Optimal Design of Experiments E-Book

Peter Goos

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 470

Veröffentlichungsjahr: 2011

Beschreibung

"This is an engaging and informative book on the modern practice of experimental design. The authors' writing style is entertaining, the consulting dialogs are extremely enjoyable, and the technical material is presented brilliantly but not overwhelmingly. The book is a joy to read. Everyone who practices or teaches DOE should read this book." - Douglas C. Montgomery, Regents Professor, Department of Industrial Engineering, Arizona State University "It's been said: 'Design for the experiment, don't experiment for the design.' This book ably demonstrates this notion by showing how tailor-made, optimal designs can be effectively employed to meet a client's actual needs. It should be required reading for anyone interested in using the design of experiments in industrial settings." --Christopher J. Nachtsheim, Frank A Donaldson Chair in Operations Management, Carlson School of Management, University of Minnesota This book demonstrates the utility of the computer-aided optimal design approach using real industrial examples. These examples address questions such as the following: * How can I do screening inexpensively if I have dozens of factors to investigate? * What can I do if I have day-to-day variability and I can only perform 3 runs a day? * How can I do RSM cost effectively if I have categorical factors? * How can I design and analyze experiments when there is a factor that can only be changed a few times over the study? * How can I include both ingredients in a mixture and processing factors in the same study? * How can I design an experiment if there are many factor combinations that are impossible to run? * How can I make sure that a time trend due to warming up of equipment does not affect the conclusions from a study? * How can I take into account batch information in when designing experiments involving multiple batches? * How can I add runs to a botched experiment to resolve ambiguities? While answering these questions the book also shows how to evaluate and compare designs. This allows researchers to make sensible trade-offs between the cost of experimentation and the amount of information they obtain.

Leseprobe

Contents

Cover

Title Page

Copyright

Dedication

Preface

Acknowledgments

1: A simple comparative experiment

1.1 Key concepts

1.2 The setup of a comparative experiment

1.3 Summary

2: An optimal screening experiment

2.1 Key concepts

2.2 Case: an extraction experiment

2.3 Peek into the black box

2.4 Background reading

2.5 Summary

3: Adding runs to a screening experiment

3.1 Key concepts

3.2 Case: an augmented extraction experiment

3.3 Peek into the black box

3.4 Background reading

3.5 Summary

4: A response surface design with a categorical factor

4.1 Key concepts

4.2 Case: a robust and optimal process experiment

4.3 Peek into the black box

4.4 Background reading

4.5 Summary

5: A response surface design in an irregularly shaped design region

5.1 Key concepts

5.2 Case: the yield maximization experiment

5.3 Peek into the black box

5.4 Background reading

5.5 Summary

6: A “mixture” experiment with process variables

6.1 Key concepts

6.2 Case: the rolling mill experiment

6.3 Peek into the black box

6.4 Background reading

6.5 Summary

7: A response surface design in blocks

7.1 Key concepts

7.2 Case: the pastry dough experiment

7.3 Peek into the black box

7.4 Background reading

7.5 Summary

8: A screening experiment in blocks

8.1 Key concepts

8.2 Case: the stability improvement experiment

8.3 Peek into the black box

8.4 Background reading

8.5 Summary

9: Experimental design in the presence of covariates

9.1 Key concepts

9.2 Case: the polypropylene experiment

9.3 Peek into the black box

9.4 Background reading

9.5 Summary

10: A split-plot design

10.1 Key concepts

10.2 Case: the wind tunnel experiment

10.3 Peek into the black box

10.4 Background reading

10.5 Summary

11: A two-way split-plot design

11.1 Key concepts

11.2 Case: the battery cell experiment

11.3 Peek into the black box

11.4 Background reading

11.5 Summary

Bibliography

Index

This edition first published 2011 © 2011 John Wiley & Sons, Ltd

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Library of Congress Cataloging-in-Publication Data

Goos, Peter. Optimal design of experiments: a case study approach / Peter Goos and Bradley Jones. p. cm. Includes bibliographical references and index. ISBN 978-0-470-74461-1 (hardback) 1. Industrial engineering--Experiments--Computer-aided design. 2. Experimental design--Data processing. 3. Industrial engineering--Case studies. I. Jones, Bradley. II. Title. T57.5.G66 2011 670.285—dc22 2011008381

A catalogue record for this book is available from the British Library.

Print ISBN: 978-0-470-74461-1 ePDF ISBN: 978-1-119-97400-0 oBook ISBN: 978-1-119-97401-7 ePub ISBN: 978-1-119-97616-5 Mobi ISBN: 978-1-119-97617-2

To Marijke, Bas, and Loes

To Roselinde

Preface

Design of experiments is a powerful tool for understanding systems and processes. In practice, this understanding often leads immediately to improvements. We present optimal design of experiments as a general and flexible method for applying design of experiments. Our view is that optimal design of experiments is an appropriate tool in virtually any situation that suggests the possible use of design of experiments.

Books on application areas in statistics or applied mathematics, such as design of experiments, can present daunting obstacles to the nonexpert. We wanted to write a book on the practical application of design of experiments that would appeal to new practitioners and experts alike. This is clearly an ambitious goal and we have addressed it by writing a different kind of book.

Each chapter of the book contains a case study. The presentation of the case study is in the form of a play where two consultants, Brad and Peter, of the (fictitious) Intrepid Stats consulting firm, help clients in various industries solve practical problems. We chose this style to make the presentation of the core concepts of each chapter both informal and accessible.

This style is by no means unique. The use of dialogs dates all the way back to the Greek philosopher Plato. More recently, Galileo made use of this style to introduce scientific ideas. His three characters were: the teacher, the experienced student, and the novice.

Though our case studies involve scripted consulting sessions, we advise readers not to copy our consulting style when collaborating on their own design problems. In the interest of a compact exposition of the key points of each case, we skip much of the necessary information gathering involved in competent statistical consulting and problem solving.

We chose our case studies to show just how general and flexible the optimal design of experiments approach is. We start off by a chapter dealing with a simple comparative experiment. The next two chapters deal with a screening experiment and a follow-up experiment in a biotechnology firm. In Chapter 4, we show how a designed response surface experiment contributes to the development of a robust production process in food packaging. In Chapter 5, we set up a response surface experiment to maximize the yield of a chemical extraction process. Chapter 6 deals with an experiment, similar in structure to mixture experiments in the chemical and pharmaceutical industries, aimed at improving the finishing of aluminum sheets. In Chapters 7 and 8, we apply the optimal design of experiments approach to a vitamin stability experiment and a pastry dough experiment run over different days, and we demonstrate that this offers protection against day-to-day variation in the outcomes. In Chapter 9, we show how to take into account a priori information about the experimental units and how to deal with a time trend in the experimental results. In Chapter 10, we set up a wind tunnel experiment that involves factors whose levels are hard to change. Finally, in Chapter 11, we discuss the design of a battery cell experiment spanning two production steps.

Because our presentation of the case studies is often light on mathematical and statistical detail, each chapter also has a section that we call a “Peek into the black box.” In these sections, we provide a more rigorous underpinning for the various techniques we employ in our case studies. The reader may find that there is not as much material in these sections on data analysis as might be expected. Many books on design of experiments are mostly about data analysis rather than design generation, evaluation, and comparison. We focus much of our attention in these peeks into the black box on explaining what the reader can anticipate from the analysis, before actually acquiring the response data. In nearly every chapter, we have also included separate frames, which we call “Attachments,” to discuss topics that deserve special attention.

We hope that our book will appeal to the new practitioner as well as providing some utility to the expert. Our fondest wish is to empower more experimentation by more people. In the words of Cole Porter, “Experiment and you'll see!”

Acknowledgments

We would like to express our gratitude to numerous people who helped us in the process of writing this book.

First, we would like to thank Chris Nachtsheim for allowing us to use the scenario for the “mixture” experiment in Chapter 6, and Steven Gilmour for providing us with details about the pastry dough experiment in Chapter 7. We are also grateful to Ives Bourgonjon, Ludwig Claeys, Pascal Dekoninck, Tim De Rydt, Karen Dewilde, Heidi Dufait, Toine Machiels, Carlo Mol, and Marc Pauwels whose polypropylene project in Belgium, sponsored by Flanders' Drive, provided inspiration for the case study in Chapter 9.

A screening experiment described in Bie et al. (2005) provided inspiration for the case study in Chapters 2 and 3, while the work of Brenneman and Myers (2003) stimulated us to work out the response surface study involving a categorical factor in Chapter 4. We adapted the case study involving a constrained experimental region in Chapter 5 from an example in Box and Draper (1987). The vitamin stability experiment in Loukas (1997) formed the basis of the blocked screening experiment in Chapter 8. We turned the wind tunnel experiment described in Simpson et al. (2004) and the battery cell experiment studied in Vivacqua and Bisgaard (2004) into the case studies in Chapters 10 and 11.

Finally, we would like to thank Marjolein Crabbe, Marie Gaudard, Steven Gilmour, J. Stuart Hunter, Roselinde Kessels, Kalliopi Mylona, John Sall, Eric Schoen, Martina Vandebroek, and Arie Weeren for proofreading substantial portions of this book. Of course, all remaining errors are our own responsibility.

Heverlee, Peter Goos Cary, Bradley Jones January 2011

2

An optimal screening experiment

2.1 Key concepts

1. Orthogonal designs for two-level factors are also optimal designs. As a result, a computerized-search algorithm for generating optimal designs can generate standard orthogonal designs.

2. When a given factor’s effect on a response changes depending on the level of a second factor, we say that there is a two-factor interaction effect. Thus, a two-factor interaction is a combined effect on the response that is different from the sum of the individual effects.

3. Active two-factor interactions that are not included in the model can bias the estimates of the main effects.

4. The alias matrix is a quantitative measure of the bias referred to in the third key concept.

5. Adding any term to a model that was previously estimated without that term removes any bias in the estimates of the factor effects due to that term.

6. The trade-off in adding two-factor interactions to a main-effects model after using an orthogonal main-effect design is that you may introduce correlation in the estimates of the coefficients. This correlation results in an increase in the variances of the effect estimates.

Screening designs are among the most commonly used in industry. The idea of screening is to explore the effects of many experimental factors in one relatively small study to find the few factors that most affect the response of interest. This methodology is based on the Pareto or sparsity-of-effects principle that states that most real processes are driven by a few important factors.