Table Of ContentA PRIMER ON THE
TAGUCHI
METHOD
SECOND EDITION
Ranjit K. Roy
Copyright © 2010 Society of Manufacturing Engineers
987654321
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Preface
My exposure to the Taguchi methods began in the early 1980s
when I was employed with General Motors Corporation at its
Technical Center in Warren, Mich. At that time, manufacturing
industries as a whole in the Western world, in particular the auto-
motive industry, were starving for practical techniques to improve
quality and reliability. Having perfected his concepts in Japan and
a few places elsewhere during the late 1940s, Dr. Taguchi intro-
duced his quality improvement methods to the United States in
the early 80s. His focus was to optimize performance and make
design robust by use of the statistical technique known as design
of experiments (DOE), which was originally introduced by R.A.
Fisher in England in the 1920s.
To make the technique more effective and easy to use, Dr. Ta-
guchi recommended a standardized version of DOE and devised
ways for practical application and analysis of results. For quality
improvement champions, this was an attractive tool. Manufac-
turing organizations of all kinds readily learned and applied the
methods to benefit the design of numerous products and processes.
Remarkable progress was made by many throughout the 1980s.
For automotive manufacturers, the process of catching up in qual-
ity with foreign manufacturers was launched.
Those of us who were actively promoting the quality improve-
ment effort within our organizations and had the responsibilities
to implement the technique were challenged to find better ways
to teach and apply the technique. In the early 80s, there were
only a handful of books and hardly any documented application
examples. The primary reference in the market was Dr. Taguchi’s
ix
x APrimerontheTaguchiMethod
own book, System of Experimental Design (Quality Resources,
1987). That book and related training materials were my first
resources to explain the Taguchi technique to others in a simpler
form. A credit to the effectiveness and acceptance of the Taguchi
technique is that there now are more than a dozen textbooks and
thousands of published reports available to practitioners.
Following the overwhelming surge of interest in learning and
implementing the technique by manufacturing companies of all
kinds, the focus shifted in the mid 1990s. Introduction of general
and company-wide quality improvement disciplines such as ISO/
QS-9000 and Six Sigma unintentionally diminished the priority
and funding for activities that required special techniques. These
general quality systems, which were value-added and beneficial
to most businesses, also required use of statistical techniques like
DOE, Taguchi methods, statistical process control (SPC), and so
on, but for most companies these were among the last few things
to do and easily postponed.
The turn of the 21st century saw the beginning of a downturn
in the economy. Auto companies were downsizing; most didn’t
have much money to spend on training as business survival over-
shadowed quality improvement concerns. Now as the economy is
starting to show signs of recovery, manufacturing companies can
refocus on implementing statistical techniques.
While teaching, training, and practicing in the 1990s, I found
greater demand for a reference on the application of the technique
rather than on the theory. Thus, the first edition of A Primer on
the Taguchi Method (Society of Manufacturing Engineers, 1990)
introduced basic concepts through application examples and case
studies. This led to my second book, Design of Experiments Using
the Taguchi Approach (John Wiley & Sons, 2001), which covered
a minimal amount of theory while describing many more applica-
tions in detail. Both books were received favorably by readers in
academia, business, and industry.
HIGHLIGHTS OF THE SECOND EDITION
The following are highlights of additions and changes in this
second edition of the Primer:
Preface xi
(cid:127) Chapters 1–4: Minor changes in clarity and in the defini-
tions of quality
(cid:127) Chapter 5: Taguchi robust design strategy and the two-step
optimization technique added
(cid:127) Chapter 6: Advanced analysis of multiple-sample results
described
(cid:127) Chapter 7: Relationship of the loss function to other per-
formance and capability statistics defined
(cid:127) Chapter 8: Comprehensive experiment planning discussions
included, and transformation to overall evaluation criteria
revised and expanded
(cid:127) Chapter 9: An example depicting current practices in ap-
plication to production problem solving added
ACKNOWLEDGMENTS
This book would not be in circulation today without the Society
of Manufacturing Engineers undertaking continued printing of the
first edition after the original publisher folded technical publish-
ing activities. For this second edition, I am indebted to Rosemary
Csizmadia of SME, who was relentless in her conviction of market
demand for the book even in difficult economic times. I would also
like to thank Ellen Kehoe of SME for her grasp of language and
insight into the technology in editing the manuscript.
I am grateful to my professional and business associates, Larry
Smith, Mike Comerford, Greg Adams, Larry Tracey, Dave White,
and Jay Chandra, for their trust in my ability to support their clients
seeking training and application of the Taguchi technique. I would
like to express my sincere thanks to Larry Smith, in particular, who
spent an extraordinary amount of time on a meticulous review, and
to Andrea Stamps, Kush Shah, Side Zhao, Fred Schenkelberg, and
Pradeep Kumar for their detailed and constructive suggestions.
Finally, I thank my wife, Krishna, who has put up with my
dedication to the life of an independent consultant, trainer, and
author for more than two decades.
Ranjit K. Roy
January 2010
Contents
Preface .......................................................................................................................... ix
Abbreviations and Symbols ........................................................................... xii
1 Quality Through Product and Process Optimization
BACKGROUND ..................................................................................................................... 1
DESIGN OF EXPERIMENTS—THE CONVENTIONAL APPROACH ......................................... 1
DESIGN OF EXPERIMENTS—THE TAGUCHI APPROACH ..................................................... 5
EXERCISES ..................................................................................................................... 6
2 Taguchi Approach to Quality and Cost Improvement
BACKGROUND ..................................................................................................................... 9
TAGUCHI PHILOSOPHY ...................................................................................................... 10
CONCEPT OF THE LOSS FUNCTION ................................................................................... 13
EXPERIMENT DESIGN STRATEGY ...................................................................................... 18
ANALYSIS OF RESULTS ...................................................................................................... 19
AREAS OF APPLICATION ................................................................................................... 21
THE NEW APPROACH—ITS APPEAL AND LIMITATIONS .................................................. 22
EXERCISES ................................................................................................................... 23
3 Measurement of Quality
THE QUALITY CHARACTERISTIC ........................................................................................ 25
VARIATION AS A QUALITY YARDSTICK .............................................................................. 26
COST OF VARIATION .......................................................................................................... 27
QUALITY AND VARIATION ................................................................................................. 27
THE QUALITY WE ARE AFTER ............................................................................................ 29
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TAGUCHI QUALITY STRATEGY ........................................................................................... 30
SELECTING DESIGN PARAMETERS FOR REDUCED VARIATION ......................................... 31
COMMON TERMINOLOGY .................................................................................................. 32
EXERCISES ................................................................................................................... 35
4 Attractions and Benefits of the Taguchi Method
THE NEW DISCIPLINE ........................................................................................................ 37
UP-FRONT THINKING ........................................................................................................ 39
EXPERIMENTAL EFFICIENCY .............................................................................................. 40
EFFECTIVE USE OF STATISTICAL PROCESS CONTROL ....................................................... 41
LONG-TERM BENEFITS ...................................................................................................... 41
QUANTIFYING COST BENEFITS—TAGUCHI LOSS FUNCTION .......................................... 41
SPECIFYING TOLERANCE LEVELS ...................................................................................... 47
EXERCISES ................................................................................................................... 48
5 Working Mechanics of the Taguchi Design of Experiments
FORMULAS FOR EXPERIMENT LAYOUT ............................................................................. 49
BASIC METHODOLOGY ...................................................................................................... 50
DESIGNING THE EXPERIMENT ........................................................................................... 53
DESIGNING WITH MORE THAN THREE VARIABLES ........................................................... 65
DESIGNS WITH INTERACTION ........................................................................................... 68
DESIGNS WITH MIXED FACTOR LEVELS ............................................................................ 85
DUMMY TREATMENT (COLUMN DEGRADING) ................................................................... 93
COMBINATION DESIGN ...................................................................................................... 98
DESIGNING EXPERIMENTS TO REDUCE VARIABILITY ..................................................... 103
ROBUST DESIGN STRATEGY ............................................................................................ 104
S/N RATIO—A SMARTER WAY TO ANALYZE MULTIPLE SAMPLE RESULTS ................... 107
TWO-STEP OPTIMIZATIONS ............................................................................................ 110
ROBUST DESIGNS AGAINST MULTIPLE NOISES .............................................................. 121
DESIGN AND ANALYSIS SUMMARY ................................................................................. 124
EXERCISES ................................................................................................................. 126
6 Analysis of Variance (ANOVA)
THE ROLE OF ANOVA ....................................................................................................... 129
ANOVA TERMS, NOTATIONS, AND DEVELOPMENT .......................................................... 129
Contents vii
ONE-WAY ANOVA ............................................................................................................. 135
ONE-FACTOR TWO-LEVEL EXPERIMENTS (ONE-WAY ANOVA) ........................................ 141
TWO-WAY ANOVA ............................................................................................................ 146
EXPERIMENTS WITH REPLICATIONS ............................................................................... 149
STANDARD ANALYSIS WITH SINGLE AND MULTIPLE RUNS ........................................... 154
APPLICATION OF S/N RATIO ........................................................................................... 172
EXERCISES ................................................................................................................. 182
7 Loss Function
DERIVATION OF LOSS FUNCTION .................................................................................... 185
AVERAGE LOSS FUNCTION FOR PRODUCT POPULATION ............................................... 189
APPLICATION OF LOSS FUNCTION CONCEPTS ............................................................... 189
LOOKS OF PERFORMANCE IMPROVEMENT ..................................................................... 196
EXERCISES ................................................................................................................. 202
8 Brainstorming—An Integral Part of the Taguchi Philosophy
THE NECESSITY OF BRAINSTORMING ............................................................................. 205
THE NATURE OF THE SESSION ........................................................................................ 206
TOPICS OF THE DISCUSSIONS ......................................................................................... 208
EXERCISES ................................................................................................................. 221
9 Examples of Taguchi Case Studies
APPLICATION BENCHMARKS ........................................................................................... 225
APPLICATION EXAMPLES, INCLUDING DESIGN AND ANALYSIS ..................................... 226
Example 9-1: Engine Valve Train Noise Study .................................................. 226
Example 9-2: Study of Crankshaft Surface Finishing Process ............................. 230
Example 9-3: Automobile Generator Noise Study ............................................. 234
Example 9-4: Engine Idle Stability Study ........................................................ 236
Example 9-5: Instrument Panel Structure Design Optimization .......................... 238
Example 9-6: Study Leading to Selection of Worst-Case Barrier Test Vehicle ...... 241
Example 9-7: Airbag Design Study .................................................................. 244
Example 9-8: Transmission Control Cable Adjustment Parameters ..................... 247
Example 9-9: Front Structure Crush Characteristics ........................................... 247
Example 9-10: Electronic Connector Spring Disengagement Force Study ............ 252
viii APrimerontheTaguchiMethod
Appendix A: Orthogonal Arrays, Triangular Tables, and
Linear Graphs ...................................................................................................... 261
Appendix B: Taguchi Experiment Flow Diagram and
F-Tables ..................................................................................................................... 281
References .............................................................................................................. 293
Bibliography .......................................................................................................... 294
Glossary ................................................................................................................... 295
Index ........................................................................................................................... 299
1
Quality Through Product
and Process Optimization
BACKGROUND
Mankind has always had a fascination with quality. Today’s
technology is testimony to man’s incessant desire to provide a
higher level of quality in products and services to increase market
share and profits. Sometimes quality is essential. A pacemaker that
controls heart action must operate continuously and precisely. An
erratic pacemaker is valueless, useless, and dangerous.
Driven by the need to compete on price and performance and
to maintain profitability, quality-conscious manufacturers are
increasingly aware of the need to optimize products and processes.
Quality achieved by means of design optimization is found by many
manufacturers to be cost effective in gaining and maintaining a
competitive position in the world market.
DESIGN OF EXPERIMENTS—THE CONVENTIONAL APPROACH
The technique of defining and investigating all possible condi-
tions in an experiment involving multiple factors is known as the
design of experiments (DOE). In the literature, this technique is
also referred to as factorial design. Design of experiments concepts
have been in use since Sir Ronald A. Fisher’s work in agricultural
experimentation during the late 1920s. Fisher [1] successfully
designed experiments to determine optimum treatments of land
for agriculture to achieve maximum yield. Numerous applications
of this approach, especially in the chemical and pharmaceutical
industries, are cited in the literature. A thorough coverage of this
subject is beyond the scope of this study, but the method and its
1
