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

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 ~

Table 2.1 Example Data

24 45 36 59 4831 70 85 62 8781 57 68 60 7827 25 37 56 6542 50 53 39 5751 51 40 34 6358 66 54 46 4382 55 55 75 6621 32 49 69 7954 23 50 68 6453 64 74 30 6560 58 52 61 4432 52 40 59 4983 84 35 76 6755 56 41 59 4764 52 28 76 7133 33 56 51 6951 43 72 73 4541 45 61 42 4658 58 63 52 62

Histogram by Minitab

Histogram by Excel

29 39 49 59 69 79 89 More0

5

10

15

20

25

30

35

Histogram

Bin

Fre

qu

ency

Bin Frequency29 639 1149 1859 2969 2079 1089 6

More 0

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 MLBroken

TipsML 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 32013 3 1000 30 100 41 178 8 24 4 72032 4 1000 18 79 37 164 14 35 5 92030 5 1000 20 81 28 146 15 38 3 62028 6 1000 21 83 39 170 10 28 6 102040 7 1000 19 80 33 152 9 25 2 32011 8 1000 12 66 29 150 5 18 7 122010 9 1000 14 69 31 149 8 24 6 102015 10 1000 16 74 30 148 7 22 9 162022 11 1000 12 66 22 136 4 16 5 92021 12 1000 13 68 27 145 11 27 2 32024 13 1000 21 83 35 158 13 31 1 12023 14 1000 22 86 29 150 10 26 6 102018 15 1000 19 80 23 138 6 20 7 12

Totals 15,000 282 1189 479 2314 129 364 68 117

Pareto Chart on Nonconformities

Pareto Chart on Monetary Losses

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

MonthNo. of Employees

Trained (000)Cost of Training

(000)January 12 23February 10 19

March 10 27April 11 20May 9 15June 6 10July 8 14

August 5 8September 6 9

October 3 5November 2 3December 2 4

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

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 10Sample number

Uppercontrol

limit

CentralLine

Lowercontrol

limit

1s

1s

2s

2s

=0

12

3

95%

99.73%

-1-2

-3

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.

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.

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

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

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

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

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

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

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

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