Mathews__Paul_G._Design_of_Experiments_with_MINITAB.pdf

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Design of Experiments
with
MINITAB
Paul G. Mathews
ASQ Quality Press
Milwaukee, Wisconsin
American Society for Quality, Quality Press, Milwaukee 53203
© 2005 by ASQ
All rights reserved. Published 2004
Printed in the United States of America
12 11 10 09 08 07 06 05 04
5 4 3 2 1
Library of Congress Cataloging-in-Publication Data
Mathews, Paul G., 1960–
Design of experiments with MINITAB / Paul G. Mathews.
p. cm.
Includes bibliographical references and index.
ISBN 0-87389-637-8 (hardcover, case binding : alk. paper)
1. Statistical hypothesis testing. 2. Experimental design. 3. Minitab. 4.
Science—Statistical methods. 5. Engineering—Statistical methods. I. Title.
QA277.M377 2004
519.5'7—dc22
ISBN 0-87389-637-8
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Preface
WHAT IS DOE?
Design of experiments (DOE) is a methodology for studying any response that varies
as a function of one or more independent variables or
knobs.
By observing the response
under a planned matrix of knob settings, a statistically valid mathematical model for the
response can be determined. The resulting model can be used for a variety of purposes:
to select optimum levels for the knobs; to focus attention on the crucial knobs and elim-
inate the distractions caused by minor or insignificant knobs; to provide predictions for
the response under a variety of knob settings; to identify and reduce the response’s sen-
sitivity to troublesome knobs and interactions between knobs; and so on. Clearly, DOE
is an essential tool for studying complex systems and it is the only rigorous replacement
for the inferior but unfortunately still common practice of studying one variable at a
time (OVAT).
WHERE DID I LEARN DOE?
When I graduated from college and started working at GE Lighting as a physicist/engineer,
I quickly found that statistical methods were an integral part of their design, process,
and manufacturing operations. Although I’d had a mathematical statistics course as an
undergraduate physics student, I found that my training in statistics was completely
inadequate for survival in the GE organization. However, GE knew from experience
that this was a major weakness of most if not all of the entry-level engineers coming
from any science or engineering program (and still is today), and dealt with the prob-
lem by offering a wonderful series of internal statistics courses. Among those classes
was my first formal training in DOE—a 20-contact-hour course using Hicks,
Fundamental Concepts of Design of Experiments.
To tell the truth, we spent most of our
time in that class solving DOE problems with pocket calculators because there was lit-
xiii
xiv
Preface
tle software available at the time. Although to some degree the calculations distracted
me from the bigger DOE picture, that course made the power and efficiency offered by
DOE methods very apparent. Furthermore, DOE was part of the GE Lighting culture—
if your work plans didn’t incorporate DOE methods they didn’t get approved.
During my twelve years at GE Lighting I was involved in about one experiment per
week. Many of the systems that we studied were so complex that there was no other
possible way of doing the work. While our experiments weren’t always successful, we
did learn from our mistakes, and the designs and processes that we developed benefited
greatly from our use of DOE methods. The proof of our success is shown by the longe-
vity of our findings—many of the designs and processes that we developed years ago
are still in use today, even despite recent attempts to modify and improve them.
Although I learned the basic designs and methods of DOE at GE, I eventually real-
ized that we had restricted ourselves to a relatively small subset of the available experi-
ment designs. This only became apparent to me after I started teaching and consulting
on DOE to students and corporate clients who had much more diverse requirements. I
have to credit GE with giving me a strong foundation in DOE, but my students and
clients get the credit for really opening my eyes to the true range of possibilities for
designed experiments.
WHY DID I WRITE THIS BOOK?
The first DOE courses that I taught were at GE Lighting and Lakeland Community
College in Kirtland, Ohio. At GE we used RS1 and MINITAB for software while I chose
MINITAB for Lakeland. The textbooks that I chose for those classes were Montgomery,
Design and Analysis of Experiments
and Hicks,
Fundamental Concepts in the Design of
Experiments,
however, I felt that both of those books spent too much time describing
the calculations that the software took care of for us and not enough time presenting the
full capabilities offered by the software. Since many students were still struggling to
learn DOS while I was trying to teach them to use MINITAB, I supplemented their text-
books with a series of documents that integrated material taken from the textbooks with
instructions for using the software. As those documents became more comprehensive
they evolved into this textbook. I still have and occasionally use Montgomery; Box,
Hunter, and Hunter,
Statistics for Experimenters;
Hicks; and other DOE books, but as
my own book has become more complete I find that I am using those books less and
less often and then only for reference.
WHAT IS THE SCOPE OF THIS BOOK?
I purposely limited the scope of this book to the basic DOE designs and methods that
I think are essential for any engineer or scientist to understand. This book is limited to
the study of quantitative responses using one-way and multi-way classifications, full
Preface
xv
and fractional factorial designs, and basic response-surface designs. I’ve left coverage
of other experiment designs and analyses, including qualitative and binary responses,
Taguchi methods, and mixture designs, to the other books. However, students who
learn the material in this book and gain experience by running their own experiments
will be well prepared to use those other books and address those other topics when it
becomes necessary.
SAMPLE-SIZE CALCULATIONS
As a consultant, I’m asked more and more often to make sample-size recommenda-
tions for designed experiments. Obviously this is an important topic. Even if you
choose the perfect experiment to study a particular problem, that experiment will
waste time and resources if it uses too many runs and it will put you and your orga-
nization at risk if it uses too few runs. Although the calculations are not difficult, the
older textbooks present little or no instruction on how to estimate sample size. To a
large degree this is not their fault—at the time those books were written the proba-
bility functions and tables required to solve sample-size problems were not readily
available. But now most good statistical and DOE software programs provide that
information and at least a rudimentary interface for sample-size calculations. This
book is unique in that it presents detailed instructions and examples of sample-size
calculations for most common DOE problems.
HOW COULD THIS BOOK BE USED IN A
COLLEGE COURSE?
This book is appropriate for a one-quarter or one-semester course in DOE. Although the
book contains a few references to calculus methods, in most cases alternative methods
based on simple algebra are also presented. Students are expected to have good algebra
skills—no calculus is required.
As prerequisites, students should have completed either: 1) a one-quarter or semes-
ter course in statistical methods for quality engineering (such as with Ostle, Turner,
Hicks, and McElrath,
Engineering Statistics: The Industrial Experience)
or 2) a one-
quarter or semester course in basic statistics (such as with one of Freund’s books) and
a one-quarter or semester course in statistical quality control covering SPC and accep-
tance sampling (such as with Montgomery’s
Statistical Quality Control).
Students should
also have good Microsoft Windows skills and access to a good general statistics pack-
age like MINITAB or a dedicated DOE software package.
Students meeting the prerequisite requirements should be able to successfully com-
plete a course using this textbook in about 40 classroom/ lab hours with 40 to 80 hours
of additional time spent reading and solving homework problems. Students must have
access to software during class/ lab and to solve homework problems.

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