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Transcript of Basic Tools for Improving Qualityweb.eng.fiu.edu/leet/Quality_Eng/chap2_2012.pdf · 2.2 Pareto...

  • 1/31/2012

    1

    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

    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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    3

    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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    4

    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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    5

    Pareto Chart on Nonconformities

    Pareto Chart on Monetary Losses

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    6

    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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    7

    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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    9

    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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    14

    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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    17

    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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    18

    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