Design of Experiments with MINITAB

521 Pages·4.226 MB·English

by  Paul G. Mathews

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 2004020013
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-
xxxiiiiiiiii
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 methodsvery 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 Experimentsand 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,Statisticsfor 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.
xvi Preface
WHY MINITAB?
Although most DOE textbooks now present and describe the solutions to DOE prob-
lems using one or more software packages, I find that they still tend to be superficial
and of little real use to readers and students. I chose to use MINITAB extensively in this
book for many reasons:
• The MINITAB program interface is designed to be very simple and easy to
use. There are many other powerful programs available that don’t get used
much because they are so difficult to run.
• Despite its apparent simplicity, MINITAB also supports many advanced
methods.
• In addition to the tools required to design and analyze experiments, MINITAB
supports most of the other statistical analyses and methods that most users
need, such as basic descriptive and inferential statistics, SPC, reliability, GR&R
studies, process capability, and so on. Why buy, learn, and maintain multiple
software packages when one will suffice?
• MINITAB has a powerful graphics engine with an easy to use interface. Most
graph attributes are easy to configure and can be edited after a graph is created.
All but a few of the graphs in this book were originally created in MINITAB.
• MINITAB has a simple but powerful integrated sample-size calculation inter-
face that can solve the most common sample-size problems. This eliminates
the need to buy and learn another program that is dedicated to sample-size
calculations. MINITAB can also be used to solve many more complex sample-
size problems that are not included in the standard interface.
• MINITAB has a very simple integrated system to package a series of instruc-
tions to form an executable macro. If you can drive a mouse you can write a
MINITAB macro. MINITAB macros are easy to edit, customize, and maintain
and can be made even more powerful with the higher-level MINITAB macro
programming language. All of the custom analysis macros that are described
in this book are provided on the CD-ROM included with the book.
• MINITAB is relatively free of bugs and errors, and its output is accurate.
• MINITAB has a very large established user base.
• MINITAB’s printed documentation, online help, and technical support are
all excellent.
• MINITAB Incorporated is a large company that will be around for many years.
• Although price should not be a primary factor in selecting statistical or DOE
software, MINITAB is priced competitively for both single users and network
installations.
Preface xvii
Despite its dedication to MINITAB,I’ve successfully taught DOE from this book to
students and clients who use other software packages. Generally the user interfaces and
outputs of those packages are similar enough to those of MINITAB that most students
learn to readily translate from MINITAB into their own program.
I’ve tried to use the conventions chosen in the MINITAB documentation to present
MINITAB references throughout the book. MINITAB commands, buttons, text box
labels,and pull-down menus are indicated in boldface.MINITAB columns like c1,c2,
. . . are indicated in typewriter (Courier) font. MINITAB file names and extensions are
indicated in italics. Variable names are capitalized and displayed in the standard font.
HOW ARE THE BOOK AND SUPPLEMENTARY
CD-ROM ORGANIZED?
Since many readers and students who would consider this book have rusty statistical
skills, a rather detailed review of graphical data presentation methods, descriptive sta-
tistics, and inferential statistics is presented in the first three chapters. Sample-size
calculations for basic confidence intervals and hypothesis tests are also presented in
Chapter 3. This is a new topic for many people and this chapter sets the stage for the
sample-size calculations that are presented in later chapters.
Chapter 4 provides a qualitative introduction to the language and concepts of DOE.
This chapter can be read superficially the first time, but be prepared to return to it fre-
quently as the topics introduced here are addressed in more detail in later chapters.
Chapters 5 through 7 present experiment designs and analyses for one-way and
multi-way classifications. Chapter 7 includes superficial treatment of incomplete designs,
nested designs,and fixed,random,and mixed models. Many readers/students postpone
their study of much of Chapter 7 until after they’ve completed the rest of this book or
until they have need for that material.
Chapter 8 provides detailed coverage of linear regression and the use of variable
transformations. Polynomial and multivariable regression and general linear models are
introduced in preparation for the analysis of multivariable designed experiments.
Chapters 9, 10, and 11 present two-level full factorial, fractional factorial, and
response-surface experiment designs, respectively. The analysis of data from these
experiments using multiple regression methods and the prepackaged MINITAB DOE
analyses is presented. Although the two-level plus centers designs are not really response-
surface designs, they are included in the beginning of Chapter 11 because of the new
concepts and issues that they introduce.
The supplementary CD-ROM included with the book contains:
• Data files from the example problems in the book.
• Descriptions of simple experiments with toys that could be performed at home
or in a DOE class. There are experiments involving magic dice, three different
kinds of paper helicopters, the strength of rectangular wooden beams, and
xviii Preface
catapults. Paper helicopter templates are provided on graph paper to simplify
the construction of helicopters to various specifications.
• MINITAB macros for analyzing factorial, fractional factorial, and response-
surface designs.
• MINITAB macros for special functions.
• A standard set of experiment design files in MINITAB worksheets.
• Microsoft Excel experiment design files with integrated simulations.
RUNNING EXPERIMENTS
No matter how hard you study this book or how many of the chapter problems or sim-
ulations you attempt,you’ll never become a proficient experimenter unless you actually
run lots of experiments. In many ways, the material in this book is easy and the hard
things—the ones no book can capture—are only learned through experience. But don’t
rush into performing experiments at work where the results could be embarrassing or
worse. Rather, take the time to perform the simple experiments with toys that are
described in the documents on the supplementary CD-ROM. If you can,recruit a DOE
novice or child to help you perform these experiments. Observe your assistant carefully
and honestly note the mistakes that you both make because then you’ll be less likely to
commit those mistakes again under more important circumstances. And always remem-
ber that you usually learn more from a failed experiment than one that goes perfectly.
Table of Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
Chapter 1 Graphical Presentation of Data . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Types of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Bar Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 Dotplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.6 Stem-and-Leaf Plots . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.7 Box-and-Whisker Plots . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.8 Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.9 Multi-Vari Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.10 An Introduction to MINITAB . . . . . . . . . . . . . . . . . . . . . 9
1.10.1 Starting MINITAB . . . . . . . . . . . . . . . . . . . . . . . 9
1.10.2 MINITAB Windows . . . . . . . . . . . . . . . . . . . . . . 9
1.10.3 Using the Command Prompt . . . . . . . . . . . . . . . . . . 11
1.10.4 Customizing MINITAB . . . . . . . . . . . . . . . . . . . . 11
1.10.5 Entering Data . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.10.6 Graphing Data . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.10.7 Printing Data and Graphs . . . . . . . . . . . . . . . . . . . 13
1.10.8 Saving and Retrieving Information . . . . . . . . . . . . . . 14
1.10.9 MINITAB Macros . . . . . . . . . . . . . . . . . . . . . . . 15
1.10.10 Summary of MINITAB Files . . . . . . . . . . . . . . . . . 17
Chapter 2 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Selection of Samples . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Measures of Location . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 The Median . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
v
vi Table of Contents
2.3.2 The Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Measures of Variation . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.1 The Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.2 The Standard Deviation . . . . . . . . . . . . . . . . . . . . . 22
2.4.3 Degrees of Freedom . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.4 The Calculating Form for the Standard Deviation . . . . . . . 25
2.5 The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6 Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.6.1 Multiplication of Choices . . . . . . . . . . . . . . . . . . . . 30
2.6.2 Factorials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.6.3 Permutations . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.6.4 Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.7 MINITAB Commands to Calculate Descriptive Statistics . . . . . . . 34
Chapter 3 Inferential Statistics . . . . . . . . . . . . . . . . . . . . . . . . 37
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2 The Distribution of Sample Means (s Known) . . . . . . . . . . . . 38
3.3 Confidence Interval for the Population Mean (s Known) . . . . . . 41
3.4 Hypothesis Test for One Sample Mean (s Known) . . . . . . . . . . 42
3.4.1 Hypothesis Test Rationale . . . . . . . . . . . . . . . . . . . . 42
3.4.2 Decision Limits Based on Measurement Units . . . . . . . . . 44
3.4.3 Decision Limits Based on Standard (z) Units . . . . . . . . . . 45
3.4.4 Decision Limits Based on the pValue . . . . . . . . . . . . . 46
3.4.5 Type 1 and Type 2 Errors . . . . . . . . . . . . . . . . . . . . 49
3.4.6 One-Tailed Hypothesis Tests . . . . . . . . . . . . . . . . . . 51
3.5 The Distribution of Sample Means (s Unknown) . . . . . . . . . . 52
3.5.1 Student’s t Distribution . . . . . . . . . . . . . . . . . . . . . 52
3.5.2 A One-Sample Hypothesis Test for the Population Mean
(s Unknown) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.5.3 A Confidence Interval for the Population Mean
(s Unknown) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.6 Hypothesis Tests for Two Means . . . . . . . . . . . . . . . . . . . . 56
3.6.1 Two Independent Samples (s 2 and s 2 Known) . . . . . . . . 56
1 2
3.6.2 Two Independent Samples (s 2 and s 2 Unknown
1 2
But Equal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.6.3 Two Independent Samples (s 2 and s 2 Unknown
1 2
and Unequal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.6.4 Paired Samples . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.7 Inferences About One Variance (Optional) . . . . . . . . . . . . . . 61
3.7.1 The Distribution of Sample Variances . . . . . . . . . . . . . . 61
3.7.2 Hypothesis Test for One Sample Variance . . . . . . . . . . . 63
3.7.3 Confidence Interval for the Population Variance . . . . . . . . 64
3.8 Hypothesis Tests for Two Sample Variances . . . . . . . . . . . . . . 65
3.9 Quick Tests for the Two-Sample Location Problem . . . . . . . . . . 68