Includes bibliographical references and index. ISBN hardcover, case binding : alk. Statistical hypothesis testing. Experimental design. M
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Paul G. Published Printed in the United States of America. Library of Congress Cataloging-in-Publication Data. Mathews, Paul G. Includes bibliographical references and index. ISBN hardcover, case binding : alk. Statistical hypothesis testing. Experimental design. Science—Statistical methods. Engineering—Statistical methods. M ISBN Not for resale. No part of this publication may be reproduced in any form, including an electronic retrieval system, without the prior written permission of ASQ.
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Box , Milwaukee, WI Visit our Web site at www. Printed on acid-free paper. 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:.
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. 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.
To tell the truth, we spent most of our time in that class solving DOE problems with pocket calculators because there was lit-. Although to some degree the calculations distracted me from the bigger DOE picture, that course made the power and efficiency offered by DOE methods v ery apparent. 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.
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. 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.
I purposely limited the scope of this book to the basic DOE designs and methods that. This book is limited to the study of quantitative responses using one-way and multi-way classifications, full. 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.
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. 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. 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. Why buy, learn, and maintain multiple software packages when one will suffice? Most graph attributes are easy to configure and can be edited after a graph is created.
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. All of the custom analysis macros that are described in this book are provided on the CD-ROM included with the book. Variable names are capitalized and displayed in the standard font.
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.
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.
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. There are experiments involving magic dice, three different kinds of paper helicopters, the strength of rectangular wooden beams, and. Paper helicopter templates are provided on graph paper to simplify the construction of helicopters to various specifications.
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. 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. And always remem- ber that you usually learn more from a failed experiment than one that goes perfectly. Table of Contents. Chapter 1. Graphical Presentation of Data. Entering Data. Chapter 2. Descriptive Statistics. The Normal Distribution. Measures of Variation.
The Mean. The Standard Deviation. The Range. Degrees of Freedom. The Calculating Form for the Standard Deviation. Multiplication of Choices. Inferential Statistics. Decision Limits Based on Measurement Units.
Hypothesis Test Rationale. Chapter 3. The Distribution of Sample Means s Known. A Confidence Interval for the Population Mean. But Equal. Two Independent Samples s 2 and s 2 2 Unknown. Paired Samples. Chapter 4. DOE Language and Concepts.
Published Printed in the United States of America 12 11 10 09 08 07 06 05 04 5 4 3 2 1. Mathews, Paul G. Includes bibliographical references and index. ISBN hardcover, case binding : alk.
Mathews Paul G. Design of Experiments With MINITAB
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