31-Jan-23

IPE 333: Quality Control and Management

Quality Control Basics, Descriptive

Statistics and Quality tools

Dr. M. Muhshin Aziz Khan

Professor
Department of IPE

Statistical Quality Control: Syllabus

IPE333 (3.00 Credits)
QUALITY CONTROL AND MANAGEMENT
Introduction to statistical quality control, SQC
Categories
Descriptive Statistics: Measure of accuracy, Measure Some Special Charts: Moving range chart,
of precision, shape of data distribution Exponentially weighted moving average chart,
Quality control tools: Pareto analysis, Cause-effect Cumulative sum charts for process mean and
diagram, Stratification, Check Sheets, Histogram, and variability.
Scatter diagram; Process Capability Analysis: Process variability,
Statistical Process Control: Process control, Salient Natural tolerance, Specification, Process capability,
features of process control, Sources of variations, Specification-Process capability relationships,
Theory behind process control, Process Control Process capability Indices and their interpretations;
Chart: Introduction, Basic components, Use, Basic Acceptance Sampling: Introduction, Advantage and
procedure, Interpretation of control chart, Errors in disadvantage of sampling, Producer and customer
making inference from control chart and its effect. risks, Operating characteristics (OC) curve:
Control Charts: General model, Suggested number of Construction, Effect of sample size and acceptance
data points, Sample size and its effect on control number on OC curve, Lot-by-lot attribute sampling
limit, Control Charts for Variables: Introduction, plan: Single sampling plans, Double sampling plans,
Control charts for mean and range, Control charts for Multiple sampling plans, Sequential sampling plan,
mean and standard deviation, Control Charts for Characterizing Sampling Plans: Average outgoing
Attribute: Control charts for fraction nonconforming, quality, Average total inspection, Average sample
Control charts for nonconformities, number;

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Statistical Quality Control: Syllabus

IPE333 (3.00 Credits)

QUALITY CONTROL AND MANAGEMENT
After the successful completion of this
part of the course, students will be able
 CO 3: explain various process
to:
capability indices and apply them to
 CO 1: identify the sources of determine whether the process is
variation and apply basic statistical capable of producing products of
quality control tools; desired quality;
 CO 2: Construct the control limits  CO 4: explain and design various
for both variable and attribute control sampling plans based on producers’
chart and apply these charts to check and customers’ risks and apply them
whether the process is in control or in lot sentencing.
not;

Statistical Quality Control: Basic Concept

❖ W. Edward Deming advocated to ❖ Statistical Quality Control
implement statistical quality
▪ A quality control system
management approach.
✔ It uses a set of statistical
❖ His philosophy behind this approach:
techniques to control the quality.
▪ All processes are vulnerable to loss of
✔ It uses the probability theory to
quality through variation: if levels of
variation are managed, they can be ▪ evaluate batch quality, and
decreased, and quality raised ▪ control the quality of processes
or products
❖ Statistical Quality Control ✔ It makes the inspection more
reliable and less costly.
❖ Quality Control
✔ It measures the performance
▪ Goal is to maintain a certain level of
indicator (either individual, group
Quality (not to improve the quality but
or departmental) calculated over
to hold the status quo).
time (hourly, daily, or weekly).
✔ A set of operational techniques and
▪ The timing and type of actions
activities used to maintain a certain
depends on whether the causes
level of Quality.
of variation are in control or not.

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Statistical Quality Control: Basic Concept

❖ Why SQC is so important!!??!

 In repetitive manufacture of a ✔ Special causes (changes in men,
product, even with refined machine, materials or tools, jigs
machinery, skilled operator, and and fixture and so on) resulting
selected material, variations are in a shift from the stable pattern
inevitable in the quality of units of variation.
produced due to interactions of
various entities.
 Statistical Quality Control
 Variation may be due to
✔ Assists in timely identification
✔ Common or random causes of
and elimination of the problem,
variation (as a result of normal
and
variation in material, method,
and so on that causes natural ✔ Hence, reduces variations in
variation in product or process process or product.
quality) resulting in stable
pattern (random pattern) of
variation.

Statistical Quality Control: Sources of Variation

 Variation exists in all processes.

 Variation can be categorized as:
 Common or Random causes of  Assignable causes of variation
variation ✔ Causes that can be identified
✔ Causes that cannot be and eliminated
identified. ▪ e.g. poor employee training,
✔ Unavoidable: inherent in the worn tool, machine needing
process. repair
✔ Normal variation in process ✔ Can be controlled by operator
variables such as material, but it needs attention of
environment, method and so management.
on.
✔ Can be reduced almost to zero
only through improvements in
the process variables.

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Statistical Quality Control: Categories

❖ Major Categories of SQC determine acceptance or

❑ Statistical quality control (SQC) rejection of the entire lot
is the term used to describe the based on the results.
set of statistical tools used by ▪ Does not help control or
quality professionals estimate the quality of
❑ SQC encompasses three broad lots.
categories of: ▪ Passes a judgment on lots.
▪ Descriptive statistics
✔ used to describe and ▪ Statistical process control
analyze quality (SPC)
characteristics and their ✔ Statistical evaluation of the
relationships. output of a process.
✔ mean, standard deviation, ▪ Quality characteristics are
and range. measured and charted.
▪ Acceptance sampling ▪ Helpful in identifying in-
✔ Used to randomly inspect a process variations.
batch of products to

Statistical Quality Control: Descriptive Statistics

 Measure of accuracy (centering)

✔ Describes/indicates ✔ Mean is used when:
▪ the central position of the ▪ The distribution is symmetrical
series of data. or not appreciably skewed to
✔ A measure of the central value is the right (positive) or to the
necessary to estimate the left (negative);
accuracy or centering of a ▪ Additional statistics e.g.
process. measure of dispersion, control
chart etc. are to be computed;
❖ The Mean ▪ A stable value is needed for
✔ The most commonly used inferential statistics.
measure of central tendency.
✔ Simply the average of a set of
data

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Statistical Quality Control: Descriptive Statistics

❖ Measure of accuracy (centering) ▪ a distribution has extreme

 The Median values, the mean will be
✔ Median becomes an effective adversely affected while the
measure of central tendency when median will remain unchanged.
the distribution is positively or
negatively skewed.  The Mode
✔ It is simply the value of middle ✔ Value that repeat itself maximum
item if the data are arranged in number of times in the series.
ascending or descending order.
▪ When the number in the series is  Mode is used:
odd, it is midpoint of the values. ▪ to describe the most typical
▪ When the number of the series is value of a distribution.
even, it lies between two middle ▪ when a quick and approximate
numbers. measure of central tendency is
needed;
 Median is used when:
▪ an exact midpoint of the
distribution is needed.

Basic Statistics and Probability: Descriptive Statistics

❖ Measure of Precision or Spread
 Describes how the data are spread  Becomes effective when the number
out or scattered on each side of the of data is too small or too scattered.
central value.  Accuracy of the range decreases as
 Commonly used methods: range, sample size increases.
variance, standard deviation,  Range is suggested to use when the
coefficient of variation etc. data is limited to a maximum of 10
observations.
❖ Range  Relatively unstable measure of
 The simplest possible measure of precision.
dispersion and provides the total  Influenced by change in the highest
spread of the data. or lowest value.
 Difference between largest and  Remains the same despite changes
smallest observations in a data set. in values lying between two
extreme values.

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Basic Statistics and Probability: Descriptive Statistics

❖ Measure of Precision or Spread
Standard Deviation
 Measures deviation of the values from  A more robust measure of variability.
the mean.  Uses all the data for its calculation.
 It is used when more precise  Used when more precise measure is
measure is needed. needed.
 Small value indicates that data
points are closely clustered around
the mean.
 Large value indicates that they are
widely scattered around the mean.

 x 
n
2
i X
σ i 1

n 1

Statistical Quality Control: Descriptive Statistics

❖Shape of Distribution of Data

▪ A measure of distribution of data. We see it only when normal
✔ Symmetric variation is present in the data.
✔ Skewed
❖Symmetric Distribution:
▪ Symmetric around the mean.
▪ For a symmetric distribution:
✔ Mean is approximately equal to
the median.
✔ Left and right tails are equally
balanced.
▪ They have about the same
length.
✔ Median (second quartile) lies in
the middle of its first and third
quartiles.

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Statistical Quality Control: Descriptive Statistics

❖Skewed Distribution:
▪ Not symmetric around the
mean.
▪ For a right skewed
distribution:
✔Mean is typically greater
than the median.
✔Tail of the distribution on
the right hand (positive)
side is longer than on the
left hand side.
✔Median is closer to the first
quartile than the third
quartile.

Statistical Quality Control: Descriptive Statistics

❖Skewed Distribution:
▪ For a left skewed
distribution:
✔Median is typically greater
than the mean.
✔Tail of the distribution on
the left hand (negative) side
is longer than on the right Is the following data set
hand side. symmetric, skewed right or
✔Median is closer to the third skewed left? Explain your
quartile than the first reasoning.
quartile. 27 28 30 32 34 38 41 42 43 44
46 53 56 62

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Statistical Quality Control: Quality Control Tools

❖Cause Effect Diagram

▪ Also called: Fishbone  Identifies many possible
diagram/ Ishikawa diagram. causes for an effect.
 Organizes the logical  Also immediately
relationships between the classifies/sorts ideas into
inputs and stages of a useful categories.
process and an output. ✔ It can be used to
✔Output is structure a brainstorming
 the successful session.
completion of the
process task. ❖ When to use
 a quality problem that ▪ To identify the possible
we hope to solve. causes of a problem.

Statistical Quality Control: Quality Control Tools

❖Cause Effect Diagram

❖Procedure
▪ Materials needed: sticky notes or ▪ Use an affinity diagram,
cards, marking pens, large work ✔ group the causes and
surface (wall, table, floor),
✔ determine headings.
flipchart paper.
▪ Use the headings as main
▪ Agree on the problem statement
causes,
(Effect).
✔ arrange the ideas on a
▪ Brainstorm all possible causes,
fishbone drawn on flipchart
using any brainstorming technique.
paper.
(recall: brainstorming and NGT).
▪ Draw the fishbone and explore
✔ Record on sticky notes or cards.
for additional ideas especially
✔ Continue until the group has run where there are few ideas on the
out of ideas. fishbone.

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Statistical Quality Control: Quality Control Tools

❖Cause Effect Diagram
❖How to draw a fishbone diagram
▪ Materials needed: flipchart or ▪ Write sub-causes as a branch
whiteboard, marking pens. branching off the main causes.
▪ Agree on the problem statement
(Effect).
⮚ Write it at the center right of
the flipchart or whiteboard.
⮚ Draw a box around it; and
⮚ Draw a horizontal arrow
running to it.
▪ Write the main of causes
(obtained from affinity diagram)
as branches from the main
arrow.

Statistical Quality Control: Quality Control Tools

❖Pareto Analysis ❖We can apply the 80/20 rule to

▪ Also called the vital few and the almost anything
trivial many. ⮚ 80% of customer complaints
▪ A statistical technique in decision- arise from 20% of your products
making. and services.
⮚ Used to select a few key causes ⮚ 80% of delays in the schedule
that produce a vast majority of result from 20% of the possible
the problem. causes of the delays.
⮚ Uses the Pareto Principle (also ⮚ 20% of your products and
known as the 80/20 rule). services account for 80% of your
▪ 20 percent of causes generate profit.
80 percent of results. ⮚ 20% of your sales force
▪ By doing 20% of the work you produces 80% of your company
can generate 80% of the revenues.
benefit of doing the entire job. ⮚ 20% of a systems defects cause
80% of its problems.

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Statistical Quality Control: Quality Control Tools

❖When to Use Pareto Analysis

▪ When we need to analyze data ⮚ How often it occurs, e.g.,
about the frequency of problems frequency (e.g., utilization,
or causes in a process. complications, errors)
▪ When there are many problems or ⮚ How long it takes, e.g., time
causes and we want to focus on ⮚ How many resources it uses,
the most significant. e.g., cost
▪ When we need to communicate ▪ Create a vertical bar chart with
with others about our data. causes on the x-axis and
count/time/cost percentage on the
❖How to Use the Tool/Pareto Analysis y-axis.
Step by Step ▪ Arrange the bar chart in
▪ Develop a list of problems, items descending order of cause
or causes to be compared. importance, i.e., the cause with
▪ Develop a standard measure for the highest count percentage first.
comparing the items.

Statistical Quality Control: Quality Control Tools

❖How to Use the Tool/Pareto Analysis

Step by Step
▪ Calculate the cumulative ⮚ This point on the x-axis separates
count/time/cost percentage for each the important causes on the left
cause in descending order. (vital few) from the less important
▪ Create a second y-axis with in causes on the right (trivial many).
increments of 10 from 0% to 100%.
▪ Plot the cumulative count/time/cost
percentage of each cause on the x-
axis.
▪ Join the points to form a curve.
▪ Draw a line at 80% on the y-axis
running parallel to the x-axis.
▪ Then drop the line at the point of
intersection with the curve on the x-
axis.

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Statistical Quality Control: Quality Control Tools

❖ Histogram
▪ A bar graph that represents the ▪ If data entries are integers,
frequency distribution of a data set. ✔ To find the lower class boundaries,
▪ It help us to identify patterns of a subtract 0.5 from each lower limit.
data set easily. ✔ To find the upper class boundaries,
▪ It has the following properties: add 0.5 to each upper limit.
✔ The horizontal scale is quantitative ▪ The upper boundary of a class will
and measures the data values. equal the lower boundary of the
✔ The vertical scale measures the next higher class.
frequencies of the classes.
✔ Consecutive bars must touch.
▪ Bars must begin and end at class
boundaries instead of class limits.
▪ Class boundaries are the numbers
that separate classes without
forming gaps between them.

Statistical Quality Control: Quality Control Tools

❑ Frequency Histogram
❖ Example: The following sample data set
lists the prices (in dollars) of 30 portable
global positioning system (GPS)
navigators.
▪ Construct a histogram for the frequency
distribution.

✔ Find the class boundaries.

✔ Choose appropriate horizontal and
vertical scales.
✔ Use the frequency distribution to find
the height of each bar. Interpretation: More than half of the
✔ Describe any patterns. GPS navigators are priced below
$226.50.

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