Table Of ContentIntroduction to Engineering Statistics and
Six Sigma
Theodore T. Allen
Introduction to
Engineering Statistics
and Six Sigma
Statistical Quality Control and Design of
Experiments and Systems
With114Figures
123
TheodoreT.Allen,PhD
DepartmentofIndustrialWeldingandSystemsEngineering
TheOhioStateUniversity
210BakerSystems
1971NeilAvenue
Colombus,OH43210-1271
USA
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Allen,TheodoreT.
Introductiontoengineeringstatisticsandsixsigma:
statisticalqualitycontrolanddesignofexperimentsand
systems
1.Engineering-Statisticalmethods2.Sixsigma(Quality
controlstandard)
I.Title
620’.0072
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Dedicated to my wife and to my parents
Preface
There are four main reasons why I wrote this book. First, six sigma consultants
have taught us that people do not need to be statistical experts to gain benefits from
applying methods under such headings as “statistical quality control” (SQC) and
“design of experiments” (DOE). Some college-level books intertwine the methods
and the theory, potentially giving the mistaken impression that all the theory has to
be understood to use the methods. As far as possible, I have attempted to separate
the information necessary for competent application from the theory needed to
understand and evaluate the methods.
Second, many books teach methods without sufficiently clarifying the context
in which the method could help to solve a real-world problem. Six sigma, statistics
and operations-research experts have little trouble making the connections with
practice. However, many other people do have this difficulty. Therefore, I wanted
to clarify better the roles of the methods in solving problems. To this end, I have
re-organized the presentation of the techniques and included several complete case
studies conducted by myself and former students.
Third, I feel that much of the “theory” in standard textbooks is rarely presented
in a manner to answer directly the most pertinent questions, such as:
Should I use this specific method or an alternative method?
How do I use the results when making a decision?
How much can I trust the results?
Admittedly, standard theory (e.g., analysis of variance decomposition,
confidence intervals, and defining relations) does have a bearing on these
questions. Yet the widely accepted view that the choice to apply a method is
equivalent to purchasing a risky stock investment has not been sufficiently
clarified. The theory in this book is mainly used to evaluate in advance the risks
associated with specific methods and to address these three questions.
Fourth, there is an increasing emphasis on service sector and bioengineering
applications of quality technology, which is not fully reflected in some of the
alternative books. Therefore, this book constitutes an attempt to include more
examples pertinent to service-sector jobs in accounting, education, call centers,
health care, and software companies.
In addition, this book can be viewed as attempt to build on and refocus material
in other books and research articles, including: Harry and Schroeder (1999) and
Pande et al. which comprehensively cover six sigma; Montgomery (2001) and
Besterfield (2001), which focus on statistical quality control; Box and Draper
viii Preface
(1987), Dean and Voss (1999), Fedorov and Hackl (1997), Montgomery (2000),
Myers and Montgomery (2001), Taguchi (1993), and Wu and Hamada (2000),
which focus on design of experiments.
At least 50 books per year are written related to the “six sigma movement”
which (among other things) encourage people to use SQC and DOE techniques.
Most of these books are intended for a general business audience; few provide
advanced readers the tools to understand modern statistical method development.
Equally rare are precise descriptions of the many methods related to six sigma as
well as detailed examples of applications that yielded large-scale returns to the
businesses that employed them.
Unlike many popular books on “six sigma methods,” this material is aimed at
the college- or graduate-level student rather than at the casual reader, and includes
more derivations and analysis of the related methods. As such, an important
motivation of this text is to fill a need for an integrated, principled, technical
description of six sigma techniques and concepts that can provide a practical guide
both in making choices among available methods and applying them to real-world
problems. Professionals who have earned “black belt” and “master black belt”
titles may find material more complete and intensive here than in other sources.
Rather than teaching methods as “correct” and fixed, later chapters build the
optimization and simulation skills needed for the advanced reader to develop new
methods with sophistication, drawing on modern computing power. Design of
experiments (DOE) methods provide a particularly useful area for the development
of new methods. DOE is sometimes called the most powerful six sigma tool.
However, the relationship between the mathematical properties of the associated
matrices and bottom-line profits has been only partially explored. As a result, users
of these methods too often must base their decisions and associated investments on
faith. An intended unique contribution of this book is to teach DOE in a new way,
as a set of fallible methods with understandable properties that can be improved,
while providing new information to support decisions about using these methods.
Two recent trends assist in the development of statistical methods. First,
dramatic improvements have occurred in the ability to solve hard simulation and
optimization problems, largely because of advances in computing speeds. It is now
far easier to “simulate” the application of a chosen method to test likely outcomes
of its application to a particular problem. Second, an increased interest in six sigma
methods and other formal approaches to making businesses more competitive has
increased the time and resources invested in developing and applying new
statistical methods.
This latter development can be credited to consultants such as Harry and
Schroeder (1999), Pande et al. (2000), and Taguchi (1993), visionary business
leaders such as General Electric’s Jack Welch, as well as to statistical software that
permits non-experts to make use of the related technologies. In addition, there is a
push towards closer integration of optimization, marketing, and statistical methods
into “improvement systems” that structure product-design projects from beginning
to end.
Statistical methods are relevant to virtually everyone. Calculus and linear
algebra are helpful, but not necessary, for their use. The approach taken here is to
minimize explanations requiring knowledge of these subjects, as far as possible.
Preface ix
This book is organized into three parts. For a single introductory course, the first
few chapters in Parts One and Two could be used. More advanced courses could be
built upon the remaining chapters. At The Ohio State University, I use each part for
a different 11 week course.
References
Box GEP, Draper NR (1987) Empirical Model-Building and Response Surfaces.
Wiley, New York
Besterfield D (2001) Quality Control. Prentice Hall, Columbus, OH
Breyfogle FW (2003) Implementing Six Sigma: Smarter Solutions® Using
Statistical Methods, 2nd edn. Wiley, New York
Dean A, Voss DT (1999) Design and Analysis of Experiments. Springer, Berlin
Heidelberg New York
Fedorov V, Hackl P (1997) Model-Oriented Design of Experiments. Springer,
Berlin Heidelberg New York
Harry MJ, Schroeder R (1999) Six Sigma, The Breakthrough Management
Strategy Revolutionizing The World’s Top Corporations. Bantam
Doubleday Dell, New York
Montgomery DC (2000) Design and Analysis of Experiments, 5th edn. John Wiley
& Sons, Inc., Hoboken, NJ
Montgomery DC (2001) Statistical Quality Control, 4th edn. John Wiley & Sons,
Inc., Hoboken, NJ
Myers RH, Montgomery DA (2001) Response Surface Methodology, 5th edn. John
Wiley & Sons, Inc., Hoboken, NJ
Pande PS, Neuman RP, Cavanagh R (2000) The Six Sigma Way: How GE,
Motorola, and Other Top Companies are Honing Their Performance.
McGraw-Hill, New York
Taguchi G (1993) Taguchi Methods: Research and Development. In Konishi S
(ed.) Quality Engineering Series, vol 1. The American Supplier Institute,
Livonia, MI
Wu CFJ, Hamada M (2000) Experiments: Planning, Analysis, and Parameter
Design Optimization. Wiley, New York
Acknowledgments
I thank my wife, Emily, for being wonderful. I thank my son, Andrew, for being
extremely cute. I also thank my parents, George and Jodie, for being exceptionally
good parents. Both Emily and Jodie provided important editing and conceptual
help. In addition, Sonya Humes and editors at Springer Verlag including Kate
Brown and Anthony Doyle provided valuable editing and comments.
Gary Herrin, my advisor, provided valuable perspective and encouragement.
Also, my former Ph.D. students deserve high praise for helping to develop the
conceptual framework and components for this book. In particular, I thank Liyang
Yu for proving by direct test that modern computers are able to optimize
experiments evaluated using simulation, which is relevant to the last four chapters
of this book, and for much hard work and clear thinking. Also, I thank Mikhail
Bernshteyn for his many contributions, including deeply involving my research
group in simulation optimization, sharing in some potentially important
innovations in multiple areas, and bringing technology in Part II of this book to the
marketplace through Sagata Ltd., in which we are partners. I thank Charlie Ribardo
for teaching me many things about engineering and helping to develop many of the
welding-related case studies in this book. Waraphorn Ittiwattana helped to develop
approaches for optimization and robust engineering in Chapter 14. Navara
Chantarat played an important role in the design of experiments discoveries in
Chapter 18. I thank Deng Huang for playing the leading role in our exploration of
variable fidelity approaches to experimentation and optimization. I am grateful to
James Brady for developing many of the real case studies and for playing the
leading role in our related writing and concept development associated with six
sigma, relevant throughout this book.
Also, I would like to thank my former M.S. students, including Chaitanya
Joshi, for helping me to research the topic of six sigma. Chetan Chivate also
assisted in the development of text on advanced modeling techniques (Chapter 16).
Also, Gavin Richards and many other students at The Ohio State University played
key roles in providing feedback, editing, refining, and developing the examples and
problems. In particular, Mike Fujka and Ryan McDorman provided the student
project examples.
In addition, I would like to thank all of the individuals who have supported this
research over the last several years. These have included first and foremost Allen
Miller, who has been a good boss and mentor, and also Richard Richardson and
David Farson who have made the welding world accessible; it has been a pleasure
xii Acknowledgments
to collaborate with them. Jose Castro, John Lippold, William Marras, Gary Maul,
Clark Mount-Campbell, Philip Smith, David Woods, and many others contributed
by believing that experimental planning is important and that I would some day
manage to contribute to its study.
Also, I would like to thank Dennis Harwig, David Yapp, and Larry Brown both
for contributing financially and for sharing their visions for related research.
Multiple people from Visteon assisted, including John Barkley, Frank Fusco, Peter
Gilliam, and David Reese. Jane Fraser, Robert Gustafson, and the Industrial and
Systems Engineering students at The Ohio State University helped me to improve
the book. Bruce Ankenman, Angela Dean, William Notz, Jason Hsu, and Tom
Santner all contributed.
Also, editors and reviewers played an important role in the development of this
book and publication of related research. First and foremost of these is Adrian
Bowman of the Journal of the Royal Statistical Society Series C: Applied
Statistics, who quickly recognized the value of the EIMSE optimal designs (see
Chapter 13). Douglas Montgomery of Quality and Reliability Engineering
International and an expert on engineering statistics provided key encouragement
in multiple instances. In addition, the anonymous reviewers of this book provided
much direct and constructive assistance including forcing the improvement of the
examples and mitigation of the predominantly myopic, US-centered focus.
Finally, I would like to thank six people who inspired me, perhaps
unintentionally: Richard DeVeaux and Jeff Wu, both of whom taught me design of
experiments according to their vision, Max Morris, who forced me to become
smarter, George Hazelrigg, who wants the big picture to make sense, George Box,
for his many contributions, and Khalil Kabiri-Bamoradian, who taught and teaches
me many things.
Contents
List of Acronyms...................................................................................................xxi
1 Introduction.............................................................................................1
1.1 Purpose of this Book......................................................................1
1.2 Systems and Key Input Variables...................................................2
1.3 Problem-solving Methods..............................................................6
1.3.1 What Is “Six Sigma”?.......................................................7
1.4 History of “Quality” and Six Sigma.............................................10
1.4.1 History of Management and Quality...............................10
1.4.2 History of Documentation and Quality...........................14
1.4.3 History of Statistics and Quality.....................................14
1.4.4 The Six Sigma Movement..............................................17
1.5 The Culture of Discipline.............................................................18
1.6 Real Success Stories.....................................................................20
1.7 Overview of this Book.................................................................21
1.8 References....................................................................................22
1.9 Problems.......................................................................................22
Part I Statistical Quality Control
2 Statistical Quality Control and Six Sigma...........................................29
2.1 Introduction..................................................................................29
2.2 Method Names as Buzzwords......................................................30
2.3 Where Methods Fit into Projects..................................................31
2.4 Organizational Roles and Methods..............................................33
2.5 Specifications: Nonconforming vs Defective...............................34
2.6 Standard Operating Procedures (SOPs)........................................36
2.6.1 Proposed SOP Process....................................................37
2.6.2 Measurement SOPs.........................................................40
2.7 References....................................................................................40
2.8 Problems.......................................................................................41
3 Define Phase and Strategy....................................................................45
3.1 Introduction..................................................................................45
