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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