates what to be done, but different from
procedures and instructions
– Eg. ‘quality is the basic business principle at
Xerox’
– Outcome is the performance standard 30
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Vision and Mission Statement
• Vision
– Be recognized as the best education provider
in Mechanical Engineering
• Mission
– The Mechanical Engineering Group is
committed
• to provide a high quality (world-class) education
in Mechanical Engineering
• to conduct strong research programs
• to foster a close partnership with industry and
– The mission is guided by a continuous
improvement philosophy
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Vision and Mission – contd..

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Vision and Mission – contd..

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Six Sigma Quality
• Developed by Motorola
• Made popular by General Electric (GE)
• Some of the companies that has adopted 6 σ are
– Wipro
– CTS
– Satyam
– General Motors
– Ford India Limited
• Uses quantitative goals, based on the measure
of process variation (σ)
• The objective is to minimize the variation from
the existing level (if it is 3 σ) to half
• The concept of 6 σ is based on the concept of
normal distribution 34
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Variation – A Simple Test

• I think the topic of quality initially seems to

be interesting or is it our instructor in
charge from Mechanical Engineering Group
making me feel so? But our seniors has said
that it is a boring course and the instructor
always pose inappropriate and invalid
questions. He used to conduct lot of class
test and call it an assignment making this
course really tough. Even though you study
hard for this subject, finally, he will provide
you with the answer sheet containing
innumerable zeros and ones. Hence most of
the times, I will not even bother to visit the
quality class!!!
(Experience of a current student in the class)35
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Solution

• I think the topic of quality initially seems to

be interesting or is it our instructor in-charge
from Mechanical Engineering Group making
me feel so? But our seniors have mentioned
that it is a boring course and the instructor
always pose inappropriate and invalid
questions. He will conduct lot of class tests
and call it as assignments making it a hectic
course. Even if you study hard for this subject,
finally, he will provide you with the answer
sheet containing innumerable zeros and ones.
Hence most of the times, I will not even
bother to visit the quality class!!!
(Experience of a current student in the class)
36
• Total no. of ‘i’s = 49 BITS Pilani, Pilani Campus
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A Normal distribution
•

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 171
Six Sigma Quality – contd..
• For a process output given by normal
distribution
– Mean is the measure of location of process
– The no. of non-conforming product will be
2700ppm (1350ppm on each tail)
– Assume a product with 1000 processes or
parts, then the no. of defects per product will
be 2.7!!! (only 7 out 100 will be defect free)
• For defect free product, the process
spread given by (+/- 3 σ) has to be
significantly less than that between USL
and LSL 38
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A Normal distribution
•

39
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 173
Six Sigma – Contd..
• Focus of Six sigma is to reduce the process
variation such that the spec. limits are 6 σ from
the mean
• If process is stable and remains centered, the
proportion of defective will be 0.001ppm on
each tail (Ideal)
• Even for a shifts by 1.5 σ from the mean, no. of
defects will be 3.4ppm on each tail
• For the example above there will be 0.0034
defect per product and the yield will be 99.66%
• Requires a fundamental change in management
philosophy and culture
40
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Quality Function
Deployment (QFD)
• A planning tool that focus on designing
quality into a product
• A system that involves cross functional
team and takes care of complete cycle of
product development
• Helps to translate customer needs into
technical requirements of products
• Called as House of Quality, Matrix
product planning, Customer drive
41
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Questions answered by QFD
• What do customers want?
• Are all preferences equally important?
• Will delivering perceived needs deliver a
competitive advantage?
• How can we change the product?
• How do engineering characteristics influence
customer perceived quality?
• How does one engineering attribute affect
another?
• What are the appropriate targets for the
engineering characteristics? 42
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QFD “house of quality”

43
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QFD - Process

• It is based on a structure called House of

Quality (HOQ)
• Objective
– Delineates the scope of the project
– Only one task is specified in the objective
• What
– Voice of the customer, which express their
needs and wants
• Rating
– Scale of 1 to 5 is used to give prioritize the
wants (1 – Least and 5 – Most Important) 44
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Customer Rating

Voice of the Customer

45
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QFD – Process (Contd..)

• Technical Descriptors (Hows)

– All possible technical / engineering
requirements are found through
Brainstorming
– Done by a cross-functional team
• Target goals
– May or may not be used
– Uses symbols

46
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Target goals

Voice of the Designer

47
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QFD – Process (Contd..)

• Co-relationship matrix
– Forms the roof of HOQ
– 4 levels of relationship – strong
positive, positive, negative, strong
negative
– Used for determining the trade-off
between ‘Hows’

48
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x = Design Trade-offs

49
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QFD – Process (Contd..)

• Customer competitive assessment

– To identify the relative position of the
organization w.r.t competitors for each
needs
– Helps to identify the strength and
weakness of the company and thereby
close the gap
– Called as Product Benchmarking

50
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Benchmarking

51
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QFD – Process (Contd..)
• Technical Competitive Assessment
– Similar to that of customer assessment of
competitor
– Done by a technical staff of the company
– Used to set objective values for the
technical descriptors

52
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Technical Competitive
Assessment

53
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QFD – Process (Contd..)
• Relationship matrix
– A mechanism to analyse how each
technical descriptors will help in
achieving ‘What’
– Represented by 0 to 5, where 0 is no
relationship 1 – low, 3 – medium and 5 -
High

54
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55
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QFD – Process (Contd..)

• Absolute and relative scores are

calculated, based on which
prioritization of needs is done
• In next phase, the ‘Hows’ will
become ‘What’

56
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U – Us
M – Maytag
W – Whirlpool
G – GE
F – Frigidaire
A - Amana

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QFD – The real meaning
• It is used to take the ‘voice of customer’
and translate it into a set of product and
process parameters and can be deployed
through a 4-phase process
– Product planning
– Part / Subsystem deployment
– Process planning
– Production planning

58
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QFD – The real meaning – contd.

technical
requirements
component
characteristics
process
operations
quality plan

59
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QFD - Advantages

• Evaluates competitor from 2

perspectives – Customer and
Technical
• Used to identify the degree of
improvements needed in the product
and process
• Reduces the product development
time as it reduces product redesign
• Improves the communication
between different department
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QFD - Disadvantages
• Enormous amount of information must be
gathered
• Matrix is too large
– Prioritize on important attributes
– Analyzes independent subsystems independently
• Customer priorities not clear
– Consider segmenting market
• QFD process is implemented in phases and
hence time consuming
• QFD is messy
– Not QFD, but rather the interaction between diverse
groups is cause
– Stick with it, the results are worthwhile
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 195

Thank You

62
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Quality Control Assurance &

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
 197
A Normal distribution
•

2
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 198
Six Sigma – Contd..
• Focus of Six sigma is to reduce the process
variation such that the spec. limits are 6 σ from
the mean
• If process is stable and remains centered, the
proportion of defective will be 0.001ppm on
each tail (Ideal)
• Even for a shifts by 1.5 σ from the mean, no. of
defects will be 3.4ppm on each tail
• For the example above there will be 0.0034
defect per product and the yield will be 99.66%
• Requires a fundamental change in management
philosophy and culture
3
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 199
Quality Function
Deployment (QFD)
• A planning tool that focus on designing
quality into a product
• A system that involves cross functional
team and takes care of complete cycle of
product development
• Helps to translate customer needs into
technical requirements of products
• Called as House of Quality, Matrix
product planning, Customer drive
4
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 200
Questions answered by QFD
• What do customers want?
• Are all preferences equally important?
• Will delivering perceived needs deliver a
competitive advantage?
• How can we change the product?
• How do engineering characteristics influence
customer perceived quality?
• How does one engineering attribute affect
another?
• What are the appropriate targets for the
engineering characteristics? 5
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 201
QFD “house of quality”

6
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 202
QFD - Process

• It is based on a structure called House of

Quality (HOQ)
• Objective
– Delineates the scope of the project
– Only one task is specified in the objective
• What
– Voice of the customer, which express their
needs and wants
• Rating
– Scale of 1 to 5 is used to give prioritize the
wants (1 – Least and 5 – Most Important) 7
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Customer Rating

Voice of the Customer

8
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 204
QFD – Process (Contd..)

• Technical Descriptors (Hows)

– All possible technical / engineering
requirements are found through
Brainstorming
– Done by a cross-functional team
• Target goals
– May or may not be used
– Uses symbols

9
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Target goals

Voice of the Designer

10
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 206
QFD – Process (Contd..)

• Co-relationship matrix
– Forms the roof of HOQ
– 4 levels of relationship – strong
positive, positive, negative, strong
negative
– Used for determining the trade-off
between ‘Hows’

11
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x = Design Trade-offs

12
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 208
QFD – Process (Contd..)

• Customer competitive assessment

– To identify the relative position of the
organization w.r.t competitors for each
needs
– Helps to identify the strength and
weakness of the company and thereby
close the gap
– Called as Product Benchmarking

13
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Benchmarking

14
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 210
QFD – Process (Contd..)
• Technical Competitive Assessment
– Similar to that of customer assessment of
competitor
– Done by a technical staff of the company
– Used to set objective values for the
technical descriptors

15
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Technical Competitive
Assessment

16
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 212
QFD – Process (Contd..)
• Relationship matrix
– A mechanism to analyse how each
technical descriptors will help in
achieving ‘What’
– Represented by 0 to 5, where 0 is no
relationship 1 – low, 3 – medium and 5 -
High

17
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213

18
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 214
QFD – Process (Contd..)

• Absolute and relative scores are

calculated, based on which
prioritization of needs is done
• In next phase, the ‘Hows’ will
become ‘What’

19
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215

U – Us
M – Maytag
W – Whirlpool
G – GE
F – Frigidaire
A - Amana

20
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 216
QFD – The real meaning
• It is used to take the ‘voice of customer’
and translate it into a set of product and
process parameters and can be deployed
through a 4-phase process
– Product planning
– Part / Subsystem deployment
– Process planning
– Production planning

21
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 217
QFD – The real meaning – contd.

technical
requirements
component
characteristics
process
operations
quality plan

22
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 218
QFD - Advantages

• Evaluates competitor from 2

perspectives – Customer and
Technical
• Used to identify the degree of
improvements needed in the product
and process
• Reduces the product development
time as it reduces product redesign
• Improves the communication
between different department
23
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 219
QFD - Disadvantages
• Enormous amount of information must be
gathered
• Matrix is too large
– Prioritize on important attributes
– Analyzes independent subsystems independently
• Customer priorities not clear
– Consider segmenting market
• QFD process is implemented in phases and
hence time consuming
• QFD is messy
– Not QFD, but rather the interaction between diverse
groups is cause
– Stick with it, the results are worthwhile
24
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Innovative Adaptation &
Performance Evaluation
• Innovation • Continuous
– Cut costs, reduce lead Improvement
time, improve
– Any one such
productivity, save
capital and human improvement takes
resources and hence place
increased revenue – Happens very
– Do not happen very frequently
often – Leads to slow and
– Result in a steep steady increase in
increase in quality quality
– High risk strategy – Eg. Benchmarking

25
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Innovation & Cont. Improvement

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Benchmarking (BM)

▪ Practice of identifying best practices in industry and

thereby setting goals to emulate them

▪ Facilitates continuous improvement

▪ Started by Xerox in the year 1970 by R.C. Camp

▪ Steps for BM differs from company to company due to

different operating concerns

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Objective of Benchmarking

• The main objective of any benchmarking activity is:

– To identify key performance measures for each function
of a company’s operations
– To measure the internal performance levels of the
company as well as that of competitors
– To ensure that its business process goals are set to exceed
the best quantitative results achieved by leading
organizations
– To incorporate best practices throughout the
organization business process
– To reach a level of maturity where benchmarking is an
ongoing part of management system in all areas of the
company

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Benchmarking Process

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Benchmarking - Requirements

▪ Not just merely identifying best practices, it should be how

practices can be adapted

▪ It needs Management commitment and should motivate

employees with rewards

▪ Training is a must on process mapping and flowcharting

▪ All resources should be made available

▪ Hard and Soft systems should mesh

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Why Benchmarking?

▪ Thorough understanding of company’s own processes,

products etc.
▪ Identify Non Value Added activities
▪ Provides an effective way to manage change and also a
roadmap to adapt best practices
▪ Impact of technological development
▪ Reduce cycle time, which in turn related to PM
▪ Enable comparison of performance measures (PM) in
different dimensions with ‘spider chart’

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Spider Chart

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Quality Audit

▪ To examine the effectiveness of management control

programs and also to identify problems

▪ 3 parties are involved – Client, Auditor and Auditee

▪ Auditor – Internal and External

▪ Purpose
▪ Suitability Quality Audit: Evaluation of Quality
program against reference standard
▪ Conformity Quality Audit: Evaluation of operations,
activities within the quality system with respect to
procedures 33
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Quality Audit – Contd..

▪ Types

▪ System Audit

▪ Most extensive

▪ Evaluation of the quality program documentation

with respect to a reference standard

▪ Includes evaluation of activities and operations

that are followed to meet the desired quality
objectives

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Quality Audit – Contd..

▪ Types – contd..

▪ Process Audit
▪ In depth evaluation of one or more processes
▪ Takes less time
▪ More focussed and less costly
▪ Used generally in process industries like
chemical industries
▪ Done when there is need for process
improvement or when there is unexpected
output

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Quality Audit – Contd..

▪ Types – contd..
▪ Product Audit
▪ Assessment of final product or service on its ability
to meet customer needs
▪ Involves conducting periodic test on products or
obtain info. from customers
▪ Separate from decision on product acceptance or
rejection and hence not part of the inspection system

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Quality Audit – Contd..

▪ Audit Quality
▪ Influenced by independence and objectivity of the
auditor
▪ Depends on being a external or internal auditor
▪ For suitability audit, external is most preferable
▪ Methods
▪ Location oriented
▪ All functions are audited in that particular location
▪ Examines the action and interaction of the elements
in the quality program at that location and may be
used to identify discrepancies between location
▪ Function oriented
▪ Examine and evaluate activities related to a particular
element or function within a quality program at all
locations
▪ Successive visits to each location is necessary to
complete the audit
▪ Utility of quality audit is derived only when remedial
actions are taken
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Tools for Continuous
Quality Improvement
• For solving the problems and involves data collection,
analysis, hypothesis and validation

• Called as 7 QC tools
– Check sheets
– Histogram
– Flow chart
– Pareto chart
– Cause and effect diagram
– Control chart
– Scatter diagram
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What are tools and techniques?
• Tools
– Tools and techniques are practical methods, skills,
means or mechanisms that can be applied to particular
tasks
– Used to facilitate positive change and improvements
– Narrow in focus and is usually used on its own
– Examples of tools are 7 QC tools
• Technique
– It has a wider application than a tool.
– Needs more thought, skill and training to use
– It can be thought of as a collection of tools
– Eg., statistical process control (SPC) employs a
variety of tools such as charts, graphs and histograms
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 235
Why to use tools and
techniques?
• Plays a key role in a company-wide
approach to continuous improvement. They
allow:
– Processes to be monitored and evaluated;
– Everyone to become involved in the
improvement process;
– People to solve their own problems;
– A mindset of continuous improvement to be
developed
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Requirement for tools and
techniques
• Requires attention to be paid to a number of
“critical success factors” to make their use and
application effective and efficient. Some of these
are:
– Full management support and commitment;
– Effective, timely and planned training;
– A genuine need to use the tool or technique;
– Defined aims and objective for use;
– A co-operative environment;
– Backup and support from improvement facilitators.
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7 QC Tools – contd.
• Check sheets
– A systematic record
keeping or data
collection
– Observations are
recorded as they
happen and reveals
pattern or trends

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7 QC Tools – Contd..
• Histograms
– Displays large amount
of data that are
difficult to interpret in
raw form
– Provides summary of
data and also reveals
whether the process is
centered, the degree of
variation etc.
– Used to identify
process capability
relative to customer
requirements

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7 QC Tools – Contd..

• Flow charts
– Shows the sequence
of events
– Mostly used in
manufacturing and
service operations
to describe working
procedures
– Valuable process
information can be
obtained in addition
to identifying
problematic areas
44
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 240
7 QC Tools – contd.
• Pareto Diagram
– helps to prioritize
the problem by
arranging them in
decreasing order of
importance

45
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 241
7 QC Tools – Contd..
• Cause and Effect diagram
–Called as Ishikawa diagram for fish
bone diagram
–Explores possible causes of
problem due to men, machine,
material and method
–To identify root cause, each cause
may be further broken down

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 242
7 QC Tools – contd.

47
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 243
7 QC Tools – Contd..
• Control charts
– Distinguishes special (assignable) causes of
variation from common causes
– Used to monitor and control a process on a ongoing
basis
– Plots a selected quality characteristic, found from
subgroups of observations, as a function of sample
number
– Central line on the control chart is the average value
of the characteristic
– Two limits, UCL and LCL are used to detect whether
the process goes out of control

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 244
7 QC Tools – contd.

49
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 245
7 QC Tools – Contd..

• Scatter Plots
– Shows the
relationship between
two variables
– Used as a follow up to
cause and effect
analysis to find
whether a stated
cause has impact on
quality

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 246

Chapter - 4

Fundamentals of Statistical
Concepts & Techniques in Quality
Control and Improvement

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 247
Basic Terminologies
• Population • Sample
– Set of all items that possess – A subset of population
a certain characteristic of – Eg. Selecting 200 plastic
interest cups from the week 23
– Eg. Average thickness of the output
plastic cups produced in • Statistic
week no. 23 (10,000) – A characteristic of a
• Parameter sample, which is used to
make inferences on the
– Is a characteristic of a population parameters
population, which describes that are unknown
it – Eg. Average thickness
– Eg. Average thickness of of 200 plastic cups is
10,000 cups 1mm
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 248
Basics of Probability

• Probability of an event describes the chance of

occurrence of that event
• A probability function is bound by 0 and 1
– 0 for non-occurrence, 1 for occurrence
• Set of all outcomes of an experiment is called ‘sample
space’ (S)
• If each outcome in sample space is likely to happen,
then the prob. of event A is given by P(A) = na / N and
probability associated with sample space is P(S) = 1

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 249
Example

A company makes plastic storage bags for the food industry.

Out of the hourly production of 2000 500-g bags, 40 were
found to be nonconforming. If the inspector chooses a bag
randomly from the hour's production, what is the probability
of it being nonconforming?

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 250
Basics of Probability – Contd..

• Events
– Simple events cannot be broken into other events
– Compound events are made up of two or more simple
events
– Complementary of an event, say A, implies the
occurrence of everything except A. i.e. P(Ac) = 1 – P(A)
• Laws
– Additive law defines the probability of the union of 2 or
more events (say A & B), i.e. implies A may happen, B
may happen or both
– P(A u B) = P(A) + P(B) – P(A n B)

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 251
Simple and Compound Events

Suppose that an inspector is sampling transistors from an

assembly line and identifying them as acceptable or not.
Suppose the inspector chooses two transistors. What are the
simple events? Give an example of a compound event. Find
the probability of finding at least one acceptable transistor.

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 252
Basics of Probability – Contd..

• Laws – contd..
– Multiplicative law defines the probability of the
intersection of 2 or more events (say A & B), i.e.
implies all the events in the group occurs
– P(A n B) = P(A).P(B | A) = P(B).P(A | B)
– P(B | A) represents conditional probability, (i.e.,
probability that B occurs if A has)
• Independence
– Two events A & B are said to be independent, if the
outcome of one has no influence on outcome of
other
– P(B | A) = P(B) and hence P(A n B) = P(A).P(B)

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 253
Basics of Probability – Contd..

• Mutually Exclusive
– Two events A & B are said to be mutually exclusive, if
they cannot happen simultaneously.
– Probability of Intersection P(A n B) = 0 and
probability of union P(A u B) = P(A) + P(B)
– For mutually exclusive, the events A & B are
dependent. If A & B are independent, the additive
rule will be P(A or B or both) = P(A) + P(B) –
P(A).P(B)

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 254
Example

In the production of metal plates for an assembly, it

is known from past experience that 5% of the plates
do not meet the length requirement. Also, from
historical records, 3% of the plates do not meet the
width requirement. Assume that there are no
dependencies between the processes that make the
length and those that trim the width. What is the
probability of producing a plate that meets both the
length and width requirements?

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 255
Example

• What proportion of the parts will not meet at least one of

the requirements?
• What proportion of parts will meet neither length nor
width requirements?

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 256
Example

Suppose the operations that produce the length and the width
are not independent. If the length does not satisfy the
requirement, it causes an improper positioning of the part
during the width trimming and thereby increases the chances
of nonconforming width. From experience, it is estimated that
if the length does not conform to the requirement, the chance
of producing nonconforming widths is 60%. Find the
proportion of parts that will neither conform to the length
nor the width requirements.

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 257

Thank You

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 258

Quality Control Assurance &

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
 259

Suppose the operations that produce the length and

the width are not independent. If the length does not
satisfy the requirement, it causes an improper
positioning of the part during the width trimming
and thereby increases the chances of nonconforming
width. From experience, it is estimated that if the
length does not conform to the requirement, the
chance of producing nonconforming widths is 60%.
Find the proportion of parts that will neither
conform to the length nor the width requirements.
2
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 260
Statistics
• Statistics is the science that deals with the collection,
classification, analysis and making of inferences from
data
• Descriptive Statistics
– Describes the characteristics of product or process
using information collected on it
• Inferential Statistics
– Draws conclusion on unknown process parameters
based on sample information
• Data Collection
– Direct observation
– Indirect observation (Questionnaires)
• No control over data and Chances of Error is more
– It can be described by random variable – continuous
or discrete 3
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 261
Statistics – Contd..

• Continuous variable
– Variable that can assume any value on a continuous scale
within a ‘range’ Eg. Viscosity of a resin
• Discrete variable
– Variable that can assume a finite number of values are called
discrete Eg. No. of defect in a shirt
– They are classified as acceptable or not
– Continuous characteristic can also be viewed as discrete. Eg.
Diameter of a hub in a tire
• Accuracy
– Refers to the degree of uniformity of the observations around
a desired value, such that on average, target is realized
• Precision
– Refers to the degree of variability of observation

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 262
Measures of Scale
• Nominal Scale
– Data variables are simply labels to identify an attribute
– Eg. Critical / Major / Minor
• Ordinal Scale
– Data has the properties of nominal data
– Data ranks or orders the observation
– Eg. Grades, 1- outstanding, 5 – poor
• Interval Scale
– Data has the properties of ordinal data and a fixed unit of
measure describes the interval between observations
– Eg. Temp. of water in diff stages of cooling during 2 hrs
interval
• Ratio Scale
– Data has the properties of Interval data and a natural
zero exists for measurement scale Eg. Wt. of cement bag:
100 kg, 100.2kg.
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Basic Statistical Concepts 263

www.phdcomics.com

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 264
Distribution

How excited are you about learning QCAR concepts?

1 2 3 4 5 6 7
Comatose Hyperventilating

1 2 2 3 4 4 5 6 7

7 Types: 1,2,3,4,5,6,7 9 Tokens: 1,2,2,3,4,4,5,6,7

BITS Pilani, Pilani Campus

 265
Properties of a
Distribution
• Shape
– symmetric vs. skewed
– unimodal vs. multimodal
• Central Tendency
– where most of the data are
– mean, median, and mode
• Variability (spread)
– how similar the scores are
– range, variance, and standard deviation

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 266
Representing a
Distribution
• Often it is helpful to visually represent
distributions in various ways
• Graphs
– continuous variables (histogram, line graph)
– categorical variables (pie chart, bar chart)
• Tables
– frequency distribution table

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 267
Distribution

• What if we collected 500 observations

instead of only 9?

…
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 268
Distribution

N = 500
50

40

30

20

10

1 2 3 4 5 6 7

BITS Pilani, Pilani Campus

 269
Central Tendency

• Mode: the most frequent score

– good for nominal scales (eye color)
– a must for multimodal distributions

• Median: the middle score

– separates the bottom 50% and the top 50%
of the distribution
– good for skewed distributions (net worth)

BITS Pilani, Pilani Campus

 270
Central Tendency

• Mean: the arithmetic average

– add all of the scores and divide by total number
of scores
– This the preferred measure of central tendency
(takes all of the scores into account)

X X
= X=
N n
population sample

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Computing a Mean 271

10 scores: 8, 4, 5, 2, 9, 13, 3, 7, 8, 5

ξΧ = 64

ξΧ/n = 6.4

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 272
Central Tendency

• Is the mean always the best measure of

central tendency?

• No, skew pulls the mean in the direction of

the skew

BITS Pilani, Pilani Campus

Central Tendency and Skew
273

Mode
Median

Mean
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Central Tendency and Skew
274

Mode
Median

Mean

BITS Pilani, Pilani Campus

 275
Distribution

• So, central tendency simplifies and

describes our distribution by providing a
representative score

• What about the difference between the

individual scores and the mean?
(variability)

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 276
Variability

• Range: maximum value – minimum value

– only takes two scores from the distribution into
account
– easily influenced by extreme high or low scores

• Standard Deviation/Variance
– the average deviation of scores from the mean of the
distribution
– takes all scores into account
– less influenced by extreme values

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 277
Standard Deviation

• most popular and important measure of

variability
• a measure of how far all of the individual
scores in the distribution are from a
standard (mean)


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Standard Deviation 278

mean mean
low variability high variability
small SD large SD

BITS Pilani, Pilani Campus

Computing a Standard Deviation 279

10 scores: 8, 4, 5, 2, 9, 13, 3, 7, 8, 5 ξΧ/n = 6.4

8 – 6.4 = 1.6 2.56

SS = 96.4
4 – 6.4 = - 2.4 5.76
5 – 6.4 = - 1.4 1.96
2 – 6.4 = - 4.4 19.36
variance = 2 = SS/N
9 – 6.4 = 2.6 6.76 10.71
13 – 6.4 = 6.6 43.56
3 – 6.4 = (X − ) 2

standard deviation =  =  =
- 3.4 11.56 2

7 – 6.4 = 0.6 0.36 N

8 – 6.4 = 1.6 2.56 3.27

5 – 6.4 = - 1.4 1.96

 BITS Pilani, Pilani Campus
 280
Standard Deviation

• In a perfectly symmetrical (i.e. normal)

distribution 2/3 of the scores will fall
within +/- 1 standard deviation

-1 +1

3.13 6.4 9.67

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 281
Variance vs. SD

• So, SD simplifies and describes the

distribution by providing a measure of
the variability of scores
• If we only ever report SD, then why
would variance be considered a separate
measure of variability?
• Variance will be an important value in
many calculations in inferential statistics

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 282
Measures of Central Tendency
• Mean
– Simple average of the observations in a dataset
– Sample Mean, Population Mean (formulae)
• Median
– Is the value in the middle, when observations are ranked
– It is more robust than mean, as it is not influenced by
extreme values in dataset
• Mode
– Is the value that occurs more frequently in a dataset
– A dataset having more than one mode is called Multi-
modal
• Trimmed Mean
– Obtained by calculating the mean of data, that remain
after a proportion of high and low values being deleted
(a% trimmed)
25
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 283

The time taken for car tune-ups (in minutes)

is observed for 20 randomly selected cars. The
data values are as follows:
15 10 12 20 16 18 30 14 16 15
18 40 20 19 17 15 22 20 19 22
find the 5% trimmed mean [i.e., T(0.05)]

26
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 284
Measures of Dispersion

• Provides information on the variability or scatter of

the observations around a given value
• Range
– Difference between largest and smallest value in the
dataset
– R = XL - XS
• Variance
– Measures the fluctuation of the observations around the
mean
– Population variance, Sample Variance (formulae)
• Why n-1 in sample variance?
– To satisfy the property of unbiasedness i.e. average of
sample variance (keeps varying between sample) should
be equal to population variance which is constant
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 285
Measures of Dispersion

• Standard Deviation
– Mostly used measure of dispersion and has the same unit as the
observation
– Measures the variability of the observation around the mean
– Population Standard Deviation, Sample Standard Deviation
• Inter Quartile Range
– Lower / First quartile (Q1) is the value such that 1/4th of the
observations fall below it and 3/4th fall above it (Q1 = 0.25 (n+1))
– Vice Versa for Third Quartile (Q3) (Q1 = 0.75 (n+1))
– Difference between 3rd quartile and 1st quartile (IQR = Q3 – Q1)
– Larger the value of IQR, greater the spread of data
– To find IQR, the data are ranked in ascending order and then Q1
and Q3 are calculated

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 286

A random sample of 10 observations of the

output voltage of transformers is taken. The
values (in volts, V) are as follows:

9.2, 8.9, 8.7, 9.5, 9.0, 9.3, 9.4, 9.5, 9.0, 9.1

Calculate the variance and standard deviation.

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 287

A random sample of 20 observations on the

welding time (in minutes) of an operation
gives the following values:
2.2 2.5 1.8 2.0 2.1 1.7 1.9 2.6 1.8 2.3
2.0 2.1 2.6 1.9 2.0 1.8 1.7 2.2 2.4 2.2

Calculate the IQR.

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 288
Measures of Skewness &
Kurtosis
• Skewness coefficient (V1)
– Describes the asymmetry of the dataset about the mean or
indicates the degree to which distribution deviates from
symmetry (formulae)
– Negatively skewed: V1= -ve, Mean < Median
– Positively skewed: V1= +ve, Mean > Median
– Not skewed: V1= 0, Mean = Median
• Kurtosis coefficient (V2)
– Is a measure of peakness of the dataset (formulae)
– Is also a measure of heaviness of the tails of distribution
– For normal distribution (Mesokurtic), V2 = 3
– Leptokurtic, More peaked, V2 > 3
– Platykurtic, Less peaked, V2 < 3

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289

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A sample of 50 coils to be used in an electrical circuit is
290
randomly selected, and the resistance of each is
measured (in ohms). Calculate the skewness coefficient
and kurtosis coefficient.

33
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 291

Thank You

34
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 292

Quality Control Assurance &

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
 293
Probability Distribution

• Sample data can be described with histograms, while population data are
described by probability distribution
• For discrete random variables, the probability distribution shows the value
that the variable can take and their corresponding probabilities
– P(xi) ≥ 1 for all i, P(xi) = P(X = xi); i = 1, 2,…
– Sum of all P(xi) = 1
– Some examples of discrete random variables are the number of defects
in an assembly, the number of customers served over a period of time,
and the number of acceptable compressors.
• Continuous random variable can take a infinite number of values and
hence probability distribution is expressed by Mathematical function
– f(x) >= 0 for all x, where P(a ≤ x ≤ b) = b∫af(x)dx
– Integration from minus infinity to plus infinity is one
– Almost all variables for which numerical measurements can be
obtained are continuous in nature: for example, the length of a pin, the
diameter of a bolt, the tensile strength of a cable, or the specific gravity
of a liquid.
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 294
Variables and Random Variables
Earlier, we saw that just like in algebra, we can use a variable to represent some
quantity, such as height.
i.e. It is just like a variable in
statistics, except each outcome has
now been assigned a probability.

1 2 3 4 5 6
0.3 0.2 0.1 0.25 0.05 0.1

“The probability
that…

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 295
Is it a discrete random variable?

The height of a person ✓

No 
Yes
randomly chosen. This is a continuous random
variable.

The number of cars that 

No ✓
Yes
pass in the next hour.

The number of countries in ✓

No 
Yes
the world. It does not vary, so is not a variable!

4
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 296
Probability Distributions vs Probability Functions
There are two ways to write the mapping from outcomes to probabilities.

The “{“ means we have a ‘piecewise

function’. This just simply means we choose
the function from a list depending on the
Probability input.
Functions

Advantages of probability function:

Can have a rule/expression based on the outcome.
Particularly for continuous random variables (in S2), it
Probability Distribution
?
would be impossible to list the probability for every
outcome. More compact.

1 2 3 4
0.1 0.2 ?0.3 0.4
The table form that you know and love.

Advantages of distribution:
Probability for each outcome more explicit.
? 5
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Example 297

Underlying Probability Distribution

Sample Space
0 1 2 3

{ HHH, ?
HHT,
HTT, Probability Function
HTH,
THH,?
THT,
TTH, ?
TTT }
6
BITS Pilani, Pilani Campus
Cumulative Distribution Function
298(CDF)

If X is the number of heads thrown

in 2 throws...
? 0 1 2
? ?
0.25 0.5? ?
0.25

0 1 2
?
0.25 ?
0.75 1 ?

7
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CDF 299

F(x)
p(x)

Shoe Size (x) Shoe Size (x)

It’s just like how we’d turn a frequency graph

into a cumulative frequency graph. 8
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 300
Cumulative Distributive function

• For a discrete random variable, F(x) = ∑ all i

p(xi) for xi ≤ x
• For a continuous random variable, F(x) = b∫a
f(t)dt
• F(x) is a non decreasing function of x such
that for limit, x tending to infinity, it is 1 and
it is 0 for minus infinity
• Expected value
– µ = E(x) = ∑ all i xi p(xi) , if x is discrete
– µ = E(x) = b∫a x f(x)dx, if x is continuous
• Variance of a random variable is given by
– Var(X) = E[(X - µ)2] = E(X2) – [E(X)]2

9
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 301

Let X denote a random variable that represents

the number of defective solders in a printed
circuit board. The probability distribution of the
discrete random variable X may be given by

the mean or expected value E(X), variance and

standard deviation.

10
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 302
Discrete Distributions
• The discrete class of probability distributions deals with those random
variables that can take on a finite or countably infinite number of values.
• Hyper geometric distribution
– Useful in sampling from a ‘finite’ population without
replacement, where the outcomes are success or
failure
– If we consider, getting a nonconforming item as
success, the probability distribution of nonconforming
item (x) is given by P(x) = Dcx . (N-D)c(n-x) / Ncn
• D: no. of defects in population, x: no. of defects in
sample
• N: Size of population, n: Size of sample
– Mean µ = E(x) = nD/N
– Variance σ2 = Var(x) = nD/N(1 – D/N)((N-D)/N-1))

11
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 303

A lot of 20 chips contains 5 nonconforming

ones. If an inspector randomly samples 4
items, find the probability of 3 nonconforming
chips.

12
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 304
Discrete Distributions
• Binomial distribution
– Useful in sampling from a ‘large’ population
without replacement, or to sample with
replacement from a finite population
– Probability of success (p) on any trial is
assumed to be a constant
– Let x denote the no. of successes, if n trials are
conducted, probability of x successes is given
by
• P(x) = ncx . px (1-p)n-x , x = 0,1, 2..
– Mean µ = E(x) = np
– Variance σ2 = Var(x) = np(1 – p)
13
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Example 305

14
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 306

A manufacturing process is estimated to

produce 5% nonconforming items. If a
random sample of five items is chosen, find
the probability of getting two nonconforming
items.

15
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 307
Discrete Distributions
• Poisson distribution
– Used to model the no. of events that happen
within a product unit, space or volume or time
period. Eg. No. of machine breakdown per
month
– Probability distribution function of the no. of
events (x) is given by
• P(x) = e-λ . λx / x! , x = 0,1, 2..
– Mean or average no. of events is given by λ
– Mean µ = Variance σ2 = λ
– It is used as an approximation to the binomial,
when ‘n’ is large and ‘p’ is small, such that np = λ
is a constant or average no. of defects per unit is
constant
16
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 308

It is estimated that the average number of

surface defects in 20 m2 of paper produced by
a process is 3. What is the probability of
finding no more than 2 defects in 40 m2 of
paper through random selection?

17
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 309
Discrete vs Continuous Distributions
You all know the distinction between discrete and continuous variables:
• Discrete: hair colour, shoe size, IQ, cars passing in the next hour, …
• Continuous: height, weight, time, …

Random variables are discrete or continuous when the outcomes are discrete or
continuous.

Discrete Random Variables Continuous Random Variables

Examples: Poisson Distributed Examples: Normally Distributed

BinomiallyExamples
Distributed Examples
Discrete Uniform Distribution

General Properties ? General Properties ?

Let’s go into more detail on
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this… BITS Pilani, Pilani Campus
 310
Probability Density Function (p.d.f.) !

For continuous variables, it doesn’t

make sense to talk about the
frequency of a specific value, e.g.
no one will have an exact height of
1.7m. We would instead use
‘frequency density’.

Earlier we saw that for histograms,

the value of the frequency density is
not particularly useful in isolation.
But when we find the area under a
bar, we get the frequency.
19
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 311
Cumulative Distribution Function
This works in exactly the same way as a discrete distribution:

20
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 312
Continuous Distribution

• Normal Distribution
– Most widely used
– Probability density function of a normal random variable is f(x)
= 1/√2πσ exp[-(x - µ)2/ 2σ2], -∞ < x < ∞
– µ = population mean, σ = population std. deviation
– Change in mean changes the location of distribution. As µ
increases, distribution shifts right and vice versa
– As variance increases, the spread about mean increases
– Normal distribution is symmetric and Mean = Median = Mode
– Proportion of population values that fall in the range of µ +/- σ
is 68.26%, µ +/- 2σ is 95.44%, µ +/- 3σ is 99.74%,
– Shape of the density function changes for diff. values of µ & σ
and hence it needs standardization

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313

22
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Continuous Distribution – 314

Contd..
• Normal Distribution
– Area within certain limits can be found by
looking up tabulated values for a ‘Std. normal
distribution’
– Standardized normal random variable z = x -
µ / σ and z is the no. of standard deviations a
raw value x is from mean and has mean of 0
and variance of 1
– Z-value can be positive or negative and at
mean it is zero
– Density function (formula)
– Cumulative density function (formula)
– Sample problem 23
BITS Pilani, Pilani Campus
 315

The length of a machined part is known to have a

normal distribution with a mean of 100 mm and
a standard deviation of 2 mm.
• What proportion of the parts will be above 103.3 mm?
• What proportion of the output will be between 98.5 and 102.0
mm?
• What proportion of the parts will be shorter than 96.5 mm?
• It is important that not many of the parts exceed the desired
length. If a manager stipulates that no more than 5% of the parts
should be oversized, what specification limit should be
recommended?
24
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 316
Continuous Distribution – Contd..

• Exponential Distribution
– Used in reliability analysis to describe the time to failure
of a component or system
– P.D.F is given by f(x) = λ exp[- λ x], x ≥ 0, λ = failure rate
– Represents a constant failure rate and is used to model
failures that happen randomly and independently
– Mostly used in the useful life period of a life cycle of a
product
– Standard deviation = Mean (µ) = 1 / λ
– Exponential cumulative distribution function (formula)
– Function is ‘memory less’ as the probability of
component’s life exceeding (s+t) time units, given that it
has lasted ‘t’ time units, is same as probability of the life
exceeding ‘s’ time units (eqn.)
– Sample problem
25
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 317

It is known that a battery for a video game has an average life

of 500 hours(h). The failures of batteries are known to be
random and independent and may be described by an
exponential distribution.
(a) Find the probability that a battery will last at least 600
hours.
(b) Find the probability of a battery failing within 200 hours.
(c) Find the probability of a battery lasting between 300 and
600 hours.
(d) Find the standard deviation of the life of a battery.
(e) If it is known that a battery has lasted 300 hours, what is
the probability that it will last at least 500 hours?
26
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 318

Thank You

27
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 319

Quality Control Assurance &

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
 320
Probability Distributions vs Probability Functions
There are two ways to write the mapping from outcomes to probabilities.

The “{“ means we have a ‘piecewise

function’. This just simply means we choose
the function from a list depending on the
Probability input.
Functions

Advantages of probability function:

Can have a rule/expression based on the outcome.
Particularly for continuous random variables (in S2), it
Probability Distribution
?
would be impossible to list the probability for every
outcome. More compact.

1 2 3 4
0.1 0.2 ?0.3 0.4
The table form that you know and love.

Advantages of distribution:
Probability for each outcome more explicit.
? 2
BITS Pilani, Pilani Campus
Example 321

Underlying Probability Distribution

Sample Space
0 1 2 3

{ HHH, ?
HHT,
HTT, Probability Function
HTH,
THH,?
THT,
TTH, ?
TTT }
3
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CDF 322

F(x)
p(x)

Shoe Size (x) Shoe Size (x)

It’s just like how we’d turn a frequency graph

into a cumulative frequency graph. 4
BITS Pilani, Pilani Campus
 323
Cumulative Distributive function

• For a discrete random variable, F(x) = ∑ all i

p(xi) for xi ≤ x
• For a continuous random variable, F(x) = b∫a
f(t)dt
• F(x) is a non decreasing function of x such
that for limit, x tending to infinity, it is 1 and
it is 0 for minus infinity
• Expected value
– µ = E(x) = ∑ all i xi p(xi) , if x is discrete
– µ = E(x) = b∫a x f(x)dx, if x is continuous
• Variance of a random variable is given by
– Var(X) = E[(X - µ)2] = E(X2) – [E(X)]2

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 324

Let X denote a random variable that represents

the number of defective solders in a printed
circuit board. The probability distribution of the
discrete random variable X may be given by

the mean or expected value E(X), variance and

standard deviation.

6
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 325
Discrete Distributions
• The discrete class of probability distributions deals with those random
variables that can take on a finite or countably infinite number of values.
• Hyper geometric distribution
– Useful in sampling from a ‘finite’ population without
replacement, where the outcomes are success or
failure
– If we consider, getting a nonconforming item as
success, the probability distribution of nonconforming
item (x) is given by P(x) = Dcx . (N-D)c(n-x) / Ncn
• D: no. of defects in population, x: no. of defects in
sample
• N: Size of population, n: Size of sample
– Mean µ = E(x) = nD/N
– Variance σ2 = Var(x) = nD/N(1 – D/N)((N-D)/N-1))

7
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 326

A lot of 20 chips contains 5 nonconforming

ones. If an inspector randomly samples 4
items, find the probability of 3 nonconforming
chips.

8
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 327
Discrete Distributions
• Binomial distribution
– Useful in sampling from a ‘large’ population
without replacement, or to sample with
replacement from a finite population
– Probability of success (p) on any trial is
assumed to be a constant
– Let x denote the no. of successes, if n trials are
conducted, probability of x successes is given
by
• P(x) = ncx . px (1-p)n-x , x = 0,1, 2..
– Mean µ = E(x) = np
– Variance σ2 = Var(x) = np(1 – p)
9
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Example 328

10
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 329

A manufacturing process is estimated to

produce 5% nonconforming items. If a
random sample of five items is chosen, find
the probability of getting two nonconforming
items.

11
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 330
Discrete Distributions
• Poisson distribution
– Used to model the no. of events that happen
within a product unit, space or volume or time
period. Eg. No. of machine breakdown per
month
– Probability distribution function of the no. of
events (x) is given by
• P(x) = e-λ . λx / x! , x = 0,1, 2..
– Mean or average no. of events is given by λ
– Mean µ = Variance σ2 = λ
– It is used as an approximation to the binomial,
when ‘n’ is large and ‘p’ is small, such that np = λ
is a constant or average no. of defects per unit is
constant
12
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 331

It is estimated that the average number of

surface defects in 20 m2 of paper produced by
a process is 3. What is the probability of
finding no more than 2 defects in 40 m2 of
paper through random selection?

13
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 332
Discrete vs Continuous Distributions
You all know the distinction between discrete and continuous variables:
• Discrete: hair colour, shoe size, IQ, cars passing in the next hour, …
• Continuous: height, weight, time, …

Random variables are discrete or continuous when the outcomes are discrete or
continuous.

Discrete Random Variables Continuous Random Variables

Examples: Poisson Distributed Examples: Normally Distributed

BinomiallyExamples
Distributed Examples
Discrete Uniform Distribution

General Properties ? General Properties ?

Let’s go into more detail on
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 333
Probability Density Function (p.d.f.) !

For continuous variables, it doesn’t

make sense to talk about the
frequency of a specific value, e.g.
no one will have an exact height of
1.7m. We would instead use
‘frequency density’.

Earlier we saw that for histograms,

the value of the frequency density is
not particularly useful in isolation.
But when we find the area under a
bar, we get the frequency.
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 334
Cumulative Distribution Function
This works in exactly the same way as a discrete distribution:

16
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 335
Continuous Distribution

• Normal Distribution
– Most widely used
– Probability density function of a normal random variable is f(x)
= 1/√2πσ exp[-(x - µ)2/ 2σ2], -∞ < x < ∞
– µ = population mean, σ = population std. deviation
– Change in mean changes the location of distribution. As µ
increases, distribution shifts right and vice versa
– As variance increases, the spread about mean increases
– Normal distribution is symmetric and Mean = Median = Mode
– Proportion of population values that fall in the range of µ +/- σ
is 68.26%, µ +/- 2σ is 95.44%, µ +/- 3σ is 99.74%,
– Shape of the density function changes for diff. values of µ & σ
and hence it needs standardization

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336

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Continuous Distribution – 337

Contd..
• Normal Distribution
– Area within certain limits can be found by
looking up tabulated values for a ‘Std. normal
distribution’
– Standardized normal random variable z = x -
µ / σ and z is the no. of standard deviations a
raw value x is from mean and has mean of 0
and variance of 1
– Z-value can be positive or negative and at
mean it is zero
– Density function (formula)
– Cumulative density function (formula)
– Sample problem 19
BITS Pilani, Pilani Campus
 338

The length of a machined part is known to have a

normal distribution with a mean of 100 mm and
a standard deviation of 2 mm.
• What proportion of the parts will be above 103.3 mm?
• What proportion of the output will be between 98.5 and 102.0
mm?
• What proportion of the parts will be shorter than 96.5 mm?
• It is important that not many of the parts exceed the desired
length. If a manager stipulates that no more than 5% of the parts
should be oversized, what specification limit should be
recommended?
20
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 339
Continuous Distribution – Contd..

• Exponential Distribution
– Used in reliability analysis to describe the time to failure
of a component or system
– P.D.F is given by f(x) = λ exp[- λ x], x ≥ 0, λ = failure rate
– Represents a constant failure rate and is used to model
failures that happen randomly and independently
– Mostly used in the useful life period of a life cycle of a
product
– Standard deviation = Mean (µ) = 1 / λ
– Exponential cumulative distribution function (formula)
– Function is ‘memory less’ as the probability of
component’s life exceeding (s+t) time units, given that it
has lasted ‘t’ time units, is same as probability of the life
exceeding ‘s’ time units (eqn.)
– Sample problem
21
BITS Pilani, Pilani Campus
 340

It is known that a battery for a video game has an average life

of 500 hours(h). The failures of batteries are known to be
random and independent and may be described by an
exponential distribution.
(a) Find the probability that a battery will last at least 600
hours.
(b) Find the probability of a battery failing within 200 hours.
(c) Find the probability of a battery lasting between 300 and
600 hours.
(d) Find the standard deviation of the life of a battery.
(e) If it is known that a battery has lasted 300 hours, what is
the probability that it will last at least 500 hours?
22
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 341
Inferential Statistics

• Talks about statistical procedures to make

inferences about a population on the basis of
sample data
• 2 main procedures: Estimation and Hypothesis
testing
• Sampling Distribution
– An estimator or statistic is used to make inferences on its
corresponding population parameter
– Studying the behavior of estimator through repeated
sampling is used to draw conclusions about the
parameter
– This behavior is called sampling distribution, expressed
as the probability distribution of statistic
• http://davidmlane.com/hyperstat/index.ht
ml 23
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 342
Inferential Statistics – Contd..

• Sampling Distribution
– Sample mean is most widely used estimator and
hence it is important to know the sampling
distribution of mean, which is given by Central
Limit Theorem (CLT)
– Suppose we have a population with mean ‘µ’ and
standard deviation ‘σ’. If random sample of size
‘n’ are selected from this, and if sample size is
large, following holds good: (CLT)
• Sampling distribution of the sample mean will be
approximately normal
• Mean of this sampling distribution of mean ‘µx’ will be
equal to population mean ‘µ’
• Std. deviation is σx = σ / √n
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 343
Inferential Statistics – Contd..

• Sampling Distribution
– The degree to which a sampling distribution of
a sample mean approximates a normal
distribution becomes greater as sample size ‘n’
becomes larger
– For population distribution that is symmetric
and uni-modal, sample size as small as 4 or 5
yield sample means that are approximately
normally distributed
– Variability of the sample mean, as measured by
standard deviation decreases as sample size
increases
25
BITS Pilani, Pilani Campus
 344

Thank You

26
BITS Pilani, Pilani Campus
 345

Quality Control Assurance &

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
 346
Inferential Statistics

• Talks about statistical procedures to make

inferences about a population on the basis of
sample data
• 2 main procedures: Estimation and Hypothesis
testing
• Sampling Distribution
– An estimator or statistic is used to make inferences on its
corresponding population parameter
– Studying the behavior of estimator through repeated
sampling is used to draw conclusions about the
parameter
– This behavior is called sampling distribution, expressed
as the probability distribution of statistic
• http://davidmlane.com/hyperstat/index.ht
ml 2
BITS Pilani, Pilani Campus
 347
Inferential Statistics – Contd..

• Sampling Distribution
– Sample mean is most widely used estimator and
hence it is important to know the sampling
distribution of mean, which is given by Central
Limit Theorem (CLT)
– Suppose we have a population with mean ‘µ’ and
standard deviation ‘σ’. If random sample of size
‘n’ are selected from this, and if sample size is
large, following holds good: (CLT)
• Sampling distribution of the sample mean will be
approximately normal
• Mean of this sampling distribution of mean ‘µx’ will be
equal to population mean ‘µ’
• Std. deviation is σx = σ / √n
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 348
Inferential Statistics – Contd..

• Sampling Distribution
– The degree to which a sampling distribution of
a sample mean approximates a normal
distribution becomes greater as sample size ‘n’
becomes larger
– For population distribution that is symmetric
and uni-modal, sample size as small as 4 or 5
yield sample means that are approximately
normally distributed
– Variability of the sample mean, as measured by
standard deviation decreases as sample size
increases
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 349

The tuft bind strength of a synthetic material

used to make carpets is known to have a mean
of 50 kg and a standard deviation of 10 kg. If a
sample of size 40 is randomly selected, what is
the probability that the sample mean will be
less than 52.5 kg?

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 350
Estimation of Product and Process
Parameters
• Can be done using Point Estimation and
Interval Estimation

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 351
Estimation – contd.

• Point Estimation
– Consists of a single numerical value that is used
to make an inference about an unknown
product or process parameter
– Eg. Estimate the length of a shaft produced in
certain month (25mm)
– A point estimator is said to be ‘unbiased’ if the
expected value or mean of sampling
distribution is equal to the parameter
– A point estimator is said to have minimum
variance, if its variance is smaller than that of
any other point estimator for the parameter
under consideration
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 352
Estimation – Contd..

• Interval Estimation
– A range of interval is determined, such that
there is some desired level of probability
that the true parameter value is contained
within it
– Called as confidence interval
– Say 2 end points (L, U), probability of
parameter ‘γ’ being contained in the interval
is some value (1 – α)
– P(L ≤ γ ≤ U) = 1 – α, which represents a 2-
sided confidence interval
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 353
Estimation – Contd..

• Interval Estimation
– If a large number of such confidence intervals
were constructed from large no. of independent
samples, then 100(1 – α)% of these intervals
would be expected to contain the parameter
value ‘γ’
– It can also be one sided. An interval of the type
L <= γ, such that P(L <= γ) = 1 – α is a one sided
lower 100(1 – α)% confidence interval for γ
– Context of the situation influence the type of
confidence interval selected

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 354
Estimation of Parameters
• Confidence interval about the mean
(Unknown)
– Case 1: Variance Known (Population)
• Based on Central Limit Theorem, the
sampling distribution of this mean is
approximately normal. A 100(1 – α)%
two-sided confidence interval for µ is
given by
X − z / 2  n
   X + z
2

n

10
BITS Pilani, Pilani Campus
 355

The output voltage of a power source is

known to have a standard deviation of 10 V.
Fifty readings are randomly selected, yielding
an average of 118 V. Find a 95% confidence
interval for the population mean voltage.

11
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 356
Estimation of Parameters
• Confidence interval about the mean
(Unknown)
– Case 2: Variance Unknown (Population)
• A random sample of size ‘n’ is chosen and the
sample mean X and sample variance is
calculated. The sampling distribution of
X - µ / (s / √n) follows ‘t’ distribution with
(n-1) degree of freedom, which is similar to
normal distribution.
s s
X − t( / 2),( n−1)    X + t( / 2),( n−1)
n n
• Sample problem
12
BITS Pilani, Pilani Campus
 357

A new process has been developed that transforms ordinary

iron into a kind of super iron called metallic glass. This new
product is stronger than steel alloys and is much more
corrosion-resistant than steel. However, it has a tendency to
become brittle at high temperatures. It is desired to estimate
the mean temperature at which it becomes brittle. A random
sample of 20 pieces of metallic glass is selected. The
temperature at which brittleness is first detected is recorded
for each piece. The summary results give a sample mean X of
600 °C and a sample standard deviation s of 15 °C. Find a 90%
confidence interval for the mean temperature at which
metallic glass becomes brittle.
13
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 358
Estimation of Parameters –
Contd..

• Confidence interval for the difference

between two mean (Unknown)
– Case 1: Variances of two populations
Known
• ‘n1’ is the sample size from 1st population
with mean x1, while ‘n2’ and x2 is for 2nd
population. A 100(1 – α)% two-sided
confidence interval is given by
 12  22  12  22
( X1 − X 2 ) − z 2 +  1 −  2  ( X 1 − X 2 ) + Z +
n1 n2 2 n1 n2
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 359
Estimation of Parameters – Contd..
• Confidence interval for the difference
between two mean (Unknown)
– Case 2: Variances of two populations
Unknown
• Two unknown variances are equal (σ12 = σ22)
1 1
( X 1 − X 2 ) − t / 2,( n1 + n2 − 2) . s p .  + 
 n1 n2 
 (1 −  2 ) 
1 1
( X 1 − X 2 ) + t / 2,( n1 + n2 − 2) . s p .  + 
 n1 n2 
 ( n − 1) s 2
+ ( n − 1) s2 
2
– Sample problem s p = 
2 1 1 2

 ( n1 + n −
2 15 2) 
BITS Pilani, Pilani Campus
 360
Estimation of Parameters – Contd..
• Confidence interval for the difference between two
mean (Unknown)
– Case 2: Variances of two populations Unknown
• Two unknown variances are not equal (σ12 ≠ σ22)
 s12 s2 2 
( X 1 − X 2 ) − t / 2, .  + 
 1
n n 2 
 (1 −  2 ) 
 s12 s2 2  s s2 
2 2
2
( X 1 − X 2 ) + t / 2, .  +  n +n 
1

 1
n n 2 
=  1 2 2  2
ν = no. of degrees of freedom  s12   s2 2 
n  n 
 1  + 2 
n1 −1 n2 −1
16
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 361

Two operators perform the same machining operation. Their

supervisor wants to estimate the difference in the mean
machining times between them. No assumption can be made
as to whether the variabilities of machining time are the same
for both operators. It can be assumed, however, that the
distribution of machining times is normal for each operator. A
random sample of 10 from the first operator gives an average
machining time of 4.2 minutes with a standard deviation of
0.5 minutes. A random sample of 6 from the second operator
yields an average machining time of 5.1 minutes with a
standard deviation of 0.8 minutes. Find a 95% confidence
interval for the difference in the mean machining times
between the two operators.
17
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 362
Estimation of Parameters –
Contd..

• Confidence interval for a proportion

– Let ‘p’ the proportion of success in binomial
distribution i.e. ‘p’ is the proportion of non-
conforming items in a process or lot. ‘p*’ is the
sample proportion (p* = x / n). The confidence
interval is given by
ˆ (1 − p
p ˆ) ˆ (1 − p
p ˆ)
ˆ − z
p pp
ˆ + z
2 n 2 n

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Estimation of Parameters
– Contd..
• Confidence interval for difference between 2
proportion
– A sample size of n1 selected with parameter p1
and a sample size of n2 selected with parameter
p2  pˆ1 (1 − p
ˆ1 ) ˆ 2 (1 − p
p ˆ2 ) 
( p1 − p2 ) − z
ˆ ˆ  + 
2  n1 n2 
 p1 − p2 
ˆ1 (1 − p
 p ˆ1 ) ˆ 2 (1 − p
p ˆ2 ) 
ˆ1 − p
(p ˆ 2 ) + z  + 
2  n1 n 2 

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 364
Estimation of Parameters
– Contd..
• Confidence Interval for Variance
– A random variable x from a normal distribution with mean µ
and variance σ2 (both unknown)
– An estimator of σ2 is the sample variance s2
– Sampling distribution of s2 follows a ‘chi-square’ distribution
with (n-1) degrees of freedom given by
(n-1)s2 / σ2 = χ2n-1
– A chi square distribution is skewed to the right and a
100%(1-α) interval for population variance is given by
( n − 1) s 2 ( n − 1 ) s 2
  2

2 / 2,n −1 12− / 2, n −1
– Sample problem

20
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 365

The time to process customer orders is known

to be normally distributed. A random sample
of 20 orders is selected. The average
processing time X is found to be 3.5 days with
a standard deviation s of 0.5 day. Find a 90%
confidence interval for the variance ó2 of the
order processing times.

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 366
Estimation of Parameters
– Contd..
• Confidence Interval for ratio of two variances
– Random variable x1, x2 from a normal distribution with mean
µ1, µ2 and variance σ12, σ22 (both unknown)
– Random sample of size n1, n2 are chosen and the variance was
found to be s12, s22
– The ratio of these 2 variances will follow an ‘F’ distribution
with (n1-1) degrees of freedom in numerator and (n2 – 1) d.o.f
in denominator given by
s12 /  12
~ F( n1 −1),( n2 −1)
s2 /  2
2 2

– A ‘F’ distribution is skewed to the right and a 100%(1-α)

interval for this ratio is given by
s 2
1  12 s12
.   2 F / 2,v
2
2 2 , v1
s 2 F / 2, v1 , v2 s2 2

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 367

The chassis assembly time for a television set is observed for

two operators. A random sample of 10 assemblies from the
first operator gives an average assembly time of 22 minutes
with a standard deviation of 3.5 minutes. A random sample of
8 assemblies from the second operator gives an average
assembly time of 20.4 minutes with a standard deviation of
2.2 minutes. Find a 95% confidence interval for the ratio of
the variances of the operators‘ assembly times.

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 368

Thank You

24
BITS Pilani, Pilani Campus
 369

Quality Control Assurance &

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
 370

Chapter - 6

Statistical Process Control using

Control Charts

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 371
Introduction to Control Charts
• Emphasis is on process control and improvement
• A Control chart is a
– Graphical tool
– For monitoring the activity of an ongoing process
– It is called as ‘Shewhart’ chart
– Values of quality characteristic is plotted along ‘ordinate’
– Sample number or subgroups (in order of time) is plotted
along ‘abscissa’
– Example for quality characteristic includes Average length,
Average tensile strength, Average service time etc.
– Quality characteristic can be categorized as
• Variable: Numerical values can be obtained

• Attribute: No numerical values, only conforming or non

conforming

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 372
Control Chart – Contd..

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More about Control Charts –
Contd..
• A Control chart has
– A centre line, represents the average value of the characteristic
– It indicates, where the process is centred
– UCL and LCL, used to make decision regarding the process
– If the points plot within the control limits and do not exhibit
any identifiable pattern, then process is in statistical control
– If a point plots outside the control limits or if an identifiable
random pattern exists process is out of statistical control
– Benefits
• Indicates when something may be wrong, so that corrective
action can be taken
• Pattern of plot can help in diagnosing the possible causes and
hence possible remedial action
• Helps in estimating the process capability of the process

BITS Pilani, Pilani Campus

 374
Causes of Variation
• Variability is part of any process
• Causes can be men, methods, machine, materials, environment
• Can be categorized in to two
• Special causes • Common causes
– Assignable causes or – Chance causes or
sporadic problem chronic problem
– Not inherent in the – Inherent in the process
process – Affects all items, as it is
part of process design
– Will not affect all items
– Exists as long as the
– Can be due to use of a process is not changed
wrong tool, improper – Can be due to vibration
raw material, operator of a machine, fluctuation
error etc. etc.

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Causes of Variation – Contd..

• Special causes • Common causes

– If an observation falls – Variation is the effect of
outside the control limits or many small causes and
a non-random pattern exists,
special causes exists
cannot be totally
eliminated
– Control chart is used to
detect the presence of – When this variation is
special causes and should be constant, called as stable
eliminated system of common causes
– 15% of all problems are due – Management is alone
to special causes responsible for common
– Action is required from both causes
management and workers – 85% of all problems are
due to common causes

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Statistical Basis for Control
Charts
• Centre line is based on the mean of a process
and is found by taking the average of the values
in sample
• Can also be desirable target or standard value
• Role of Normal distribution
– Value of the statistic plotted on a control chart are
assumed to have an approximately normal
distribution
– Any sample from population distribution that is
uni-modal and symmetric, the central limit theorem
states that if the plotted statistic is a sample
average, it tend to have a normal distribution
8

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 377
Control Chart – Contd..

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Statistical Basis – Contd..
• Why 3σ limits?
– Chosen in such a way that probability of the sample points
falling between them is ‘1’, if the process is in statistical
control
– Normal distribution theory states that a sample statistic will
fall within the limits 99.74% of the time, if the process is in
control
• Most common basis for deciding whether a process is out
of control is “the presence of a sample statistic outside the
control limits” and also it depends on other rules
• A control chart is a means of online process control
• If the control limits are calculated from current data, then
it tells whether the process is presently in control or not
• If the control limits are calculated from previous data,
based on a process that was in control, it helps to find
whether the process has drifted out of control

• Control chart can also estimate process parameters such

as10mean, standard deviation and fall outs
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Statistical Basis for Control
Charts – Contd..
• It can be used to determine the capability of process
i.e, ability of the process to produce within desirable
specifications
– Process capability studies help in making major
management decisions like make or buy, investment in
machines, vendor selection etc.
• Issues in construction of control chart are:
– Selection of control limits, No. of items in the sample,
Frequency of sampling, Minimizing error in inferences,
Interpretation of control charts etc.

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Selection of Control Limits

• Let ‘θ’ is the mean diameter of parts produced by the

process and θ* would be sample mean diameter of parts
chosen from the process
– E(θ*) is the mean or expected value and σ(θ*) be the standard
deviation of the estimator θ*
• Then the centre line and control limits are given by
• CL = E(θ*)
• UCL = E(θ*) + k σ(θ*)
• LCL = E(θ*) - k σ(θ*)
– Where k = no. of standard deviations of the
sample statistic that the control limits are
placed from the centre line
– Generally value of k is chosen as 3

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Selection of Control Limits –
Contd..
• Sample statistic is assumed to have an normal
distribution
• Value of k = 3 implies that there is a probability of
only 0.0026 of a sample statistic falling outside the
control limits, if the process in in control
• k is also chosen, based on the desired probability of
sample statistic falling outside the control limits,
when process is in control. These limits are called
“Probability limits”
• Choice of k is influenced by the Error consideration
(Type I error and Type II error)

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Errors in making inferences

• Making inferences from a control chart is similar to testing a

hypothesis
• Control limits are the critical points that separate the rejection and
acceptance region
• If a sample values fall above UCL or below LCL, then we reject null
hypothesis or say that process is out of control
• Type I error
– Inferring that a process is out of control, when it is actually in control
– Probability of Type I error is given by ‘α’
• Type II error
– Inferring that a process is in control, when it is really out of control
– All points may fall within limit, but process mean has changed

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Example

A control chart is to be constructed for the average breaking

strength of nylon fibers. Samples of size 5 are randomly chosen
from the process. The process mean and standard deviation are
estimated to be 120 kg and 8 kg, respectively.
(a) If the control limits are placed 3 standard deviations from the
process mean, what is the probability of a type I error?
(b) If the process mean shifts to 125 kg, what is the probability of
concluding that the process is in control and hence making a type II
error on the first sample plotted after the shift?
(c) What is the probability of detecting the shift by the second
sample plotted after the shift if the samples are chosen
independently?

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(1 -0.0548)(0.0548) = 0.0518 0.0548 + 0.0518 = 0.1066.

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Operating Characteristics
curve (OC Curve)
• An OC curve is a measure of goodness of a control chart’s
ability to detect changes in process parameters
• A plot between the probability of the Type II error versus the
shifting of a process parameter value from its in-control value
• Helps us to determine the chances of not detecting a shift of a
certain magnitude in a process parameter on a control chart
• Shape of the curve is similar to inverted ‘S’
• For small shifts in the process mean, the probability of non-
detection is high
• If the change in process mean is high, the probability of
detection increases
• The ability of the control chart to detect changes quickly is
indicated by the steepness of the OC-curve and the quickness
with which the probability of non-detection reaches zero

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OC Curve

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Effect of control limits on
errors in inference making
• Choice of the control limits influence the occurrence of
Type I error and Type II error
• As control limit are placed farther apart, the probability
of Type I error decreases
– For 3σ limit, the probability of Type I error is 0.0026
while for 2σ limit, it is 0.0124
• But probability of making Type II error increases,
showing that both these errors are inversely related
• If all other process parameters held fixed, probability of
Type II error decreases with an increase in sample size
– As n increases, standard deviation decreases and hence
control limit will be nearer, and reduces probability of
Type II error.

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errors in inference making –
Contd..
• It involves making a judicious choice of control limit
selection
• Generally, control limits are placed at 3σ distance from
centre line, restricting the occurrence of ‘false alarm’
• For critical process, it is often necessary to detect small
changes as early as possible, hence tighter control limits
are preferable
• Warning limits
– Are usually placed at 2σ limits from the centre line
– When a point falls outside the warning limits, but within
control limits, process ‘may’ go out of control
– For a normally distributed statistic, the probability of falling in
a band between the warning and control limit is 4.3%

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Effect of sample size on
control limits
• Sample size affects the standard deviation of the sample statistic
plotted
• In a control chart, for the sample mean standard deviation is given by
σx = σ / √n
• Standard deviation and sample size are inversely related
• n increases, σ decreases, i.e. it provides more information and hence
less variability, which reduces the frequency of inference error
occurrence
• Average run length
– An alternate measure of performance of control chart
– Denotes the no. of samples, on an average is required to detect the out
of control signal
– Let Pd denote the probability of observation plotting outside the
control limit, then run length is 1, with probability of Pd and run length
is 2, with probability of Pd(1 – Pd)
– ARL = Pd * ∑ j (1–Pd) j – 1 = 1 / Pd (Based on expansion of infinite series)

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Average Run Length –
Contd..
• For a process in control, Pd = α
• For a 3σ control chart, detection of out of control condition is given
by ARL = 1 / Pd = 1 / 0.0026 = 385, i.e. an observation will plot
outside the control limit every 385 samples on average
• For a process in control, the ARL to be large, so that observation
plotting outside control limit is less or it does not create a false
alarm
• For an out of control process, the ARL should be small, so that out
of control can be easily detected. In this case, Pd = 1 – β and hence
ARL = 1 / 1 – β
• ARL curves can also be constructed for the control chart based on
the shift in mean with respect to ‘σ’ and ARL
• ARL can be expressed in terms of expected number of individual
unit sampled I. It is given by I = n (ARL)

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Selection of Rational samples

• Shewhart described the fundamental criteria for the

selection of rational sub group
• Rational sample is chosen in such a manner that the
variations within sample is considered to be due to
common causes alone
• Samples are selected such that special causes if present,
will occur between samples
• i.e. the difference between sample will be ‘maximized’
while difference within sample is ‘minimized’
• It can be done by the instant-of-time method i.e.,
Observation are selected at approximately the same time
for the population under condition

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Selection of Rational samples – Contd..
• Sample size
– It is dependent on the expected degree of shift in the
process parameter
– For detecting slight change in the process parameter, a
large sample size is needed
– If we can tolerate smaller changes in the process
parameters, then a small sample size might suffice
• Frequency of Sampling
– It must be decided before constructing control charts
– Options are: choosing small sample size at frequent
intervals or choosing large sample size at infrequent
intervals
– Generally small sample size at frequent intervals is
adopted
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Selection of Rational samples –
Contd..
• Other factors that influence sample size
and frequency are
– Type of inspection for getting data –
destructive or non-destructive
– Current state of process
– Cost of sampling and inspection per unit
– Loss incurred due to non-conforming
items etc.

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Analysis of patterns in control
chart
• Criteria other than a plotted point falling outside the
control limits are also used to determine whether a process
is out of control
• Plot patterns often indicate whether the process is in
control or not
• Analysing these patterns is more difficult than plotting the
chart
• Identifying the causes of non-random patterns require a
knowledge of the process, equipment and operation
conditions as well as their impact of characteristic of
interest

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ARL

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Rules for Control chart

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Analysis of control chart –
contd..
• Rules
– A process is assumed to be out of control, if a single point plots outside
the control limits

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Analysis of control chart –
contd..
• Rules – contd.
– A process is assumed to be out of control, if two out of three
consecutive points fall outside the 2σ warning limits on the same side
of the centre line

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Analysis of control chart –
contd..
• Rules – contd.
– A process is assumed to be out of control, if four out of five consecutive
points fall beyond the 1σ unit on the same side of the centre line

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Analysis of control chart –
contd..
• Rules – contd.
– A process is assumed to be out of control, if 9 or more consecutive
points fall to one side of the centre line

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Analysis of control chart – contd..
• Rules – contd.
– A process is assumed to be out of control, if there is a run of
six or more consecutive points, steadily increasing or
decreasing

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Analysis of control chart –
contd..
• Rules – contd.
– For a process in control, roughly equal number
of points should be above or below the centre
line with no systematic patterns

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Interpretation of plots
• Five rules for determining out of control conditions are not
all used simultaneously
• Rule 1 is routinely used along with a couple of other rules
• Reason for not using all rules is that it increases the chance
of Type – I error, i.e., Probability of false alarm increases
• Suppose a number of independent rules are used for out of
control criteria is ‘k’. Let αi be the probability of type I error
of rule ‘I’.
• Then the overall probability of type I error is α = 1 – product
(1 – αi)
• This is under the assumption that rules are independent, but
generally rules are not independent and hence it is
approximate only
• Even if all rules are applied, the process may be out of
control, for which the experience, judgement and
interpretive skills are needed

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Other important considerations

• Determination of causes of out of control points

– Task of control chart is not just identification of out-of control points,
but should identify the causes behind that
– Requires a thorough knowledge of the process and also the sensitivity
of the output quality characteristic to process parameter
– Determination of causes is a team effort
– Generally cause and effect diagram is used
• Maintenance of control chart
– Should be done on continuous basis, as it involves changing the centre
line and limits and when process goes out of control
– Should be easily accessible to the person, who is responsible for that
quality characteristic
– Should be placed in shop floor so that all can know about the current
situation

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The diameter of cotter pins produced by an automatic machine is a characteristic of interest.

Based on historical data, the process average diameter is 15 mm with a process standard
deviation of 0.8 mm. If samples of size 4 are randomly selected from the process:
(a) Find the 1ó and 2ó control limits.
(b) Find the 3ó control limits for the average diameter.
(c) What is the probability of a false alarm?
(d) If the process mean shifts to 14.5 mm, what is the probability of not detecting this
shift on the first sample plotted after the shift? What is the ARL?
(e) What is the probability of failing to detect the shift by the second sample plotted
after the shift?
(f) Construct the OC curve for this control chart.
(g) Construct the ARL curve for this control chart.

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 407

The length of industrial filters is a quality characteristic of interest. Thirty samples, each of
size 5, are chosen from the process. The data yields an average length of 110 mm, with the
process standard deviation estimated to be 4 mm.
(a) Find the warning limits for a control chart for the average length.
(b) Find the 3ó control limits. What is the probability of a type I error?
(c) If the process mean shifts to 112 mm, what are the chances of detecting this shift by the
third sample drawn after the shift?
(d) What is the chance of detecting the shift for the first time on the second sample point
drawn after the shift?
(e) What is the ARL for a shift in the process mean to 112 mm? How many samples, on
average, would it take to detect a change in the process mean to 116 mm?

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 408

A health care facility is monitoring daily expenditures for a certain diagnosis-

related group (DRG). Individual observations are selected. After 50 samples, the
average and standard deviation of daily expenditures (in hundreds of dollars) are
estimated to be 15 and 2, respectively.
(a) Find the 3ó control limits.
(b) Suppose that Rules 1 and 2 are used simultaneously for the detection of outof-
control conditions. Assuming independence of the rules, what is the overall
probability of a type I error? Explain the meaning of a type I error in this context.
(c) Suppose that the average daily expenditures for the same DRG increases to
$1750. What is the chance of detecting this shift by the second sample drawn after
the shift?
(d) What is the ARL?

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Thank You

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Quality Control Assurance &

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
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Chapter - 8

Control Charts for

Attributes
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Introduction

• Attribute
– It is a quality characteristic for which a numerical value is not
specified
– It is measured on a nominal scale, i.e., it does or does not meet
certain guidelines
– It is categorized according to the scheme or levels
• Nonconformity
– A quality characteristic that does not meet certain standards or
specification is said to be non conformity
– Eg. Length of a bar 40 ± 0.5. Both 40.6 and 42 are nonconformity
• Nonconforming item
– A product with one or more non-conformities such that it is unable
to meet the intended standards and is unable to function as
required
– It is possible to have several non-conformities on a product without
being classified as a nonconforming item

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Introduction – Contd..
• Types of charts
– Based on binomial distribution
• Proportion of non conforming items (p-chart)
• No. of non conforming items (np-chart)
– Based on Poisson distribution
• Total number of non conformities items (c-chart)
• Non conformities per unit chart (u-chart)
– Used in situation where the size of the sample varies
from sample to sample
– Based on weights
• Chart for Demerit per unit (U-chart)
– Deals with combining nonconformities on a weighted
basis, based on the severity of the non conformity 4

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Advantages and Disadvantages
of Attribute charts
• A variable quality characteristic can be measured as an
attribute, because of limited time, money, worker
availability etc., if attribute information is alone
sufficient
• Advantages
– For a given product, if variable charts are used for each of its
quality characteristic, no. of charts constructed will be very high
and in such case, attribute control chart provides overall quality
information
– Can be used to summarize information about several
components of a product
– Attributes are encountered at all levels of an organization
(company, plant, department, operator level etc), but variable
charts are used at lower only (machine level)
– Provides effective information to top management
– Helps in going from the general to more focussed level

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Advantages and Disadvantages of
Attribute charts – Contd..
• Disadvantages
– Attribute information does not indicate the degree to which
specification are met or not met, but variable provide more
information a process and performance
– Variable plots provide more information on the potential
causes and hence makes the identification of remedial
action easier for out of control situation
– Variable chart can forewarn, when the process goes out of
control, while attribute does not detect a lack of control,
until the process parameters are changed
– When specification limit are equal or tighter than the
inherent variability of the process, attribute chart indicates
out of control process
– Attribute chart requires larger sample size, to ensure
adequate protection against the certain level of process
changes
• If no historical information is available, attribute
control charts are used first and once problem area is
identified, it is replaced by a variable control chart
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Preliminary decisions
• Level
– Decide on the level at which it has to used – plant, department,
operator etc.
• No. of quality characteristic
– Chart for single quality characteristic, multi quality
characteristic or for a product
– Depends on no. of potential quality characteristic, no. of
products produced, cost and time required for inspection
• Sample size
– Should be large enough to allow non conformities or non
conforming items to be observed in the sample
– Eg. Non conformance rate is 2.5%, while sample size is 25,
average no. of non conforming per sample is 0.625
– Small sample size leads to misleading inference
• Nonconformity
– What will be considered a nonconformity should be defined
– It depends on product, functional use and customer needs
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Preliminary decisions – Contd..
• Frequency of sampling
– Depends on production rate, cost of sampling etc.
• Choice of measuring instruments
– Accuracy of the instruments directly influences the quality of
the data calculated
– Should be calibrated and tested
– Characteristic being controlled, the desired degree of
measurement precision, both impacts the selection
• Design of data recording forms
– Includes part name, sample number, date, time, raw values of
data, no. of non conforming items, operator name, machine,
gauge, comments etc.
• One, two or three-sigma zones and rules related to it are
not used because the underlying theory in non-normal
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Control chart for proportion
nonconforming (p-chart)
 p-chart is one of the most versatile chart
 Used to control the acceptability of single quality
characteristic or a whole product
 Also used to measure the quality of an operator,
machine, department or entire plant and also the
performance of a CEO
 Provides fair indication about the general state of the
process based on the average quality level of the
proportion non conforming
 It can act as a source of locating problems and
provides information for improving product quality
 Based on binomial distribution

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p-chart – Contd..
 Assumptions
– Probability of obtaining a non conforming item
must be constant
– Sample must be identical
– Samples are independent, but is not valid for
samples manufactured in groups (Eg. Steel ingots
– batch production)
– For a given sample, proportion of non conforming
is given by

x
ˆ
p =
where x = no .of nonconforming item in sample, n
n
= sample size
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p-chart – Contd..
 The distribution of no. of nonconforming item in a
sample is given by binomial distribution
p x (1 − p )
n! n− x
P( X = x) =
(n − x )! x!
where x = 0,1,2,.....n
 p = probability of getting a non conforming item
on each trial
 Mean and variance of sample proportion non
conforming is given by
E ( pˆ ) = p
p (1 − p )
Var( pˆ ) =
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p-chart – Contd..
 No standard given
– Proportion of non conforming is specified, it must
be estimated from the sample information
x
pˆ =
n
– Average of these individual sample proportions non
conforming is used as the centre line g g

g = no. of samples
 pˆ i  xi
CLp = p = i =1 = i =1
xi = no. of non conforming items g ng
– Variance is calculated from
p (1 − p )
Var ( pˆ ) =
n 12

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p-chart – Contd..
 No standard given – contd..
– True value of ‘p’ is not known, hence value of
p is used as an estimate
– Control limits are given by
p (1 − p )
UCLp = p + 3 .
n
p (1 − p )
LCLp = p − 3 .
n

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p chart – contd..

No. of defectives

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p chart – contd..
g g

 pˆ  x i i
CLp = p = i =1
= i =1
0.129
g ng

p (1 − p ) 0.129 +
UCLp = p + 3 . 3 [0.129(1 – 0.129)/50]
n
= 0.271
p (1 − p )
LCLp = p − 3 .
n 0.129 -
3 [0.129(1 – 0.129)/50]
=0 15
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p chart – contd..

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p-chart – Contd..
Standard given
– If the target value of the proportion of non
conforming item is known, the centre line is
selected as that target value, i.e.
– Control limits are given by
CLp = p0
p0 (1 − p0 )
UCLp = p0 + 3 .
n
p0 (1 − p0 )
LCLp = p0 − 3 .
– If lower limit turns out ton be negative, then
LCL is taken as zero

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p chart – contd..

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Problem
Twenty-five samples of size 50 are chosen
from a plastic-injection molding machine
producing small containers. The number
of nonconforming containers for each
sample is shown in Table 8-2, as is the
proportion nonconforming for each
sample,

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p-chart – Contd..

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Problem
Management has decided to set a standard of
3% for the proportion of nonconforming test
tubes produced in a plant. Data collected
from 20 samples of size 100 are shown in
Table 8-3, as is the proportion of
nonconforming test tubes for each sample.

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p-chart – Contd..

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p-chart – Contd..
 Unique features
– If the p-chart shows continuously increase in the
average proportion non conforming, management
should investigate the reasons behind the
increase rather than revising the limit
– Causes can be lower incoming quality from
vendor or tightening of specification limit
– Downward trend in the proportion
nonconforming is most desirable
 Control limits for representative sample
sizes
– Based on those sizes that occur more frequently
– Should span the range of sample sizes
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p-chart – Contd..
 Variable sample size
– Size varies due to rate of production, lack of inspection
personnel, change in unit cost of inspection
– Change in sample size results in change in control
limits though the centre line remains constant
– Sample size increases, control limits become narrower
– Control limits for individual sample sizes are given by
p (1 − p )
UCL = p + 3 .
ni
p (1 − p )
LCL = p − 3 .
ni
– If lower limit turns out to be negative, then LCL is
taken as zero
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p chart – contd..

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p chart – contd..

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p chart – contd..

Day 1 2 3 4 5 6 7 8 9 10

n 500 550 700 625 700 550 450 600 475 650

D 5 6 8 9 7 8 16 6 9 6

p 0.010 0.011 0.011 0.014 0.010 0.015 0.036 0.010 0.019 0.009

pbar 0.014 0.014 0.014 0.014 0.014 0.014 0.014 0.014 0.014 0.014

UCL 0.029 0.028 0.027 0.028 0.027 0.028 0.030 0.028 0.030 0.027

LCL 0 0 0 0 0 0 0 0 0 0
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p chart – contd.. p-chart

0.060
0.050
0.040
0.030
p

0.020
0.010
0.000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Day
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Problem

Twenty random samples are selected from a

process that makes vinyl tiles.
The sample size as well as the number of
nonconforming tiles are shown in Table 8-4.

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Control chart for proportion
nonconforming (p-chart) – Contd..
 Control limits based on average sample
size g

n
– Mean of these sample size is i
n= i =1
g g

– Centre line is given by

g
 pˆ i  xi
g = no. of samples CLp = p = i =1 = i =1
xi = no. of non conforming items g ng
p (1 − p )
– Control limits are given by UCL = p + 3 .
n
p (1 − p )
– Certain precautions should beLCL
taken= while
p − 3 . making
inferences and individual control limits have to ben
calculated to allow a proper decision to be made
regarding the particular sub group
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p chart – contd..

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p-chart – Contd..

 Standardized control chart

– Used for varying sample size
– Value of the proportion non conforming of a sample is expressed as
the sample’s deviation from the average proportion non
conforming in units of standard deviation
– They have a mean of zero and control limits are ±3 and are constant
– Mean is given by and standard deviation is given by
 pˆ =
(
p 1− p )
E( pˆ ) = p
n
p = true process non-conformance rate n = sample size
– Standardized value of proportion non-conforming for the ith
sample is pˆ i − p
Z =
p (1 − p )
ni
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p chart – contd..

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Special considerations for p-chart
 Observations below the LCL
– Points falling below LCL is desirable as
it indicates an improvement in process
– Care should be taken such that error
measurement has not occurred
 Comparison with a specified standard
– When standard is given and if points
fall outside the UCL and no special
causes can be assumed, then existing
process is not capable

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Special considerations for p-chart
 Impact of design specifications
– Non conforming product refers to quality
characteristics that do not meet ‘certain
specifications’ and hence even if process is in
control, average proportion of non conforming is
high
– Requires change in the design or specification of
the product and tolerance should be loosened
with no deviation from customer needs
 Information about overall quality level
– Used for aggregating information and can be used
at plant with many product lines, machine etc and
will provide overall product non conformance rate

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BITS Pilani, Pilani Campus

 450
Chart for No. of nonconforming
items (np-chart)
 Based on the count of no. of nonconforming items in
sample
 Operator may feel easy to use this chart
 Assumptions used in p-chart is applicable for this chart
also
 Drawback of np-chart
– If sample size changes, the centre line and control limit
changes, and hence inference becomes difficult
 No standard given g
– Centre line is given by
– xi = no. of non-conforming for ith sample
x i

– g = no. of samples CLnp = np = i =1

– n = sample size
g
 np = np (1is
– Standard deviation of number of nonconforming − p)
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BITS Pilani, Pilani Campus

 451
np-chart – contd..
 Control limits are given by

UCLnp = np + 3 . np (1 − p )
LCLnp = np − 3 . np (1 − p )
 If LCL is negative, then it is taken as zero
 Standard given
– If standard is specified for number of non conforming
items is given as npo, then the limits are given as
CLnp = npo
UCLnp = npo + 3 . npo (1 − po )
LCLnp = npo − 3 . npo (1 − po ) 42

BITS Pilani, Pilani Campus

 452
np chart – contd..

No. of defectives

43

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 453
Problem

Data for the number of dissatisfied customers

in a department store observed for 25
samples of size 300 are shown in Table 8-6.
Construct an np-chart for the number of
dissatisfied customers.

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454

45

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455

46

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 Control chart for the456
number of
nonconformities (c-chart)
 Nonconformity
– Defined as the quality characteristic that does not meet some
specification
– Non conforming item has one or more nonconformities that
make it non functional
 Introduction
– A c-chart is used to track the total no. of non conformities in a
sample of constant size
– When the sample size varies, u-chart is used to track the no. of
non conformities per unit
– Size of the sample is also called as “Area of Opportunity”
– Area of opportunity may be a single or multiple units of a
product or it can also be continuous
– If average no. of nonconformities per unit and area of
opportunity are small, then most observations show zero non
conformities, which is misleading and hence it is beneficial to
choose large area of opportunity

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BITS Pilani, Pilani Campus

 457
c-chart – Contd..
 Introduction – contd..
– Occurrence of nonconformities is assumed to follow a ‘poisson
distribution’
– Poisson distribution is well suited to model the number of
events that happen over a specified amount of time, space or
volume
 Assumptions
– Opportunity for the occurrence of non conforming should be
large
– Average no. of non conformities per unit must be small
– Occurrences of non conformities must be independent of each
other
– Each sample should have an equal likelihood of the occurrence
of non conformities
– Eg. Different screw drivers are used to tighten the screws in a
product, the opportunity for change in torque will vary and
hence should not be used 48

BITS Pilani, Pilani Campus

 458
c-chart – Contd..
 If ‘x’ represents the no. of
nonconformities in the sample unit and
‘c’ is the mean, then the poisson
distribution is given as e−cc x
p ( x) =
x!
 p(x) is the probability of observing ‘x’ non conformities
– Mean and variance are equal for poisson distribution
 No standard given
– Average no. of nonconformities per sample is found
from the sample observation, denoted by ‘c-bar’ and 49
the limits are CLc = c
UCLc = c + 3. c
LCLc = c − 3. c BITS Pilani, Pilani Campus
 459
c-chart – Contd..
 Standard given
– Let the specified goal for the no. of non
conformities per sample unit be co

CLc = co
UCLc = co + 3 . co
LCLc = co − 3 . co

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BITS Pilani, Pilani Campus

 460
c chart – contd..

51

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 461
Problem

Samples of fabric from a textile mill, each 100

m2, are selected, and the number of
occurrences of foreign matter are recorded.
Data for 25 samples are shown in
Table 8-7. Construct a c-chart for the number
of nonconformities.

52

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462

53

BITS Pilani, Pilani Campus

 Control chart for the463
number of
nonconformities per unit (u-chart)
 Introduction
– Used, when the area of opportunity changes
– Used, when companies inspect all items produced or
services rendered, for the presence of non conformities
– Generally output per production run vary, because of
fluctuating supplies of labour, machines, raw material
and hence no. of units inspected changes, thus resulting
in varying sample size
– The control limits change as the sample size varies, but
centre line remains same
 No standard given
– When sample size varies, the no. of non conformities per
unit for the ith sample is given by ui = ci / ni
– ci is the no. of non conformities in the ith sample
– ni is the size of ith sample and it may not be a integer
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BITS Pilani, Pilani Campus

 464
Control chart for the number of
nonconformities per unit (u-chart) – Contd..
 No standard given – contd..
– Average no. of nonconformities per unit and the control
limits are given by
g u
c UCLu = u + 3 .
i =1
i
ni
CLu = u = g

 ni
i =1
LCLu = u − 3 .
u
ni
 As the sample sizes increases, control limits draws
closer
 If ni = 1, all formula will be equal to that of c - chart

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BITS Pilani, Pilani Campus

 465
u-chart – Contd..
 In a textile finishing plant, dyed cloth is
inspected for the occurrence of defects
per 50 square meters. The data on ten
rolls of cloth are shown below. Use these
data to set up a control chart for
nonconformities per unit. The center line
of the chart should be the average
number of non-conformities per
inspection unit--that is, the average
number of nonconformities per 50
square meters.

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BITS Pilani, Pilani Campus

 466
u chart – contd..
Roll Number Number of Number of Number of Number of UCL LCL
Square Noncon Inspecti Noncon
Meters formitie on formitie
s Units in s per
Roll, n Inspecti
on Unit

1 500 14 10 1.4
2 400 12
3 650 20
4 500 11
5 475 7
6 500 10
7 600 21
8 525 16
9 600 19
10 625 23 57

BITS Pilani, Pilani Campus

 467
u chart – contd..

58

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 468
Problem
The number of nonconformities in carpets
is determined for 20 samples, but the
amount of carpet inspected for each sample
varies. Results of the inspection are shown
in
Table 8-8. Construct a control chart for the
number of nonconformities per 100 m2

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469

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BITS Pilani, Pilani Campus

 Charts for Demerits
470 per unit

(U-chart)
 ‘c’ and ‘u’ chart treat all types of non conformities
equally, regardless of their degree of severity
– Eg. Monitor A has trouble in colour while Monitor B has 5
scratch marks on its surfaces – here Monitor A defect is
more serious than Monitor B’s
 An alternative approach is to assign “weights” to non
conformities according to their relative degree of
severity
 The quality rating system, which rates demerits /
unit is called U-chart and is often helpful in service
applications
 Classification of non conformities
– Classification is based on degree of seriousness, ANSI
standard A3 classifies in the following manner:
• Class 1 defects: Very serious and defects lead directly to
‘severe’ injury or to catastrophic economic losses

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BITS Pilani, Pilani Campus

 Charts for Demerits
471 per unit

(U-chart) – Contd..
 Classification of non conformities – contd..
• Class 2 defects: serious and defects that lead to
‘significant’ injury or to significant economic losses
• Class 3 defects: major and defects that cause ‘major’
problems with normal use of product or service rendered
• Class 4 defects: minor and defects that cause ‘minor’
problems with normal use of product or service rendered
 Once classification of defects or non conformities has
been established, demerits per unit are assigned to each
class
 Definition of classes and no. of classes are not rigid and
varies with respect to organization and the problem
environment
 Assigned weights for defects is also user dependent, while
ANSI standard uses 100, 50, 10, 1 for the above
mentioned classes
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BITS Pilani, Pilani Campus

 Charts for Demerits
472 per unit

(U-chart) – Contd..
 Construction
– Let us have 4 categories of non conformities
– Let the sample size be ‘n’
– Let c1, c2, c3 and c4 denote the total no. of non
conformities in the sample for 4 categories
– Let w1, w2, w3 and w4 denote the weights
assigned to each category
 Assumption
– Non conformities in each category is
independent of defect in other categories
– Occurrence of non conformities in each
category is given by Poisson distribution
 For a sample size of ‘n’, total no. of demerits is given by
D = w1c1 + w2c2 + w3c3 + w4c4
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BITS Pilani, Pilani Campus

 Charts for Demerits
473 per unit

(U-chart) – Contd..
 Demerits per unit of the sample are given by
D w1c1 + w2 c2 + w3c3 + w4 c4
U= =
n n
 U is the linear combination of independent
poisson random variable
 Centre line of the U chart is U = w1u1 + w2u2 + w3u3 + w4u4
– u1 ,....u4 average no. of non conformities per
unit in respective classes g
and are calculated
as 
i =1
ci
u = g
 ni
i =1
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BITS Pilani, Pilani Campus

 Charts for Demerits
474 per unit

(U-chart) – Contd..
 Estimated standard deviation of U is given by
w1 u1 + w2 u2 + w3 u3 + w4 u4
2 2 2 2

ˆU =
n
 Control limit of the U chart is
UCLU = U + 3.ˆU
LCLU = U − 3.ˆU
 If LCL is negative, then take LCL as zero

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 475
Problem

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 476
U chart – contd..

67

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 477
U chart – contd..

68

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 478

Thank You

69
BITS Pilani, Pilani Campus
 479

Quality Control Assurance &

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
 480

BITS Pilani
Pilani Campus

Control Charts for Variables

2
Introduction 481

• Variables are those quality characteristics that are measurable

on a numerical scale, e.g. length, viscosity
• It is necessary to control the mean value of a quality
characteristic as well as its variability
• Mean gives an indication of the central tendency of a process
• Variability provides an idea of the process dispersion
• When there is a change in process mean or process standard
deviation, the proportion of parts that do not meet specification
increases
• Control chart aid in detecting such changes in process parameters
• Variables provide more information than attributes
• Attributes deal with qualitative information, whether an item is
non-conforming or not ok, but didn’t show the degree to which a
quality characteristic is nonconforming
• Eg. 40 ± 0.5. Both 40.6 and 42 are nonconforming

3
BITS Pilani, Pilani Campus
Introduction – Contd.. 482

• Cost of obtaining variable data is usually higher than for

attributes because
– Attribute data is collected by means such as go / no-go gages,
which are easier to use and hence less costly also
– Total cost of data collection is the sum of two costs – fixed and
variable cost
– Fixed cost include cost of inspection equipment, while variable
cost include cost of inspecting
– More the parts inspected, higher the variable costs and fixed
cost is unaffected
– With the use of automated devices for measurement, the
differences in variable unit cost between variable and attribute
may not be much, but fixed cost may increase
– Attribute chart for the proportion of non-conforming may
represent the general operational level of the plant but not the
variable chart
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BITS Pilani, Pilani Campus
Selection of Characteristics
483 of
Investigation
• A single component has usually several quality
characteristic
• Number of quality characteristic that affect a product
will be large
• Not feasible to maintain control chart for all as decision-
making becomes difficult
• Involves selecting a few vital characteristics and
selection is based on those that cause more non-
conforming items and increase cost
• Pareto analysis plays a major role in selection
• It is desirable to measure process characteristic that
have a casual relationship to product characteristic

5
BITS Pilani, Pilani Campus
Preliminary decisions 484

• Selection of Rational samples

– Sampling method should maximize differences
between samples and minimize differences within
sample
– Lot from which samples are chosen should be
homogeneous
– For detecting shift in process parameter, samples
should be made up of item produced at same time
– For non-conformance of items produced since the
previous sample, then samples should be selected
from items produced since that time

6
BITS Pilani, Pilani Campus
Preliminary decisions – contd..
485

• Sample size
– Size is normally between 4 and 10 and in industry it
will be 4 to 5
– Larger the sample size, better the chance of detecting
small shifts
– Based on factors like cost of inspection or cost of
shipping a nonconforming item to the customer etc.
• Frequency of sampling
– Depends on the cost of obtaining information
compared to the cost of non detecting a non
conforming item
– As process is brought to control, frequency of
sampling decreases

7
BITS Pilani, Pilani Campus
Preliminary decisions – Contd..
486

• Choice of measuring instruments

– Accuracy of the instruments directly influences the
quality of the data calculated
– Should be calibrated and tested
– Characteristic being controlled, the desired degree of
measurement precision, both impacts the selection
• Design of data recording forms
– Recording forms should be designed based on the
control chart to be used
– Includes sample no., date, time, raw values of data, part
name, lot number, operator name, machine, gauge, unit
of measurement, specification etc.

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Control chart format 487

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BITS Pilani, Pilani Campus
Control chart for Mean and
488Range

• Development of chart
– Using a pre-selected scheme and sample size record
measurements of the selected quality characteristic
– For each sample, calculate the sample mean and range
Ri = xmax - xmin x1 + x 2 +  + x n
x=
n
– Obtain and draw the centre line and trial control limit
• Find the mean of all sample mean (Formula)
• Find the mean range of all samples (Formula)
– 3σ control limits for Mean chart is given by
 ˆ
  Z / 2 x =   Z / 2 X  3 X = X  3
n n
– For normally distributed population, the distribution of the
statistic’s relative range (w) = R / σ and it is dependent on
sample size ‘n’
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BITS Pilani, Pilani Campus
Control Chart for Mean (Xbar)
489

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BITS Pilani, Pilani Campus
Control chart for Mean and
490Range –
Contd..
– Mean of w is given by d2
– Estimate of the process standard deviation is
ˆ = R /d 2
– (UCL, LCL) = X  3 R = X  A2 R
d2 . n

– Control limits for R chart is given by R  3 R

– R = σ.w and hence σR = σ. σw
– Mean of σw is given as d3 and we also know that
Hence ˆ = R /d 2 R
 = .d
R 3
d2
– UCL = D3 R LCL = D4 R

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Control Chart for Range (R) 491

13
BITS Pilani, Pilani Campus
Control chart for Mean and
492Range –
Contd..
• Plot the values of the range on the chart and find
whether points are in statistical control
– An R chart is analysed before X-bar chart to determine
out of control situations, as R chart reflect process
variability, which should be brought to control.
– If R chart shows out of control, then the X-bar chart is
meaningless
• Delete the out of control points for which remedial
action has been taken to remove special causes and
the remaining samples are used to obtain revised
limits
• A point of interest is about the point that falls
below the LCL, when LCL is greater than zero
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BITS Pilani, Pilani Campus
Control chart for Mean and
493Range –
Contd..
• These points are desirable because they indicate
unusually small variability, within the sample
and might be due to special causes
• This condition helps in further reducing our
process variability
• Implement the control chart
Why two charts?
• X bar chart monitors the mean between sample
values
• R chart monitors the variation within sample.
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Example 494

16
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Example – contd.. 495

17
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Example – contd.. 496

18
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Example – contd.. 497

In this case, D3 = 0 for n = 5

and hence LCL = 0
19
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Example – contd.. 498

20
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Example – contd.. 499

21
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500

22
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501

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BITS Pilani, Pilani Campus
Standardized control chart
502

• When the sample size varies, it results in fluctuating

control limits and hence we need standardized control
chart
• Standardized values represent a deviation from the
mean in units of standard deviation
• They are dimensionless and have a mean of zero
• Control limits for this are ±3 and are constant
• Easier to interpret the shift in the process
• Sample size for sample i is ni and let Xi* and si denotes
its mean and standard deviation
g

 ni X i
• Mean of sample average X = i =1g
n i
24 i =1
BITS Pilani, Pilani Campus
Standardized control chart
503– Contd..

• An estimate of the process standard deviation σ* is

given by g

 (n − 1) si
2
i
ˆ = i =1
g

 (n
i =1
i − 1)

• For sample i, standardized value for the mean zi is

Xi − Xi
zi =
ˆ
ni
• A plot of the Zi values on a control chart with the centre
line at ‘0’ , UCL at 3 and LCL at -3 is standardized X-bar
chart

25
BITS Pilani, Pilani Campus
Standardized control chart
504– Contd..

– To standardize a Range chart, the range Ri for sample

‘i’ is first divided by the estimate of the process
standard deviation r = Ri
i
ˆ
ri − d 2
– Standardized value of Range is given by ki = d3
– Value of ki are plotted with a centre line at ‘0’ and UCL
= ‘3’ and LCL = ‘-3’
• Control Limits for a given target or Standard
– Management may specify values for the process mean
or standard deviation
– These values are the goals or desirable standards or
target values, which helps to determine process able to
meet standard
26
BITS Pilani, Pilani Campus
Control limits for a given505
target or
Standard - Contd..
– Let X o and  o represent the target values of the
process mean and standard deviation respectively
and the centre line and limits are given by
CLX = X 0
0
UCLX = X 0 + 3 . = X 0 + A . 0
n
0
LCLX = X 0 − 3 . = X 0 − A . 0
– For R - chart n

R
CLR = d 2 . 0 (ˆ = )
d2
UCLR = R + 3 . R = d 2 . 0 + 3. d 3 0 = D2 . 0
LCLR = R − 3 . R = d 2 . 0 − 3 . d 3 0 = D1. 0
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BITS Pilani, Pilani Campus
Interpretation and Inferences
506

• Caution
– Sample plots may fall outside the limit, even
though no special causes are present
– Reason being that desirable standards may
not be consistent with the process conditions
– It is easy to meet a desirable target value for
process mean than it is for process
variability (Range)

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BITS Pilani, Pilani Campus
Interpretation and Inferences
507 –
Contd..
• Interpretation
– Difficult and needs thorough knowledge
about different process parameters on
quality characteristic
– When R-chart is brought to control, many
special causes for the Xbar chart are
eliminated as well
– Xbar chart monitors the centering of the
process and a jump indicates process
average has jumped
29
BITS Pilani, Pilani Campus
Interpretation and Inferences
508– Contd..

– Increasing trend indicates the process centre is

gradually increasing and requires adjustments in
machine settings or such controllable parameters as
proper tool, proper depth of cut, feed etc.
– Reducing process variability in order to allow an R-
chart to exhibit control is difficult and needs “quality
improvement”
– Process capability can be estimated from the process
standard deviation, and helps to determine how the
process performs with respect to specification limits
and also in determining the proportion of output that
is non conforming

30
BITS Pilani, Pilani Campus
Control chart patterns and
509corrective
action
• A ‘non-random identifiable’ pattern in the
plot of a chart might provide reason to look
for special cause in a process
• There are about 15 typical patterns
identified by Western Electric company and
9 of them have been discussed here
• Natural Patterns
– No identifiable arrangement of the plotted point
exists
– No point fall outside the control limits
– Majority of the points are near the centre line and
few points close to control limits
– Demonstrates the presence of stable system of
common causes
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Control chart patterns – contd..
510

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Control chart patterns – Contd.
511

• Sudden shifts in the level

– Can occur because of changes intentional or
otherwise in process settings (temperature, depth of
cut etc.)
– New operators, new equipment, new vendors, new
methods are the reasons for sudden shift

33
BITS Pilani, Pilani Campus
Control chart patterns– Contd..
512

• Gradual shifts in the level

– Occurs when a process parameter changes gradually over a period
of time
– X-bar chart might exhibit such a shift because of incoming quality
of raw materials that would have changed with time
– Change in style of supervision, maintenance program etc.
– R-chart might exhibit such a shift because of new operator,
decrease in worker skill due to fatigue etc.

34
BITS Pilani, Pilani Campus
Control chart patterns – Contd..
513

• Trending pattern
– Differs from gradual shift in level, that trends do not stabilize or
settle down
– Represents changes that steadily increase or decrease
– For X-bar chart, can be due to tool wear, deterioration of
equipment, build up of debris on jigs and fixtures, change in
temperature etc.
– For R-chart, it may be due to improvement in operator skill due to
on job training, decrease due to fatigue etc.

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BITS Pilani, Pilani Campus
Control chart patterns – Contd..
514

• Cyclic patterns
– Characterized by repetitive periodic behaviour in the system
– Cycles of low and high points will appear on the control chart
– X-bar chart may exhibit because of rotation of operators, periodic
change of temperature or humidity, seasonal variation in incoming
components
– R-chart may exhibit this pattern because of operator fatigue and
getting energized in subsequent breaks, a difference between shifts,
periodic maintenance of equipments etc.
– If samples are taken so infrequently, only the high and low points will
be represented

36
BITS Pilani, Pilani Campus
Control chart patterns – Contd..
515

• Wild patterns
– Can be classified as Bunches and Freaks
– Cluster of several observation that are different
from other points and special causes are
associated with these points
– Freaks
• are caused by external disturbances that influence one or
more samples
• They are points that are too small or large with respect to
control limits and fall outside the control limits and
hence easy to identify
• Care should be taken that no measurement or recording
error is associated with that freak point
• Some special causes may be sudden, very short-lived
power failures, use of new tool for a brief test period etc.
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BITS Pilani, Pilani Campus
Control chart patterns – Contd..
516

38
BITS Pilani, Pilani Campus
Control chart patterns and
517corrective
action – Contd..
• Wild patterns – Contd.
– Bunches
• Cluster of several observation that are different from other
points
• Possible causes may be use of new vendor, use of a different
machine, use of new operator etc., for a short time period.

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BITS Pilani, Pilani Campus
Control chart patterns and
518corrective
action – Contd..
• Mixture patterns
– Effect of two or more population in the sample
– Characterized by points that fall near the control limits, with
absence of points near the centre line
– Might be due to material from two different vendors, different
production method, two or more machine being represented

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BITS Pilani, Pilani Campus
Control chart patterns and
519corrective
action – Contd..
• Stratification patterns
– Is also due to presence of two or more population distribution
– Output is combined or mixed and samples are selected from it
– Majority of the points fall close to centre line, with very few points
near the control limits
– Can be misinterpreted as indicating unusually good control

41
BITS Pilani, Pilani Campus
Control chart patterns and
520corrective
action – Contd..
• Interaction patterns
– Occurs when the level of one variable affects the
behaviour of other variables associated with the quality
characteristic
– Interaction pattern can be detected by changing the
scheme for rational sampling
– Example, low pressure and low temperature may
produce a desirable effect on output characteristic
– Effective sampling method would involve controlling
the temperature at several high values and then
determining the effect of pressure on output
characteristic for each temperature value
– If the R-chart shows the sample range to be small, then
information regarding the interaction could be used to
establish desirable process parameter settings
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BITS Pilani, Pilani Campus
Control chart patterns – Contd..
521

• Interaction patterns

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BITS Pilani, Pilani Campus
Control chart for Mean and Standard
522
deviation (X-bar and s chart)

• R-chart is easy to construct and use, but a

standard deviation chart (s-chart) is preferable
for large sample sizes (> 10)
• Reason is that range accounts only for the
maximum and minimum sample values and is
less effective for large samples, where as sample
standard deviation serves as a better measure of
process variability
• Population distribution of a quality
characteristic is assumed to be normal with a
population standard deviation denoted by σ

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BITS Pilani, Pilani Campus
Control chart for Mean and Standard
523
deviation (X-bar and s chart)

• Mean and standard deviation of the sample

standard deviation is given by
E (s) = c4
 s =  . 1 − c4 2 where c4
depends on the sample size given by

1   ( n − 2)  ! 
 2    2 
2 
c4 =    ( n − 3) 
 ( n − 1)     !
  2  
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BITS Pilani, Pilani Campus
Control chart for Mean and Standard
524
deviation (X-bar and s chart) – Contd..
g
• No Given Standards s i
– Centre line of a s-chart is CLs = s =
i =1
g
s
where g is the no. of samples and  = c
ˆ
4
si is the standard deviation of the ith sample
– UCLs= s + 3. s = s + 3. . 1 − c4
2

– Estimate of a population standard deviation is

– Hence control limits are given by
s
UCLs = s + 3. . 1 − c4 = B4 s
2

c4
s
LCLs = s − 3. . 1 − c4 = B3 s
2

c4 46
BITS Pilani, Pilani Campus
Control chart for Mean and Standard
525
deviation (X-bar and s chart) – Contd..

• No Given Standards
• X-bar chart
– Centre line is similar to that of X-bar chart
– Control limits are given by
s
UCLX = X + 3. = X + A3 s
c4 n
s
LCLX = X − 3. = X − A3 s
c4 n
• S-chart is constructed first as the standard deviation of
X-bar is dependent on ‘s’ and if the s-chart is not in
control, any estimate of the standard deviation of X-bar
chart is unreliable
47
BITS Pilani, Pilani Campus
Control chart for Mean and Standard
526
deviation (X-bar and s chart) – Contd..

• Given Standard
– If the target standard deviation is given as σ0 then, centre line of
a s-chart is
CLs = c4 0
– Hence control limits are given by
UCLs = c4 0 + 3 s = c4 0 + 3. 0 . 1 − c4 = B6 0
2

LCLs = c4 0 − 3 s = c4 0 − 3. 0 . 1 − c4 = B5 0

2

– X-bar Chart
• Target value is specified as Xo then control limits are given
by CL = XX 0

3
UCLX = X 0 + A 0 , where A =
n
LCLX = X 0 − A 0 48
BITS Pilani, Pilani Campus
Example 527

The thickness of the magnetic coating on audio tapes is an important

characteristic. Random samples of size 4 are selected, and the thickness
is measured using an optical instrument. Table 7-3 shows the mean Xand
standard deviation s for 20 samples. The specifications are 38 ±4.5
micrometers. If a coating thickness is less than the specifications call
for, that tape can be used for a different purpose by running it through
another coating operation.(Sum X=743.5, Sum s=95.8)

49
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 528

(a) Find the trial control limits for an X- and an s-chart.

(b) Assuming special causes for the out-of-control points,

determine the revised control limits.

(c) Assuming the thickness of the coating to be normally

distributed, what proportion of the product will not meet
specifications?

(d) Comment on the ability of the process to produce items that

meet specifications.

(e) If the process average shifts to 37.8 micrometre, what

proportion of the product will be acceptable?

50
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Control chart for individual
529 units – MR
Chart
• Chart for sample size is 1, i.e. for individual units
• Reasons for sample size to be ‘1’
– The rate of production is low
– Testing process may be destructive and the cost of the item is
very high
– If every manufactured unit is inspected
• The value of the quality characteristic is expressed as ‘X’
• Variability of the process is estimated from the ‘Moving
Range’, that are found from successive observations
– Moving Range of 2 observations is simply the difference
between them
– Moving Range are co-related, because they use common rather
than individual values and hence the pattern of MR chart must
be interpreted carefully

51
BITS Pilani, Pilani Campus
Control chart for individual
530 units – MR
Chart – Contd..
• Also, it can’t be assumed that X-values for the individual
units are normally distributed as in other control charts
• Hence checking of the distribution of individual values
is done first, by using frequency histogram to verify the
shape, skewness, kurtosis of the distribution
• No Given Standards
– An estimate of the process standard deviation is
– Where MR is the average of moving range of successive
MR
observation ˆ =
– If there are ‘g’ observations, there will be (g -1) moving rangesd 2
– Centre line is given by CL = MR
MR

52
BITS Pilani, Pilani Campus
Control chart for individual
531 units – MR
Chart – Contd..
– Control limits are given by
MR
UCLMR = MR + 3. = D4 MR
d2
MR
LCLMR = MR − 3. = D3 MR
d2
– For n = 2, D4 = 3.267, D3 = 0 and hence UCL = 3.267MR and LCL
=0
• X-Chart
– Centre line of X-chart is given by CL X = X
– Control limits are given by
MR
UCLX = CL + 3 = X + 3.
d2
MR
LCLX = CL − 3 = X − 3.
d2
53
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Example 532

54
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Example 533

55
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Example 534

56
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Example 535

57
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Control chart for individual
536 units – MR
Chart – Contd..
• Given Standards
– If standard values are specified as Xobar and σ0, then,

CLX = X o
UCLX = X o + 3. o
LCLX = X o − 3. o
– Assuming n = 2, (difference between 2 values only)

CLMR = d 2 o = 1.128 o
UCLMR = D4 d 2 o = 3.685 o
LCLMR = D3d 2 o = 0
58
BITS Pilani, Pilani Campus
Example 537

Table shows the Brinell hardness numbers of 20 individual steel

fasteners and the moving ranges. The testing process dents the parts
so that they cannot be used for their intended purpose. Construct the
X-chart and MR-chart based on two successive observations.
Specification limits are 32 ± 7.

59
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538

60
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 539

Thank You

61
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 540

Quality Control Assurance &

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
 541

Chapter - 11

Reliability

2
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 542
Introduction

• Why to study about Reliability?

– “Reliability is a measure of the quality of the product over the long
run.”
– We expect the product will function according to certain
expectations over a stipulated period of time
– To ensure customer satisfaction during the performance phase we
must address measures to improve reliability in the design phase
itself.
– The complex nature of products requires many components in their
construction, and its necessary to have a good reliability for the
whole system itself. This is called as “System Reliability.”
– With the customer and warranty costs in mind, one must know the
chances of successful operation of the product for at least a certain
stipulated period of time
– Such information helps the manufacturer to select the parameters
of a warranty policy
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 543
Definition of Reliability

• What is Reliability?
– “Reliability is the probability of a product performing its
intended function for a stated period of time under certain
specified conditions”
• Four aspects of Reliability
– Reliability is a probability related concept
– Functional performance of the product has to meet certain
stipulations
• Product design will ensure development of product that meet
or exceed stipulated requirements
• Eg. Strength of cable = 1000Kg, operation it should be more
– Reliability implies successful operation over a certain
period of time
– Operating or environmental condition under which product
use takes place are specified.
• Example: Reliability of a cable is given as having a
probability of successful performance of 0.90 in
withstanding 1000Kg of load for 2 years under dry 4
condition BITS Pilani, Pilani Campus
 544
Life cycle curve
• Most product goes through three distinct phases from
product creation to wear out
• A life cycle curve is a plot between failure rate λ and time
• Also called as ‘Bathtub curve’ (Figure)
• Consists of three phases, namely: Debugging or infant
mortality, Chance failure / useful life time, Wear out / aging
• Debugging phase exhibits a drop in the failure rate as initial
problems identified during prototype testing are ironed out
• In chance failure phase, the failure rate is constant and here
failure occurs randomly and independently. Also, it is called
as useful period
• In wear out phase, an increase in failure rate is observed, as
the product approaches its end of their useful life as parts
age and wear out
5
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 545
Life cycle curve – contd..

6
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 546
Probability distributions

• Used to model the failure rate

• Exponential distribution
– During the chance failure phase, the failure rate is constant
– Hence ‘exponential distribution’ can be used to describe the
time to failure of the product for this phase
– Probability density function is given by
f (t ) = e − t t  0
 is failure rate
– Mean time to failure (MTTF) for exponential distribution is
given by
MTTF = 1

– If the failure rate is constant, MTTF is the reciprocal of the
failure rate
7
BITS Pilani, Pilani Campus
 547
Probability distributions – contd..

• Exponential distribution – contd..

– For repairable equipment MTTF = mean time
between failure MTBF
– There will be a difference between MTBF and MTTF
only if there is a significant repair or replacement
time upon failure of the product.
– “Reliability at time t is R(t): is the probability of the
product lasting up to at least time t” and it is given by
• R(t) = 1 – F(t)
F(t) represents the cumulative distribution function
at time ‘t’
– Cumulative distribution function for the exponential
distribution is shown (Figure)

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 548
Probability distributions – contd..

9
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 549
Probability distributions – contd..

10
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 550
Probability distributions – contd..
• Exponential distribution – contd..
– Reliability function R(t) for the exponential distribution is
shown in the figure
– At time 0, reliability is 1 and
t
it decreases exponentially
with time
= 1 −   e dt = e
−t −t

– “Failure-rate function r(t) is the ratio of the time to failure

probability density function to reliability function”
f (t )
r (t ) =
R(t )
– For exponential distribution, implying a constant failure
rate, then 𝜆𝑒 −𝜆𝑡
𝑟(𝑡) = =𝜆
𝑒 −𝜆𝑡
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BITS Pilani, Pilani Campus
 551
Problem
• An amplifier has an exponential time-to-
failure distribution with a failure rate of
8% per 1000 hours. What is the reliability
of the amplifier at 5000hours? Find the
mean time to failure.
• What is the highest failure rate for a
product if it is to have a probability of
survival (i.e., successful operation) of
95% at 4000 hours? Assume that the time
to failure follows an exponential
distribution. 12
BITS Pilani, Pilani Campus
 552
Problem
• What is the highest failure rate for a
product if it is to have a probability of
survival (i.e., successful operation) of
95% at 4000 hours? Assume that the
time to failure follows an exponential
distribution.

13
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 553
Probability distributions – contd..
• Weibull distribution
– “It is used to model the time to failure of
products that have a varying failure rate
– Hence a candidate to model the debugging or
wear out phase
– It is a three parameter distribution where
density function is given by

  t − 
 −1
  t −   
f (t ) =   e −   , t  
       
– The parameters are:
• Location parameter is given by
• Scale parameter is  (−      )
• Shape parameter is  (  0 )
 (  0 ) 14
BITS Pilani, Pilani Campus
 554
Probability distributions – contd..
• Weibull distribution – contd..
– The probability density function varies for
different values of these parameters (Figure)
– Weibull distribution reduces to exponential
distribution, when  = 0 and β = 1
– For reliability modelling, the location parameter
=0
– For α = 1 and β = 1, the failure rate decreases
with time and can therefore be used to model
components in debugging phase”
– For α = 1 and β = 3.5, the failure rate increases
with time and so can be used to model products
in the wear out phase”. In this case, the weibull
distribution approximates normal

15
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 555
Probability distributions – contd..

• Weibull distribution – contd..

– Reliability function for the Weibull distribution is
by 
R(t ) = exp −

( )
t


 


– Mean time to failure is given by

1 
MTTF =  + 1

 
– Failure rate function is given by
f (t ) t  −1
r (t ) = =
R(t ) 
– The failure rate function for the weibull failure
density function, for values of the parameter β =
0.5, 1, and 3.5 (Figure) 16
BITS Pilani, Pilani Campus
 556
Probability distributions – contd..

17
BITS Pilani, Pilani Campus
 557

Capacitors in an electrical circuit have a time-

to-failure distribution that can be modeled by
the Weibull distribution with a scale
parameter of 400 hours and a shape
parameter of 0.2. What is the reliability of the
capacitor after 600 hours of operation? Find
the mean time to failure. Is the failure rate
increasing or decreasing with time?

18
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 558
System Reliability
• System reliability
– “Reliability of the product (made up of a number of
components) is determined by the reliability of each
component and also by the configuration of the system
consisting of these components”
– Product design, manufacture, maintenance influence
reliability, but design has a major role
– One common approach for increasing the reliability of the
system is through “redundancy in design”, which is usually
achieved by placing components in parallel.
– As long as one component operates, the system operates
• Systems with components in series
– For the system to operate, each component must operate
– It is assumed that the components operate independently
of each other (Failure of one component has no influence on
the failure of any other component)
A B C
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 559
Series System Example

20
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 560
System Reliability – contd..

• Systems with components in series – contd..

– If there are ‘n’ components in series, then system
reliability is given by Rs = R1 x R2 x - - - - - - Rn
– System reliability decreases as the number of
components in series increases
– Manufacturing capability and resource
limitations restrict the maximum reliability of any
given component
– Product redesign that reduces the no. of
components in series is the viable alternative

21
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 561

A module of a satellite monitoring system has

500 components in series.
The reliability of each component is 0.999.
Find the reliability of the module. If the
number of components in series is reduced to
200, what is the reliability of the module?

22
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 562
System Reliability – contd..
• Systems with components in series – contd..
– Use of the Exponential Model
• If the system is in chance failure phase, a constant
failure rate could be justified based on which we can
calculate failure rate, mean time to failure and system
reliability
• Suppose the system has ‘n’ components in series
• Each component has exponentially distributed time-to-
failure with failure rates given by
• The system reliability is given by  ,  − − − −
1 2 n

Rs = e−1t X e−2t X e−3t X − − − − − − − − − e−nt

  n  
 −   i  t 
=e   i =1  
BITS Pilani, Pilani Campus
 563
System Reliability – contd..
• Systems with components in series – contd..
– Use of the Exponential Model
• Thus if each component that fails is replaced
immediately with another that has the same failure rate,
the mean time to failure for the system is given by
1
MTTF = n

 i
i =1 i =  = constant
• When all components have same failure rate, If
then

1
MTTF =
n

BITS Pilani, Pilani Campus

 564
System Reliability – contd..

• Systems with components in parallel

– System reliability can be improved by
placing components in parallel as system
will operate as long as at least one of the
components operates.
– The only time the system fails is when all
the parallel components fail
– All components are assumed to operate
simultaneously.
– A system having ‘n’ components in parallel,
with the reliability of the ith component
denoted by Ri, i=1, 2, ----- n.
– Also assume that the components operate
randomly and independently of each other.
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 565
Parallel System Example

26
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 566
System Reliability – contd..
• Systems with components in parallel –
contd..
– The probability of failure of each component is
given by Fi = 1-Ri.
– System fails only if all the components fail and
hence the probability of system failure
n
is
Fs = (1 − R1 )(1 − R2 ) − − (1 − Rn ) =  (1 − Ri )
i =1

– Reliability of the system is the complement of Fs

and is given by
n
Rs = 1 − Fs = 1 − 1 − Ri
i =1
27
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 567
System Reliability – contd..
• Systems with components in parallel –
contd..
– Use of Exponential model
• If the time to failure of each component can be
modelled by the exponential distribution,
each with a constant failure rate λi, then the
system reliability, assuming independence of
component operation is

= 1 −  (1 − e )
n
− i t
Rs
i =1
• Time to failure of the system is not
exponentially distributed
28
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 568
System Reliability – contd..
• Systems with components in parallel –
contd..
– Use of Exponential model
• In the special case, where all the components have the
same failure rate the system reliability is

( ) Rs = 1− (1 − e )
n
−t n
Rs = 1 −  1 − e − i t

i =1

• Mean time to failure for a system of n components in

parallel is given by

29
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 569
System Reliability – contd..

• Complex system
– A complex system is one which has
components that are both in series and in
parallel
– Assumption
• Components operate independently
• Time to failure of each component is assumed
to be exponentially distributed
– The above described methods are used for
calculating the reliability and failure rate
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 570
Complex system – Example

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 571
Complex system – Example

32
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 572
Complex system – Example

33
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 573
System Reliability – Home work
• A company assembles a product from four major
components arranged as follows
B

A C D
• The components are purchased from different
vendors, who have supplied the following
reliability data:
Vendor

Component 1 2 3
A 0.94 0.95 0.92
B 0.86 0.80 0.90
C 0.90 0.93 0.95
34
D 0.93 0.95 0.95
BITS Pilani, Pilani Campus
 574
System Reliability – contd..
• System with standby components
– “In a stand by configuration one or more
parallel components wait to take over
operation upon failure of the currently
operating component”
– It is assumed that only one component in
parallel configuration is operating at any
given time
– Hence the system reliability is higher than
for comparable systems with components
in parallel
– In parallel systems, all components are
assumed to be operating simultaneously
35
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 575
Standby system – Example

36
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 576
System Reliability – contd..
• Standby components – contd..
– A standby system with a basic component and
two standby components in parallel (Figure) is
shown
Am

As
As
– Typically a failure sensing mechanism triggers
the operations of a stand by component when
the currently operating component fails

37
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 577
System Reliability – contd..
• System with standby components – contd..
– Use of Exponential Model – contd..
• If the time to failure of the components is assumed to
be exponential with failure rate , the number of failure
in a certain time ‘t’ adheres to a Poisson distribution
with parameter t
• Hence probability of ‘x’ failures in time ‘t’ is given by

P ( x) =
(t ) x
e t
x!
• For a system that has a basic component in parallel
with one standby component, the system will be
operational at time ‘t’ as long as there is no more than
one failure. Therefore, the system reliability would be :

Rs = e − t
+e − t
(t ) 38
BITS Pilani, Pilani Campus
 578
System Reliability – contd..
• System with standby components –
contd..
– Use of Exponential Model – contd..
• For a system (stand by) with a basic
component and two standby components, the
system will be operational if the number of
failures is less than or equal to 2, then

Rs = e t + e −t (t ) + e −t

( t )2

2!
• For n components on stand by, the reliability
and mean time to failure is given by
− t


Rs = e 1 + t +
( t )2
+
( t )3
+ ....... +
(t )n

 MTTF =
n +1
 2! 3! n!  
BITS Pilani, Pilani Campus
 579
Problems
• System with standby components –
Exercise Problem 14
• A standby system has a basic unit with four standby
components. The time to failure of each component
has an exponential distribution with a failure rate of
0.008 per hour.
– For a 400 hour operation period, find the reliability of the
standby system.
– What is its mean time to failure of the above system?
– Suppose all five components are operating simultaneously
in parallel, what would be the system reliability?
– What would be the mean time to failure for the parallel
system?

40
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 580
Problems – contd..
• System with standby components –
Exercise Problem 14 Solution
− t


R = e 1 + t +
(t )2
+
(t )3
+ ....... +
(t )n

 MTTF =
n +1
s  n!  
 2! 3!
• Rs = exp[-0.008(400)] [1 + 0.008(400) +
(0.008(400))2 / 2 + (0.008(400))3 / 6 +
(0.008(400))4 / 24 = 0.7806

• MTTF = (n+1) /  = 5 / 0.008 = 625 hours

41
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 581
Problems – contd..
• System with standby components –
Exercise Problem 14 Solution
• If all five units were operating in parallel,
system reliability would be
– Rs = 1 – [1 – exp(-0.008(400))5] = 0.18786
• In that case, MTTF is
– (1/0.008) (1+ ½ + 1/3 + ¼ + 1/5) = 285.4167
hours

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 582

BITS Pilani
Pilani Campus

QC in Service Sector and

Reliability
43
 583
Introduction
• Service sector accounts for more than 70% of jobs and the
number continues to grow
• Major difference exists in the ‘quality characteristics’ of
manufacturing and service and accordingly both the
measurement process and management focus differ in these two
sectors
• For example, in service industry, not only the product must meet
high standards, but employee’s behavior must also be
satisfactory
• The service sector therefore works on total service concept,
which is a combination of technical and human behavioral
aspects
• Human behavioral aspects are difficult to quantify, measure and
control
• Example: Airline industry – Goal is to transport people between
cities in desirable time, depends on aircraft design for speed,
scheduling etc, that are quantifiable
• Also depends on airhostess, ticket agents and other people to
run the show
44
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 584

Chapter – 13

• Quality Control in the

Service Sector

45
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 585
Introduction – contd..
• Few more examples include personal services,
education, banking, medicinal, financial, public
utilities, transportation etc.
• Service industries provide a tangible product and an
intangible component that affects customer
satisfaction
• Two parties are involved – one that assists or provides
the service (Vendor) and the party receiving service
(Vendee)
• Service functions are found in manufacturing also
done by staff personnel – provides expertise to the
operating departments
– Includes, customer services, accounting, payroll, R&D etc.
• Differences in the manufacturing and service sector
– A detailed differences are tabulated

46
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 586
Differences in manufacturing and
service sector
• Manufacturing • Service
– Product is tangible – Tangible and intangible
– Back orders are possible – Cannot be stored, if not
– Producer or company is used
the only party involved – Producer and consumer
in the making of the are both involved in the
product delivery of service
– Product can be resold – Service cannot be resold
– Formal specifications – No formal specification
provided by customer given by customer
– Customer acceptance of – Customer satisfaction is
product is quantifiable difficult to quantify

47
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 587
Service quality characteristics
• Quality of service can be broken down into two categories:
– Effectiveness deals with meeting the desirable service
attributes that are expected by the customer.
– Efficiency concerns the time required for the service to be
rendered
• Service quality characteristics can be grouped under 4
categories
– Human factors and behavioral characteristics
• Influenced by the attitude and behaviour of the provider
• Includes eagerness to help, thoughtfulness, complacency, courtesy
etc
• Can be developed through training while some are inherent in
individual
• Hence proper screening of employees and assignment of job is
important
– Behavioral characteristics
• Attitude of the customers is beyond the organization control
• Customer mind-sets are often a function of what they expect to
receive
48
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 588
Service quality characteristics –
contd..
• Behavioral characteristics – contd..
• Customer expectations can be influenced by advertisement
and reputation
• In turn, behavioural pattern gets affected
• Measurement of attitudes and behavioural characteristics
is not as simple and well-defined
• Timeliness characteristics
• Service that is not used in a given span of time cannot be
stored
• Timeliness with which a service is performed is critical to
customer satisfaction
• Characteristics related to timeliness are categorized by the
service phase, which they are associated
• Categories might include the time to order the service, the
waiting time before the service is performed, the time to
serve, and the post service time
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Service quality characteristics –
contd..
• Service nonconformity characteristics
• A nonconformity is a deviation from the ideal level
• Eg. - No. of errors per 100 vouchers, no. of data entry errors
per 1000 keystrokes, No. of complaints per 50 guests etc
• Target performance level should be zero nonconformities
• Goal is to achieve this through quality improvement measures
• Quality characteristics in this category are well defined and
more readily measured
• Facility related characteristics
• Physical characteristics of faculty associated with service and
delivery can affect customer satisfaction
• Eg. – Ambience in the restaurant, Cyber cafe in a petrol bunk,
Appearance of waiter etc.
• Characteristics are not as clearly defined and measurable but
better than behavioural
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Service quality characteristics –
Examples
• Facility related
characteristics

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Service quality characteristics –
Examples
• Behavioral
characteristics

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Service quality characteristics –
Examples

• Service nonconformity characteristics

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Service quality characteristics –
Examples

• Timeliness characteristics
• Service nonconformity characteristics
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Measuring service quality

• Characteristics • Measures
– No. of customer complaints,
– Human factors and
No. of compliments based
behavioural on behavioural factors of
persons in service
– Time to process a
– Timeliness transaction, Waiting time to
receive the baggage, etc
– No. of billing errors in
mobile phone usage, No. of
– Service nonconformity errors in data entry of
marks in database etc.
– No. of complaints due to
insufficient legroom in bus,
– Facility related Lack of lab facilities in a
institute etc.

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Measuring service quality – contd..
• In terms of ease of quantification and measurement,
categories can be ranked as service nonconformity,
timeliness, facility related and human and behavioural
factors
• Success of many service functions is determined by the
interaction between the provider and the customer
• Because of subjectiveness of quality characteristics,
measurement and evaluation of service quality is difficult,
rather defining the measurement unit itself is problematic
• Many factors influence the behavioral aspects and are
outside the influence of the company and they cannot be
predicted and may cause large performance variation
• Eg. Family life, mental outlook, unforeseen personal events
affect employee behaviour
• To counteract these performance variations in human
behavior, procedures that generate representative statistics
of performance can be devised

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Measuring service quality – contd..
• Randomly choosing samples of performance from the time
interval under consideration is one way to eliminate the bias
• In situation where we know that behavioral patterns vary
greatly based on the time period (for instance, if error rates
are high in the first and eighth hours of an 8 hour work per
day), we can select sampling plan that adequately reflect this
(stratified sampling)
• Another difficulty is that significant difference exists
between individuals.
• Thus, even though the scheme of stratified sampling is used
to select appropriate samples that reflect the performance of
an individual, it is not obvious whether this same scheme can
be collectively applied to group of individuals
• Individuals vary in their peak performance periods, as
people work best in early morning and others at night and
sampling plan can be designed to reflect them

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Techniques for Evaluating Service
Quality
• In the service sector, ergonomic, anthropometric, and
behavioral characteristics are important as are the physical
characteristics of the service systems and timeliness with
which the service is provided
• Descriptive statistics that provide numerical measures and
the corresponding graphical methods can be used to
describe distributions of service quality characteristics and
their summary measures
• Eg. Distribution of waiting time before seen by physician can
be shown by frequency histogram and trend chart to find
busy time
• Understanding variability in service quality characteristics is
important to the control and improvement of service quality
• In addition to variation due to equipment, process and
environment, performance variation is also due to person to
person, project to project variation etc.
• Use of Control charts are used to monitor service processes
and to determine status of statistical control
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Techniques for Evaluating Service
Quality – contd..
• Variable control chart are used to measure
quantifiable characteristics like time to serve a
customer in a restaurant, temperature maintained in
a plane etc.
• Attribute control chart are used to service
nonconformity characteristics like proportion of
billing errors, while ‘c’ and ‘u’ charts are applied to
service nonconformity, facility-related and behavioral
characteristics
• Sampling techniques in service operations
– 100% sampling
– Convenience sampling
– Judgment sampling
– Probability sampling
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Techniques for Evaluating Service
Quality – contd..
• 100% sampling
– Used when the cost of external errors or nonconformities is high
– Cost of sampling and inspection is high, but better than a
nonconformity found by a customer
• Convenience sampling
– Samples are chosen by the ease of drawing them and are
influenced by the subjectivity of the individual
– Eg. Selecting a thin file or selecting the top file during audit
• Judgment sampling
– Samples are chosen based on expert opinion
– Can also create bias and hence should be cautious in making
statistical inferences
• Probability sampling
– Has a statistical basis and is the most preferable
– Each item has an equal chance of being selected and done using
random number tables 60
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A model for service quality
• Key concepts
– Customer satisfaction is a function of the perceived quality
of service, which is a measure of how actual quality
compares to expected quality.
– External and Internal factors affect customer perceptions of
quality
– External factors
• Are not directly under the control of a service organization
• Includes the social values and lifestyles of customers,
knowledge of service, and the services offered by the
competitors
– Internal factors
• Are directly under the control of service organization
• Includes the image management, client management and
service delivery system

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A model for service quality – contd..

• Internal factors – contd..

– Image Management
• Is central to retaining and attracting new customers
• Corporate culture, products and services delivered, market
share etc, impact the reputation
• Advertisement, Annual company reports, quarterly sales
report are some techniques for image management
– Client Management
• Is important for improving the service and to meet the
changing customer needs
• Interviews, polls, surveys and making changes in the facilities
and service provided to meet these needs facilitate retaining
and expanding customer base
– Service delivery management
• Involves creating a corporate culture that motivate employees
and depends on
• Quality assurance philosophy, channels of open management,
customer participation, employee attitude etc.

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A model for service quality – contd..
• Components of service
– Core service and peripheral service and the benefits are
both tangible and intangible
– Eg. For a travel agency providing bus service
• Core service is transport of people between cities
• Peripheral service are comfort and safety of the bus stations,
meal services, pick up and drop etc.
– Peripheral service play a major role in influencing the
customer to select one company over another
• Factors involved in service quality
– Timeliness of the service, Adequacy of the service, price of
the service
– Evidence of good service spread through mouth
– Delivery of service must change with customer expectations

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Applications
• Discussion is about application of quality control and
improvement techniques in the service sector
• Different applications discussed are
– Administrative operations
– Banking
– Education
– Food industry
– Federal, state and local government
– Health care
– Insurance
– Public utilities
– Transportation

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Applications – contd..
• Education
– Amount of knowledge retained is a function of the individual
receiving the service and the service delivery process
– Controlling quality in education is unique because it involves
transformation of human qualities and values into learning
and retaining knowledge
– Behavioral characteristics
• A major influence on quality is the competency and behavioral
characteristics of the teachers
• Knowledge of their subject is a must, but is not enough and
delivery process is crucial
• Enthusiasm and the ability to stimulate interest and curiosity in
students are traits of a good teacher
• There are not easily quantified, rather they are subjective
• Other measures of teacher quality can be technical background,
certification and recognition by other professional associations,
research and publication in the area of expertise etc.
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Applications – contd..
• Education – contd..
– Facility related characteristics
• Science and technology requires current laboratory facility and
equipment
• An adequate library with holding of books and periodicals
complements the delivery process
• Modern computer facilities are especially pertinent today
– Timeliness characteristics
• Proper scheduling of classes, tests, assignments etc.
• Lead time for release of grade sheets, degree certificates
• Proper completion of syllabus, and returning of graded answer
books etc.
– Service nonconformity characteristics
• Proportion of students passing the board exams or in a class, No.
of complaints about the library, or lab facilities, No. of billing
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Applications – contd..
• Education – contd..
– The model
• Customers in educational model has conflicting objectives
• Parents want quality education at lower costs
• Employers want graduates exposed to cutting-edge technology
• Board of trustees want to minimize the operational expenditure
of the university
• Others include tax payers, alumni, etc.
• Students are of course customers, but also acts as co-producers
• They play a significant role in determining the quality of end
product through the degree and intensity of their effort and
motivation
• Students are considered as “work-in-process” inventory
• Finished product is the graduate, while the vendor is the high
schools and junior colleges
• Barriers in the system are due to communication between
departments, schools and colleges and flow of information is
curtailed, which prevents the improvement of quality of service
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Applications – contd..

• Education – contd..
– Role of quality
• In education, it is possible to achieve certain degree of
control can be achieved over the customers – students by
selectively choosing the students based on GPA/marks,
scores on standardized tests, Interview etc.
• This directly affects the degree of control on quality of
output
• Characteristics that measure the quality of output have
tangible and intangible components
• Tangible measures may be proportion of graduates
receiving job offers or average salary of graduates with job
offers etc.
• Intangible measure may be satisfaction and fulfillment that
comes from obtaining a quality education – not easily
quantifiable
• Potential of quality control and improvement methods are
pretty complex
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Applications – contd..
• Education – contd..
– Quality tools
• Evaluating the teaching performance by students – does it really
measure the ability and devotion of the teacher?
• Response of student may be motivated by his grade in the class!!
• Solution is carefully planned evaluation form – questionnaire
• Control chart for average score and range of the score can
indicate trends or special causes
• Control charts can also be used to evaluate facility and service
delivery characteristics
• Eg. No. of students unable to register for a certain course – c chart
helps in identifying a extra section for that course
• Methods of improvement could be handled by Pareto analysis and
cause-and-effect diagram
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Applications – contd..
• Administrative operations
– Involves a high volume of paperwork and hence opportunity for error
is high
– To improve the efficiency, a through analysis of the flow of paperwork
is necessary and should eliminate redundant steps
– Mistakes can also be reduced by redesign of form – where data are
entered, Eg., employee filling travel expense form
– Factors that affect are: Form design, Information required, sequence
of actions for processing the desired service function and the
individuals involved
– Form design should be simple and layout should be such that
individuals processing the information can conduct their operations
sequentially and also flipping of pages to be removed
– Personnel training influences efficiency and error rate
– Stability of this service functions can be checked through control
charts – ‘p’ charts and ‘c’ charts can be used
– Eg. No. of errors per 100 purchase orders, Proportion of bills that
have errors in mail order company
– Tools for improvement are Pareto analysis, cause and effect analysis,
experimental design
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Applications – contd..
• Banking
– Involves a high volume of activity and necessary to apply quality
control and improvement procedures
– Automation helped in performing tasks quickly and timely manner,
but risk of errors are high
– Behavioral characteristics like courtesy, communication have a major
impact on customer satisfaction
– Timeliness characteristics like waiting time, transaction processing
time also of concern to customer and processing time varies based on
nature of transaction
– Perfect accuracy is expected as far as service nonconformity
characteristics and hence 10% of bank employee work on detection
and correction of errors
– Attribute sampling plan and process control techniques play a major
role
– One important activity is use of MICR which has impact on the quality
of checks
– The requirements of these magnetic characters and the process
through which they are created are very stringent
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Applications – contd..
• Banking – contd..
– For example, the characters has to lie within certain regions of the
check area, the ink should be uniformly distributed, properties of ink
etc plays a major role
– If the reader cannot sense the characteristics, the check need to be
processed manually thereby increasing the processing cost
– Hence incoming quality of printed checks and encoding process by
which the check amount is entered requires careful control
– Sampling plans such as ANSI/ASQC Z1.4 can be used to measure the
quality of documents like checks, forms etc.
– Example
• Say MICR Checks are printed in a batch of 30000 each
• Table 10-8, sample size code is K assuming inspection level I
• Assume normal inspection and AQL of 0.4%, Table 10-9 gives sample
size is 125, with a rejection number of 2
– Process control methodology can be used for check processing and
other clerical operations – use of ‘p’ chart and ‘c’ chart
– A measure of process capability is obtained from the center line and
the control limits of the attribute charts
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Applications – contd..
• Food industry
– Several quality characteristics differentiate unit of food products and
impact product acceptability
– More clearly an attribute is defined and measured, the easier it is to
judge the quality of the food
– Some quality characteristics are readily measurable – proportion of
fat in milk, % of foreign material in a cereal, etc.
– Other characteristics are not as easily quantifiable – smell of a ripe
fruit, taste of a particular brand of strawberry etc.
– Requirements for the level of quality are set by customer –
wholesaler, distributor etc.
– Specifications and requirements are also influenced by federal
agencies like Food and Drug Administration, FPI, BIS etc.
– Total quality systems approach is required in which the level of
quality is monitored at each step from raw materials to processing to
packing and delivery
– For perishable foods - packaging, delivery and storage of the food
items are important
– Variety of quality attributes exists in food industry

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Applications – contd..
• Food industry – contd..
– A consumer may combine specific attributes to arrive at a single
measure of quality, generally referred to as sensory quality
– Sensory quality includes attributes as appearance, flavor and
kinesthetic associated with the product
– Appearance may be color, size, shape while flavor refers to smell and
taste. Kinesthetic or muscle sense includes attribute as texture and
viscosity
– Amount of force required to initiate a saliva flow is a measure of
these two attributes
– Requirements for the level of quality are set by customer –
wholesaler, distributor etc.
– These characteristics are not usually under strict government control
and depends on customer preference
– Another class of quality characteristic are quantitative in nature and
deals with amount of particular component in the product, Eg.
Proportion of protein, fat etc.
– These characteristics are easy to measure and control chart for mean
and range can be used

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Applications – contd..
• Food industry – contd..
– Certain quality characteristics cannot be readily judged by senses of
the consumer as they cant detect the presence of toxic items
– This is where the government plays an important role
– Tools that can be used are:
– Xbar and R charts for % of water, protein etc, while c-chart for the
micro organism or bacteria count while p chart can be used in
poultry and egg to monitor the egg shell shape and texture
• Federal, State and Local government
– Provides variety of services like recreational needs, housing,
environmental quality, small business, safety etc.
– Some government agencies provide service directly to consumer and
others are regulatory that deal with upkeep of desired quality levels
for the protection of consumer
– They generate numerous statistics and use frequency or relative
frequency histograms
– Eg. The income distribution families receiving food subsidies from
the government is obtained from relative frequency histogram
– Trend charts can be used to find the total amount allocated by the
government in budget preparation
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Applications – contd..
• Federal, State and Local government – contd..
– Opportunities to use control charts and sampling
techniques are wide ranging
– Eg. Income tax: to determine whether tax returns to be
audited or the ratio of adjusted gross income to taxable
income can be monitored using p-chart
– In case of agriculture department, proportion of insect-
infested cocoa beans and the proportion of moldy wheat
can be monitored through p-chart in addition to know
about no. of errors in misclassification of a family,
miscounting etc can be monitored through c-chart
– For a environmental protection agency, if certain
standards are mandated by law, the degree of
conformance to those standards can be done using
process capability analysis
– Level of pesticide in the mineral water can be monitored
with Xbar and R charts
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Applications – contd..
• Health care
– Provision of healthcare services is a national concern
– Consumer also influences the level of quality and also other groups
like Health department is highly influential in setting guidelines for
quality health care
– Unusual circumstances exist in health care. Patients are not always in
a position to judge the technical competency of the service provided
– Neither the administrators also, but only peer reviews by physician
can judge the quality
– In other services, consumer pays for the service rendered, while in
health care its not the case
– Federal government assists certain segments of the population
through Medicare / Medicaid programs
– Program guidelines which limit the maximum amount that may be
paid affect the quality and profitability of services
– Healthcare executives set service-level policies based on providing
adequate service at a reasonable price and plan their execution

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Applications – contd..
• Health care – contd..
– Another unusual feature is the organizational structure of hospital
administration
– Governing board and administrative officers are separate from the
medical staff
– In private hospitals, board of trustees may be the owners or
representative of the owners and not physician, while in pubic
hospitals, board members are selected from local citizenry, but may
have professional expertise, contributing to effective management of
hospital
– Executive policies set by board are carried out hospital
administration
– Physicians too have authority and they mostly serve as consultants,
who have contracts to provide specific service like surgery
– These two administrative powers must act in harmony for total
quality system, but their objectives conflict
– Best health care is not always profitable as government has used cost
cutting measures such as ‘diagnosis related group’
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Applications – contd..
• Health care – contd..
– In this system, a patient is classified into a DRG based on the
diagnosis and other characteristics like age, length of stay in the
hospital, surgical procedures etc.
– DRG then defines the maximum amount for which hospitals will be
reimbursed by the federal government, which has direct impact on
the quality of service
– Third party insurers also have an indirect impact on the quality of
service, as patients can go to hospitals approved by the insurer
– Depending on plans, insurers also control patient’s choice of
physicians
– To summarize, hospitals are under extreme pressure to cut costs and
yet give high quality service
– Hence hospitals must come up with effective quality control and
improvement measures for both service and cost
– An error free environment is the objective
– Patients demand better levels of service – clean rooms, home like
atmosphere etc.
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Applications – contd..
◼ Health care – Quality characteristics and methods of control
◼ Pareto chart and cause and effect diagram is used for quality
improvement techniques reducing waiting time, admit time etc.
• Blood pressure, pulse rate etc. • Run chart
• Time to obtain an appointment
• Response time of ambulances
• Admit time in emergency
• Xbar and R charts
room services
• No. of adverse comments per
week on nurse’s performance
• No. of errors in blood tests per
100 samples • ‘c’ chart
• Proportion of cases with
inaccurate diagnosis
• Proportion of tests performed
incorrectly
• ‘p’ chart
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Applications – contd..
• Insurance
– Consumer needs insurance for protection from accidents, hazards,
and casualties
– Personal insurance:- insurance for home, automobile, life (medical
insurance) while Group insurance:- Medical insurance to employees
of an organization
– Organizations also purchase insurance from other agencies to
provide their customers a sense of security
– In these cases, service nonconformity quality characteristics are
critical and the goal is to have no errors
– It involves people and hence training and motivation are critical
– Important functions
• Data collection
• Inputting the data for calculation of casualty probabilities
• Estimating payoffs
• Underwriting policies
• Processing claims etc. which requires human operations and
interactions
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Applications – contd..
• Insurance – contd..
– Timeliness characteristics like correcting a complaint or error,
processing a claim or obtaining damage appraisals from
adjusters should be performed within time limit
– Objective of insurance seller
• Increasing profits is the primary concern here
• Pareto analysis helps to identify vital characteristics of improving
profit
• Cause and effect diagram helps to identify the focus areas
• Cutting operations costs and avoid errors through well
documented procedures (Documentation
• Sellers are interested in reducing risks to their own company by
specifying limitations and exclusions in policies
• But this conflicts with the buyers objective of obtaining
protection against all types of risk
– Statistical techniques are widely used: Premiums are set based
on historical data, sampling methods are used to obtain data
– They are used to estimate and analyze the probability of fire,
accident, amount of loss etc.
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Applications – contd..
• Insurance – contd..
– Control of sampling and non-sampling errors are vital to the
accuracy of the estimation process
– Generally random sampling is used along with stratified
sampling and cluster sampling techniques
– Non sampling errors include incorrect data transcription,
inaccurate data input to models used for estimation purposes,
use of inappropriate or outdated models for estimation, faulty
computer programming etc.
– Several control charts can also be used:
• P-chart monitor the proportion of unacceptable documents,
proportion of claims not processed or paid etc.
• C- chart can be used to monitor no. of incorrect entries per 100
documents and no. of underwriters per 500 customer accounts
• Xbar and R chart could apply to characteristics as processing time
for claims and the amount paid by the company for policies in
similar category etc.
– Run chart can be used to track the total amount paid on a
monthly basis
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Applications – contd..
• Personal services
– Providers deal with individual customers on a frequent basis
– Eg. Beauty shops, hotels and motels, laundry, travel agency etc.
– Providers rely heavily on repeat business, and hence should know the
characteristics and attributes that satisfy the customers as well those
that make them hate the service
– Individuals taste and preference vary and hence businesses try to
incorporate flexibility in the design of services
– Eg. Hotel industry, some customer prefer indoor swimming pool,
others may be interested in snack bar while some would like
washbasin to be outside while some inside
– There are 2 groups of factors – those cause customer satisfaction and
those cause customer dissatisfaction
– Dissatisfied customers do not come back and also spread the word
– Reputation is everything and hence customer feedback is important,
which should be obtained by providing incentives
– Facility related quality characteristics that cause service
nonconformities fall in the customer dissatisfaction category
– Eg. Dirty carpet in a hotel room, inadequate temp. control in a saloon
etc.
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Applications – contd..
• Personal services – contd..
– Eliminating causes of customer dissatisfaction should be 1st step but it is
not enough and other factors that influence the perceived quality level to
exceed expectations is most important
– Eg. A hair dresser providing a head massage after his basic service, while
a beauty parlor providing a free mehendi design
– This added touch may lead the customers feel that they have obtained
more for their money’s worth
– Such customers act as a best source of advertisement for business and
spread the word making way for repeat business as well new customers
– Factors that cause customer satisfaction fall in human factors and
behavioral or timeliness category. Eg. Courteous behavior of the front
desk attendant in a hotel or a minimal waiting time to be seated in a
restaurant etc.
– Xbar and R chart can be used to control – time to register and check in at
a hotel, time for the suit to be dry cleaned etc.
– P-chart can be used for proportion of rooms available for occupancy or
proportion of on-time delivery of pizza etc.
– Demerit charts may be used to control the weighted quality points from
customer report cards

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Applications – contd..
• Public utilities
– include electric power gas and telephone etc.
– Characteristics
• Unique feature is that companies providing these facilities are
nearly monopolies or oligopolies.
• Are regulated by public service commissions that set the rate
structure for the service and not the customer directly
• Indirectly, though, consumer opinions have an impact on the
negotiated rate structure approved by the public service
commission.
• The standard for quality is imposed by the regulatory agencies.
• Customer expects continuous, uninterrupted service
• Utilities have a guaranteed customer base and hence operating
scenario is different from other service industries

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Applications – contd..
• Public utilities – contd..
– Recently competition in utility services is the talk of the day.
– Another feature of utilities is that consumer controls the
consumption and generates instantaneous demand, thereby lead
time for demand is zero and hence rely on forecasting
– Providing adequate service under these circumstances is both
science and art. The art is forecasting. (the predictive function).
– Mathematical models are developed to forecast demands.
– There is an art in deciding what model components to consider,
what measures of demand to use. What information from historical
demand to use, and how to weight them.
– These services cannot be stored. It is not feasible to over produce
and store power to meet peak demand at a later point in time while
gas can be stored

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Applications – contd..
• Public utilities – contd..
– Service nonconformity and facility related characteristics are
critical to electric power and gas industry
– All 4 categories are important for telephone industry
– Xbar and R chart can be used for variables such as the amount
purchased from outside sources, time to restore service after
failure, waiting time to get telephone installed etc.
– Trend chart track electrical power or gas consumption on a
monthly basis for a single customer or group of customer and help
identify patterns in consumption thereby helps in developing the
model for forecasting
– No. of errors in meter readings per 100 customers, No. of customer
complaints per month, No. of human errors per month in a power
plant can be monitored by c-chart

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Applications – contd..
• Transportation
– All 4 categories of quality characteristics play a major role
– Level of quality is largely influenced by customer and some
government agencies also have regulatory powers
– Eg, Civil Aeronautics Board in US receives customer complaints
regarding air travel and summarizes the findings to the airline
companies
– Airline companies can improve based on the remedial action for
the above complaints, but customers don’t write to CAB, rather
they switch airlines
– Other methods like rating forms should be used to find out the level
of customer satisfaction and expectation
– The response rate may be low and can be increased through free
gifts
– Important quality characteristics is safety of operations and the
fatal and nonfatal accidents should always have a goal of zero
– Prevention of accidents through equipment maintenance, checking
and training of personnel is a priority

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Applications – contd..
• Transportation – contd..
– Other quality characteristics deal with operation and delivery of
service
– Behavioral characteristics include courtesy of check-in agent, flight
attendants or the cab driver of taxi etc.
– No. of complaints received per month can be monitored by c-chart
– Timeliness characteristics include waiting time at the check-in
counter, waiting time to retrieve baggage, flight delay in arriving at
a destination etc.
– Xbar and R chart may be used to monitor the above measures
– Service nonconformity characteristics include no. of damaged or
lost bags per month, no. of flight cancellation etc which can be
monitored through np-chart
– No. of mistake in reservation per month, no. of airport security
problems per month are monitored through c-chart

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Thank You

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Quality Control Assurance &

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
 632

BITS Pilani
Pilani Campus

Process Capability

2
 633
Process Capability
Process capability represents the performance of a process in a
state of statistical control. It is determined by the total
variability that exists because of all common causes present in
the system.

BITS Pilani, Pilani Campus

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SPECIFICATION LIMITS AND
CONTROL LIMITS
• Tolerance limits are generally preferred in evaluating
manufacturing or service requirements, whereas specification
limits are more appropriate for categorizing materials,
products, or services in terms of their stated requirements.
• In general, tolerances are a subset of specifications.
• Remember that the control limits on an X bar-chart are a
measure of variability of the sample means. Specification
limits represent the acceptable bounds of variability for
individual items.

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example
The diameter of a part has to fit an assembly. The
specifications for the diameter are 5 ± 0.015 cm. The
samples taken from the process in control yield a sample
mean X of 4.99 cm and a sample standard deviation sigma
of 0.004 cm. Find the natural tolerance limits of the
process. Would you consider adjusting the process center?

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SPECIFICATIONS AND PROCESS CAPABILITY

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Process Capability
Process capability is the ability of the process to meet the
design specifications for a service or product.
Nominal value is a target for design specifications.
Tolerance is an allowance above or below the nominal
value.

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Process Capability

Nominal
value

Process distribution
Lower Upper
specification specification

20 25 30

Process is capable

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Process Capability

Nominal
value

Process distribution
Lower Upper
specification specification

20 25 30

Process is not capable

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Process Capability Ratio, Cp

Process capability ratio, Cp, is the tolerance width divided by 6 standard

deviations (process variability).

Upper specification - Lower specification

Cp =
6

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Example
The relative humidity in a greenhouse is expected to be
between 65 and 85 %. Random samples taken over a span
of one week yield the following values: 60,78,70,84,81, 80,
85, 60, 88, 75. Find and interpret the process capability
index.

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Process Capability Index, Cpk

Process Capability Index, Cpk, is an index that measures the potential

for a process to generate defective outputs relative to either upper
or lower specifications.

=x – Lower specification
Upper specification – x=
Cpk = Minimum of ,
3 3

We take the minimum of the two ratios because it gives the worst-
case situation.

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Intensive Care Lab
Example
The intensive care unit lab process has an average turnaround time
of 26.2 minutes and a standard deviation of 1.35 minutes.
The nominal value for this service is 25 minutes with an upper
specification limit of 30 minutes and a lower specification limit of 20
minutes.
The administrator of the lab wants to have three-sigma performance
for her lab. Is the lab process capable of this level of performance?

Upper specification = 30 minutes

Lower specification = 20 minutes
Average service = 26.2 minutes
 = 1.35 minutes

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Intensive Care Lab
Assessing Process Capability
Example Upper specification = 30 minutes
Lower specification = 20 minutes
Average service = 26.2 minutes
 = 1.35 minutes

= =
Cpk = Minimum of
x – Lower specification ,
Upper specification – x
3 3

26.2 – 20.0 30.0 – 26.2

Cpk = Minimum of
3(1.35) , 3(1.35)

Process
Cpk = Minimum of 1.53, 0.94 = 0.94 Capability
Index

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Intensive Care Lab
Assessing Process Capability
Example
Upper specification - Lower specification
Cp =
6
30 - 20
Cp = = 1.23 Process Capability Ratio
6(1.35)

Does not meet 3 (1.00 Cpk) target due to a shift in mean

(Note variability is ok since Cp is over 1.0)

Before Process Modification

Upper specification = 30.0 minutes Lower specification = 20.0 minutes
Average service = 26.2 minutes
 = 1.35 minutes Cpk = 0.94 Cp = 1.23

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Example
In an electrical circuit, the capacitance of a component
should be between 25 and 40 picofarads (pF). A sample of
25 components yields a mean of 30 pF and a standard
deviation of 3 pF. Calculate the process capability index
Cpk, and comment on the process performance. If the
process is not capable, what proportion of the product is
nonconforming, assuming a normal distribution of the
characteristic?

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23
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Example
In an assembly operation in a semiconductor manufacturing
company, the lower and upper specification limits are given by
4.8 and 5.2 seconds. A random sample of 25 completion times
gave a mean and standard deviation of 5.12 and 0.06 seconds,
respectively. Can we conclude that the Cp index for this operation
exceeds 1, so as to be considered acceptable by the customer?
Test at a significance level of 0.05.

24
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Example
In an assembly operation in a semiconductor manufacturing
company, the lower and upper specification limits are given by
4.8 and 5.2 seconds. A random sample of 25 completion times
gave a mean and standard deviation of 5.12 and 0.06 seconds,
respectively. Can we conclude that the Cp index for this operation
exceeds 1, so as to be considered acceptable by the customer?
Test at a significance level of 0.05.

26
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Example

A process in control has an estimated standard deviation of 2 mm.

The product produced by this process has specification limits of
120 ± 8 mm and a target value of 120 mm. Calculate the process
capability indices Cp, CPL, CPU, Cpk, Cpm, and Cpmk for the
process if the process mean shifts from 118 mm first to 122 mm
and then to 124 mm, but the process variability remains the same.

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Numericals
The amount of a preservative added to dairy products should not exceed certain
levels of 23 ± 6 mg (set by the Food and Drug Administration). Samples of size
5 of processed cheese produced the values of the average and range shown in
Table.
(a) Construct appropriate control charts and determine stability of the process.
(b) If the process is out of control, assuming remedial actions will be taken, estimate
the process mean and standard deviation.
(c) Assuming normality and a target value of 23 mg, determine the indices Cp, Cpk,
Cpm and Cpmk.
(d) What proportion of the dairy products meets government standards, assuming
normality?
(e) Find a 95% confidence interval for Cpk, assuming normality.
(f) Can we conclude that Cpk is less than 1? Use a = 0.05.

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Thank You

36
BITS Pilani, Pilani Campus
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Quality Control Assurance

Reliability

BITS Pilani Dr. Sudeep Kumar Pradhan, PhD.

Pilani Campus
668

2
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 669
Numericals
The amount of a preservative added to dairy products should not exceed certain
levels of 23 ± 6 mg (set by the Food and Drug Administration). Samples of size
5 of processed cheese produced the values of the average and range shown in
Table.
(a) Construct appropriate control charts and determine stability of the process.
(b) If the process is out of control, assuming remedial actions will be taken, estimate
the process mean and standard deviation.
(c) Assuming normality and a target value of 23 mg, determine the indices Cp, Cpk,
Cpm and Cpmk.
(d) What proportion of the dairy products meets government standards, assuming
normality?
(e) Find a 95% confidence interval for Cpk, assuming normality.
(f) Can we conclude that Cpk is less than 1? Use a = 0.05.

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Acceptance Sampling

5
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Definition

Let us take a sample of size n randomly from a batch. If the number

of defective articles in the sample is not greater than a certain number
c, then the batch is accepted; otherwise, it is rejected.

This is how we define acceptance sampling plan.

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Probability of Acceptance

Let us assume that the proportion of defective articles in the batch is

p. Then, when a single article is randomly chosen from a batch, the
probability that it will be defective is p. Further assume that the batch
size is sufficiently larger than the sample size n so that this
probability is the same for each article in the sample. Thus, the
probability of finding exactly r number of defective articles in a
sample of size n is
n!
P (r ) = p r (1 − p )
n−r

r !( n − r )!

Now the batch will be accepted if r ≤ c, i.e., if r=0 or 1 or 2 or….or c.

Then, according to the addition rule of probability, the probability of
accepting the batch is

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Operating Characteristic

r =c
n!
Pa ( p ) = P ( r = 0 ) + P ( r = 1) + P ( r = 2 ) + + P (r = c) =  p r (1 − p )
n−r

r = 0 r !( n − r ) !

Pa ( p )
This tells that once n and c are Ideal OC Curve

known, the probability of 1

accepting a batch depends
only on the proportion of
defectives in the batch. Thus, Practical OC Curve

Pa(p) is a function of p. This

function is known as
Operating Characteristic
(OC) of the sampling plan. p

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Construction of OC curve

we assume that the sample is chosen from an isolated lot of finite size.

we assume that a stream of lots is produced

If the lot size is large and the
by the process and that the lot size is large
probability of a nonconforming item is
(at least 10 times) compared to the sample
small
size.
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Construct an OC curve for a single sampling plan where the lot size is 2000,
the sample size is 50, and the acceptance number is 2.

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Acceptable Quality Level (AQL) p=p1

This represents the poorest level

of quality for the producer’s Pa ( p )
process that the consumer would
consider to be acceptable as 1 
process average. Ideally, the 1− 

producer should try to produce

lots of quality better than p1.
Assume there is a high
probability, say 1-, of accepting
a batch of quality p1. Then, the
probability of rejecting a batch of p
p1
quality p1 is , which is known as
producer’s risk.
When p = p1 then Pa ( p1 ) = 1 − .
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Lot Tolerance Proportion Defectives (LTPD) p=p2>p1

This represents the poorest level

of quality that the consumer is Pa ( p )
willing to accept in an individual
lot. Below this level, it is 1 
1− 
unacceptable to the consumer. In
spite of this, let there will be a
small chance (probability)  of
accepting such a bad batch by the

consumer,  is known as 
consumer’s risk. p
p1 p2
When p  p2 then Pa ( p2 ) = .
LTPD is also known as rejectable
quality level (RQL).
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Producer and consumer risk can also be demonstrated through the

OC curve. Suppose that our numerical definition of good quality
(indicated by the AQL) is 0.01 and that of poor quality (indicated by
the LQL) is 0.11. From the OC curve, the producer's risk alpha is 1 -
0.986 = 0.014. We consider batches that are 1 % nonconforming to
be good. If our sampling plan is used, such batches will be rejected
about 1.4% of the time. Batches that are 11% nonconforming, on
the other hand, will be accepted 8.8% of the time. The consumer's
risk is therefore 8.8%.

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Some Key points

• Number of acceptance will be change if

proportion of nonconformity varies

• Changing sample size causes drop in

acceptance probability

• probability of acceptance decreases for a

given lot quality as the acceptance number c
decreases.

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In a single sampling plan, the information obtained from one sample

is used to make a decision to accept or reject a lot. There are two
parameters in this sampling plan: the sample size n and the acceptance
number c.

A double sampling plan involves making a decision to accept the lot,

reject the lot, or take a second sample. If the inference from the first
sample is that the lot quality is quite good, the lot is accepted. If the
inference is poor lot quality, the lot is rejected. If the first sample
gives an inference of neither good nor poor quality, a second sample is
taken.

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Rectifying inspection as it applies to lots that are rejected

through sampling plans. Usually, such lots go through 100% inspection,
known as screening, where nonconforming items are replaced with
conforming ones.

The average outgoing quality (AOQ) is the average quality level of a series
of batches that leave the inspection station, assuming rectifying inspection,
after coming in for inspection at a certain quality level p.

Taking N as the lot size, n as the sample size, p as the incoming lot quality,
and Pa as the probability of accepting the lot using the given sampling plan,
the average, outgoing quality is given by

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Single sampling plar N = 2000, n = 50, c = 2. Suppose that the

incoming quality of batches is 2% nonconforming.

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The average outgoing quality limit (AOQL) is the maximum value, or peak, of the
AOQ curve. It represents the worst average quality that would leave the inspection
station, assuming rectification, regardless of the incoming lot quality.

If rectifying inspection is conducted for lots rejected by the sampling plan, another
evaluation measure is the average total inspection (ATI). The ATI represents the
average number of items inspected per lot.

For single sampling plans, the average total inspection per lot for lots with an
incoming quality level p is given by

For a double sampling plan, the ATI is given by

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 689

Construct the ATI curve for the sampling plan where N = 2000, n = 50, c = 2.
Consider the calculations for a given value of the lot quality p of 0.02. The probability of
accepting such a lot using the sampling plan is Pa = 0.920. The ATI for this value of p is

ATI = 50 + (1 - 0.920)(2000 - 50) = 206

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Find a single sampling plan that satisfies a producer's risk of 5% for lots that
are 1.5% nonconforming.

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 693

Find a single sampling plan that will satisfy a consumer's risk of 10% for
lots that are 8% nonconforming.

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 695

Find a single sampling plan that satisfies a producer's risk of 5% for lots
that are 1.8% nonconforming, and a consumer's risk of 10% for lots that are 9%
nonconforming.

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 698

Construct the Average Total Inspection (ATI) curve for the

sampling plan where N = 2000, n = 50, c = 2.
Given value of the lot quality p of 0.02. The probability of
accepting such a lot using the sampling plan is Pa = 0.920. The ATI
for this value of p is

ATI = 50 + (1 - 0.920)(2000 - 50) = 206

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Thank You

33
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