Table Of ContentD. H. Stamatis
SIX SIGM A
AND BEYOND
Design of
Experiments
ST. LUCIE PRESS
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Library of Congress Cataloging-in-Publication Data
Stamatis, D.H.
Six sigma and beyond: foundations of excellent performance / Dean H. Stamatis.
p. cm.—(Six Sigma and beyond series)
Includes bibliographical references.
ISBN 1-57444311-9 (v.1 : alk. paper)
1. Quality control—Statistical methods. 2. Production management—Statistical
methods. 3. Industrial management. I. Title. II. Series.
TS156 .S73 2001
658.5′62—dc21 2001041635
CIP
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Volume V: Design of Experiments: ISBN 157443143
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Dedication
To my father,
Χαραλαµπος
(Charalambos)
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Preface
Like the other volumes in this series, this book started in a small way. The intention
was to write a brief manual of sorts for those who would be doing some analytical
work in the pursuit of the six sigma methodology. And that is how it began. It soon
became obvious, however, that it did not seem possible to write a brief exposition
of design of experiments (DOE) that anyone pursuing DOE would be happy with.
So, here is another volume in the Six Sigma and Beyond series that concentrates
on the DOE aspects of analytical work. The choice was made to describe it in a
separate volume for three reasons.
First, we believe that DOE is a general data analytic system that is close to the
theoretical and inferential preoccupations and methods of scientific research. If
science’s main job is to explain natural phenomena by discovering and studying the
relations among variables, then DOE is a general and efficient method to help do this.
Second, DOE and its rationale is one of the most important components of
multivariate methods. Once DOE is mastered, all other methods become very easy
to comprehend.
Third, the strongest motivation for devoting a complete volume to this series is
that, at present, the issue of quality is in the midst of a conceptual and technical
revolution. The effects of this revolution are becoming apparent in the demands that
producers and customers make on each other.
The structure of this volume is fairly simple. There are two parts. Part I provides
the foundations of DOE in the classical sense, and Part II provides the Taguchi
approach to experimentation. The appendixes include a review of some of the
mathematical concepts, tables and several formulas for calculations, as well as
annotated computer commands for several software packages.
Specifically, each chapter will cover the following:
Chapter 1: The planning and managing of the “process” of experimentation
Chapter 2: Considerations of experimental designs
Chapter 3: Analysis of existing data
Chapter 4: Analysis of means (ANOM)
Chapter 5: Analysis of variance (ANOVA)
Chapter 6: Factorial designs
Chapter 7: Full factorials
Chapter 8: Model building—utility of models with experiments
Chapter 9: Fractional factorial designs
Chapter 10: Three-level designs
Chapter 11: Special topics in experimental design
Chapter 12: Introduction to Taguchi and parameter design
Chapter 13: A new attitude and approach
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Chapter 14: Orthogonal and linear graphs
Chapter 15: Parameter design
Chapter 16: Taguchi and ANOVA
Chapter 17: Case studies
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Acknowledgments
As in the past, so many individuals have helped either directly or indirectly in this
project that I am afraid I will forget to recognize someone. If I do, let me assure
you that it is not because I did not value your comments, suggestions and opinions.
Rather, it is because I am reaching the age which “senior moments” are to blame.
Seriously, I am indeed thankful for all of you who lifted me up with your suggestions
and encouraging words in the marathon to complete this series on six sigma.
Specifically, I want to thank Dr. B. Price from Wayne State University, who
introduced me to statistics, and Drs. R. Richey and D. Marcotte, also from Wayne
State University, who guided me through the rough spots in understanding not only
the beauty of statistics but also its power in application.
Special thanks go to Dr. R.K. Roy, who was kind enough to provide the com-
puterized case studies for Chapter 17 using the software Qualitek4; to Mr. L. Scott
for helping and running the DOE on Design Ease; and to Cary Stamatis for his
valuable help with the Excel spreadsheet in setting the OA and calculations for the
examples.
I want to also thank Dr. G. Taguchi for his comments on robust design during
our extensive meeting in New Delhi, India. I have tried to incorporate some of his
principles into this work. I want to also thank Mr. C. Taguchi for the fruitful
discussions on linear graphs and his insight into robust design. I will not forget our
lengthy discussions in Adelaide, Australia.
Also, special thanks go to American Supplier Institute for giving me permission
to use some of the orthogonal arrays and linear graphs used in Appendix A.
My thanks and appreciation go to my wife Carla, who has put up with me during
this project.
Thanks also go to my students at Central Michigan University for their sugges-
tions and comments for making this volume a better product. I am indebted also to
my seminar participants for their comments and suggestions on how to make the
material less “dry” and more “friendly.” I have tried to incorporate as many of their
suggestions as possible.
Finally, I want to thank the folks at CRC Press for the outstanding cooperation,
direction and help they have shown me during this project.
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About the Author
D.H. Stamatis, Ph.D., ASQC-Fellow, CQE, CMfgE, is currently president of
Contemporary Consultants in Southgate, Michigan. He received his B.S. and B.A.
degrees in marketing from Wayne State University, his Master’s degree from Central
Michigan University and his Ph.D. degree in instructional technology and busi-
ness/statistics from Wayne State University.
Dr. Stamatis is a certified quality engineer for the American Society of Quality
Control, a certified manufacturing engineer for the Society of Manufacturing Engi-
neers and a graduate of BSI’s ISO 9000 lead assessor training program.
He is a specialist in management consulting, organizational development and
quality science and has taught these subjects at Central Michigan University, the
University of Michigan and Florida Institute of Technology.
With more than 30 years of experience in management, quality training and
consulting, Dr. Stamatis has served and consulted for numerous industries in the
private and public sectors. His consulting extends across the United States, Southeast
Asia, Japan, China, India and Europe. He has written more than 60 articles and
presented many speeches at national and international conferences on quality. He is
a contributing author to several books and the sole author of 20 books. In addition,
he has performed more than 100 automotive-related audits and 25 pre-assessment
ISO 9000 audits, and has helped several companies attain certification. He is an
active member of the Detroit Engineering Society, the American Society for Training
and Development, the American Marketing Association, the American Research
Association and a fellow of the American Society for Quality Control.
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Contents
PART I Traditional Experimental Design
Introduction................................................................................................................3
Fundamental Concepts.....................................................................................3
Anatomy of an Experiment.............................................................................4
Factors.....................................................................................................5
Responses...............................................................................................5
Environmental Variables.........................................................................6
Principles of Conduct.......................................................................................7
Variation...........................................................................................................8
The Loss Function Concept...................................................................9
General Types of Designs....................................................................10
Logic of Hypothesis Testing................................................................12
Experimental Error.........................................................................................14
Expected Values....................................................................................15
Degrees of Freedom.......................................................................................17
Coding and Data Analysis.............................................................................18
Interaction.......................................................................................................20
Fixed, Random and Mixed Models...............................................................20
EMS Rules.....................................................................................................24
Example......................................................................................25
References......................................................................................................26
Selected Bibliography....................................................................................26
Chapter 1 Planning and Managing the Process
of Experiment.....................................................................................29
Plan.................................................................................................................29
Do...................................................................................................................31
Study...............................................................................................................32
Act..................................................................................................................32
Getting Started with Experimental Design....................................................33
Recognition and Statement of the Problem.........................................33
How Might the Team Select or Clarify the Problem?.........................33
Choosing Factors and Levels......................................................33
Response Variable Selection.......................................................35
Experimental Design Choice......................................................36
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Performing the Experiment........................................................37
Data Analysis..............................................................................37
Communicating the Results........................................................38
Chapter 2 Considerations of Experimental Designs..........................................41
Statistical Fundamentals................................................................................41
Variation and Variables.........................................................................41
Populations and Samples......................................................................42
Frequency Distributions.......................................................................42
Histograms and Frequency Curves......................................................42
Measures of Location.....................................................................................43
The Average or Mean.....................................................................................43
Median..................................................................................................44
Measures of Central Tendency......................................................................44
Measures of Dispersion.................................................................................44
Range....................................................................................................44
Variance................................................................................................46
Standard Deviation...............................................................................46
Shape of Distribution.....................................................................................46
The Normal Distribution......................................................................48
Characteristics of the Normal Distribution................................48
The Standardized Normal Distribution......................................50
Limitations of the Normal Distribution......................................52
The Distribution of Xbar............................................................52
Structure and Form of Experimental Designs...............................................54
Validity of Experimentation...........................................................................55
Design Types..................................................................................................56
Pre-Experimental Designs....................................................................56
True Experimental Designs..................................................................56
Quasi-Experimental Designs................................................................57
Interpretation of the Design Format....................................................58
References......................................................................................................65
Selected Bibliography....................................................................................66
Chapter 3 Analysis of Existing Data..................................................................69
Variance and Covariance................................................................................69
Simple Regression..........................................................................................71
A Fictitious Example............................................................................72
Test for Significance......................................................................................76
Multiple Regression.......................................................................................79
Regression Weights: b and b ...............................................................80
Calculation of the Squared Multiple Correlation Coefficient.......................83
Computer Programs.......................................................................................83
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References......................................................................................................84
Selected Bibliography....................................................................................84
Chapter 4 Analysis of Means.............................................................................87
Hypothesis Testing.........................................................................................87
Statistical Hypothesis/Null Hypothesis.........................................................87
Tests of Hypothesis..............................................................................87
Hypothesis Testing Steps.....................................................................89
Selected Test Statistics for Large Samples..........................................92
Selected Tests for Small Samples........................................................93
Sample Size Considerations...........................................................................93
Data Collection Schemes and Design of Experiment.........................94
Characteristics of a Well Planned Data Collection
or Experimental Program.....................................................................95
Analysis of Means (ANOM).........................................................................98
Sources of Variation Analysis (SVA)...........................................................100
Formulas for Sources of Variation.....................................................100
Other “Means” Tests....................................................................................104
Estimation Error and Confidence Intervals.................................................104
Confidence Interval Concept..............................................................105
Confidence Intervals for a Mean with Known Variance...................105
Confidence Intervals for Means When the Variance is Unknown....108
Confidence Intervals: Difference Between Two Means,
Variance Unknown.............................................................................112
Independent Samples...................................................................................112
Dependent Samples............................................................................113
Selected Bibliography..................................................................................114
Chapter 5 Analysis of Variance (ANOVA).......................................................117
Assumptions of Analysis of Variance..........................................................119
Common Designs for Experiments.............................................................120
Complete Randomization for
Background Conditions................................................................................122
The One-Way ANOVA................................................................................122
Two-Way ANOVA........................................................................................125
Randomized-Block Design for Background Conditions.............................127
Latin-Square Design for Background Conditions.......................................128
Other Designs...............................................................................................128
Types of ANOVA.........................................................................................129
Type I Problems.................................................................................129
Type II Problems................................................................................129
After ANOVA, What?..................................................................................130
Means Effects.....................................................................................130
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