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Chapter 2
Basic Tools for
Improving Quality
7 Basic Tools by Ishikawa
• Histogram • Pareto chart • Scatter plot • Control chart • Cheek sheet • Cause-and-effect diagram • Defect concentration diagram
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2.1 Histogram
• A histogram is a bar chart that shows the relative
frequencies of observations in each of several
classes.
• Rule for determining the number of classes: – “Power of 2 rule”: for n observations, we would use a
classes, where 2a-1 < n < 2a
– Roundup a = ln n / ln 2 (=ROUNDUP(LN(100)/LN(2), 0)
– a ~ 𝑛
Table 2.1 Example Data
24 45 36 59 48
31 70 85 62 87
81 57 68 60 78
27 25 37 56 65
42 50 53 39 57
51 51 40 34 63
58 66 54 46 43
82 55 55 75 66
21 32 49 69 79
54 23 50 68 64
53 64 74 30 65
60 58 52 61 44
32 52 40 59 49
83 84 35 76 67
55 56 41 59 47
64 52 28 76 71
33 33 56 51 69
51 43 72 73 45
41 45 61 42 46
58 58 63 52 62
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Histogram by Minitab
Histogram by Excel
0
5
10
15
20
25
30
35
29 39 49 59 69 79 89 More
Fre
qu
en
cy
Bin
Histogram
Bin Frequency
29 6
39 11
49 18
59 29
69 20
79 10
89 6
More 0
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2.2 Pareto Charts
• A Pareto chart is a bar graph that shows the
relative frequencies of observations in a
descending order. – draws its name from an Italian economist, Vilfredo
Pareto (1848–1923)
– J. M. Juran is credited with being the first person to
apply it to industrial problems
Table 2.3 Nonconformities and
Associated Monetary Losses
Lot # Date NI Scratches ML Broken
Tips ML Spots ML Others ML
2014 1 1000 22 $86 36 $160 6 $20 3 $6
2026 2 1000 23 88 39 170 3 10 2 3
2013 3 1000 30 100 41 178 8 24 4 7
2032 4 1000 18 79 37 164 14 35 5 9
2030 5 1000 20 81 28 146 15 38 3 6
2028 6 1000 21 83 39 170 10 28 6 10
2040 7 1000 19 80 33 152 9 25 2 3
2011 8 1000 12 66 29 150 5 18 7 12
2010 9 1000 14 69 31 149 8 24 6 10
2015 10 1000 16 74 30 148 7 22 9 16
2022 11 1000 12 66 22 136 4 16 5 9
2021 12 1000 13 68 27 145 11 27 2 3
2024 13 1000 21 83 35 158 13 31 1 1
2023 14 1000 22 86 29 150 10 26 6 10
2018 15 1000 19 80 23 138 6 20 7 12
Totals 15,000 282 1189 479 2314 129 364 68 117
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Pareto Chart on Nonconformities
Pareto Chart on Monetary Losses
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2.3 Scatter Plots
• A scatter plot is another simple graphical device
• The simplest type is a bivariate scatter plot, in
which two quantities are plotted.
• Scaling of the two axes is somewhat arbitrary
• A time sequence plot is a type of scatter plot in
that data on one variable are plotted against a
second variable, time.
• A probability plot is another type of scatter plot.
Table 2.4 Data for Quality
Improvement Program
Month No. of Employees
Trained (000) Cost of Training
(000)
January 12 23
February 10 19
March 10 27
April 11 20
May 9 15
June 6 10
July 8 14
August 5 8
September 6 9
October 3 5
November 2 3
December 2 4
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Table 2.4 Data for Quality
Improvement Program
Variations of Scatter Plots
• Use number or special symbols for duplicated data
points.
• Use “range frames”, instead of scales
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2.4 Control Charts
• A control chart is a time sequence plot with
“decision lines” added.
• These decision lines are used to try to determine
whether or not a process is in control. – Type I and II errors
Typical Control Chart
1 2 3 4 5 6 7 8 9 10
Sample number
Upper
control
limit
Central
Line
Lower
control
limit
1s
1s
2s
2s
=
0
1s
2
s
3s
95%
99.7
3%
-1s
-2
s
-3s
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2.5 Check Sheet
• A check sheet is a means of recording historical
data on causes of nonconformities or
nonconforming units. – The general idea is to record all pertinent information
relative to nonconformities and nonconforming units, so
that the sheets can facilitate process improvement.
– Such information might include notes on raw materials,
machine performance, or operator changes.
2.6 Cause-and-Effect Diagram
• The cause-and-effect diagram was introduced in
Japan in 1943 by Professor Kaoru Ishikawa of the
University of Tokyo. – For that reason it is sometimes called an Ishikawa
diagram; it has also been called a fishbone chart.
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Cause-and-Effect Diagram
2.7 Defect Concentration Diagram
• It is simply a schematic diagram that shows the
various sides of a unit of production, with the
positions where nonconformities occur pinpointed.
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Defect Concentration Diagram
2.8 The 7 Newer Tools
• Affinity Diagram
• Interrelationship Digraph
• Tree Diagram
• Prioritization Matrix
• Matrix Diagram
• Process Decision Program Chart
• Activity Network Diagram
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2.8.1 Affinity Diagram
• An affinity diagram is a set of ideas about a particular topic
that are grouped into clusters.
• The diagram is the end product of brainstorming that is
performed in a prescribed manner.
2.8.1 Affinity Diagram
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2.8.2 Interrelationship Digraph
• An interrelationship digraph is used for identifying and
exploring causal relationships between related ideas.
• This is a step beyond an affinity diagram, as an
interrelationship digraph is a figure with arrows indicating
relationships between ideas.
2.8.2 Interrelationship Digraph
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2.8.3 Tree Diagram
• A tree diagram is somewhat similar to a cause-and-effect
diagram in that a desired effect (e.g., reducing delivery
delays) can be shown pictorially as related to the factors
that can lead to the effect.
• A tree diagram will generally more closely resemble a
company organizational chart in appearance than a cause-
and-effect diagram.
• A tree diagram is a more structured display than either an
affinity diagram or an interrelationship digraph.
2.8.3 Tree Diagram
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2.8.4 Prioritization Matrix
• A prioritization matrix is a relative ranking of issues jobs,
objectives, products, and so on.
• The ranking is accomplished by comparing the components
pairwise so that a logical and consistent ranking results.
2.8.4 Prioritization Matrix
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2.8.5 Matrix Diagram
• A matrix diagram is used for showing relationships between
two or more sets of ideas, projects, and so on.
• The matrix can have one of several different forms.
• At least five forms have been used: – C-shaped
– L-shaped
– T-shaped
– X-shaped, and
– Y-shaped
2.8.5 Matrix Diagram
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2.8.6 Process Decision Program
Chart
• A process decision program chart is a listing of undesirable
events and corresponding contingency actions relative to
planned actions.
• It is used when there is considerable concern about the
possibility of negative unanticipated outcomes.
2.8.6 Process Decision Program
Chart
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2.8.7 Activity Network Diagram
• This is essentially a combination of two well-known
techniques: PERT (Program Evaluation and Review) and
CPM (Critical Path Method).
2.8.7 Activity Network Diagram
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