Department Of Metallurgical Engineering; NED UET 1
MY-409:
Metallurgical Plants
and Quality Control
• Course Instructor :Assistant Prof. Sajida Sheikh
• Department : Metallurgical Engineering
• Year: Final Year
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QUALITY CONTROL
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Quality Basics
Definition of Quality
Variables and Attributes
Quality Characteristic
Control charts
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LECTURE 3A
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Learning out comes
To Define cumulative and relative frequency
To construct a Histogram and Pareto chart
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STATISTICAL
QUALITY
CONTROL
Department Of Metallurgical Engineering; NED UET
Cumulative frequency
The cumulative frequency is calculated by adding
each frequency from a frequency distribution table
to the sum of its predecessors. The last value will
always be equal to the total for all observations,
since all frequencies will already have been added
to the previous total.
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Relative Frequency And Relative Cumulative
Frequency
A relative frequency is the fraction of times an event,
occurs.
Relative frequencies can be written as fractions, percents,
or decimals.
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CUMULATIVE FREQUENCY
FREQUENCY CUMULATIVE
FREQUENCY
6
8
9
19
12
5
TOTAL
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CUMULATIVE FREQUENCY
FREQUENCY CUMULATIVE
FREQUENCY
6
8
9
19
12
5
TOTAL
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RELATIVE FREQUENCY
FREQUENCY REL.FREQ. CUM.REL.FREQ
2
4
6
10
12
14
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A histogram is a graphical display of data
using bars of different heights. In
a histogram, each bar groups numbers into
ranges. Taller bars show that more data falls
in that range. A histogram displays the shape
and spread of continuous sample data.
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Histogram
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Class interval F
10-20 6
20-30 9
30-40 15
40-50 7
50-60 14
60-70 8
7--80 4
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Mineral water bottle consumption
Contry per citizen CF
Italy 183.6 183.6
Mexico 168.5 352.1
United Arab Emirates 163.5 515.6
Belgium and Luxembourg 148 663.6
France 141.6 805.2
Spain 136.7 941.9
Germany 124.9 1066.8
Lebanon 101.4 1168.2
Switzerland 99.6 1267.8
Cyprus 92 1359.8
United States 90.5 1450.3
Saudi Arabia 87.8 1538.1
Czech Republic 87.1 1625.2
Austria 82.1 1707.3
Portugal 80.3 1787.6
total sum 1787.6
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Portugal
Austria
Czech Republic
Saudi Arabia
United States
Cyprus
Switzerland
Lebanon Series1
Germany
Spain
France
Belgium and Luxembourg
United Arab Emirates
Mexico
Italy
0 50 100 150 200
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1 Obstruction without warning 7
2 Road Repair under construction 39
3 Loose surface Material 13
4 Soft or lower shoulder 20
5 Holes 8
6 Standing water 25
7 Worn Road Surface 6
8 Others 7
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S.no Problem_category Frequency
2 Road Repair under construction 39 39 0.312
6 Standing water 25 64 0.512
4 Soft or lower shoulder 20 84 0.672
3 Loose surface Material 13 97 0.776
5 Holes 8 105 0.84
1 Obstruction without warning 7 112 0.896
8 Others 7 119 0.952
7 Worn Road Surface 6 125 1
125
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S.no Problem_category FrequencyCF RF %
2 Road Repair under construction 39 39 0.312 31%
6 Standing water 25 64 0.512 51%
4 Soft or lower shoulder 20 84 0.672 67%
3 Loose surface Material 13 97 0.776 78%
5 Holes 8 105 0.84 84%
1 Obstruction without warning 7 112 0.896 90%
8 Others 7 119 0.952 95%
7 Worn Road Surface 6 125 1 100%
125
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40
35
30
25
20
Series1
15 Series2
10
0
Road Repair Standing Soft or Loose Holes Obstruction Others Worn Road
under water lower surface without Surface
construction shoulder Material warning
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45 120%
40
100%
35
30 80%
25
60%
Series1
20
Series2
15 40%
10
20%
5
0 0%
Road Repair Standing Soft or lower Loose surface Holes Obstruction Others Worn Road
under water shoulder Material without Surface
construction warning
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A Pareto chart is a special type of histogram
that represents the Pareto philosophy (the
80/20 rule) through displaying the events by
order of impact
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In the late 1800s, Italian economist Vilfredo Pareto
observed that 80 percent of the land in Italy was owned
by 20 percent of the population.
So was born the “Pareto Principle,” sometimes called
as the “80-20 rule”. It’s the idea that 80 percent of
value comes from 20 percent of input.
80 percent of a firm’s revenues come from 20 percent of
the business developers. Or 80 percent of earnings come
from 20 percent of your clients. It’s useful if you want to
maximize resources by focusing on highest yielding
tasks.
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A histogram may be used to represent the number of
students who scored between a certain score range, such as
0 to 20%, 20 to 40%, etc.
A Pareto chart may be used to analyze the causes of
customer dissatisfaction. The causes would be ordered by
frequency of occurring, allowing the team to focus on those
issues with the biggest impact on customer satisfaction.
A histogram is a bar graph that illustrates the frequency of
an event occurring using the height of the bar as an
indicator.
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