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Optimal Design of Experiments
A Case Study Approach

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Optimal Design of Experiments
A Case Study Approach

Peter Goos
University of Antwerp and Erasmus University Rotterdam

Bradley Jones
JMP Division of SAS

A John Wiley & Sons, Ltd., Publication

This edition first published 2011 © 2011 John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, SouthernGate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs andPatents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronicformats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in thisbook. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Library of Congress Cataloging-in-Publication DataGoos, 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 Acatalogue 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 Set in 10/12pt Times by Aptara Inc., New Delhi, India.

To Marijke, Bas, and Loes To Roselinde

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Contents
Preface Acknowledgments 1 A simple comparative experiment 1.1Key concepts 1.2 The setup of a comparative experiment 1.3 Summary An optimal screening experiment 2.1 Key concepts 2.2 Case: an extraction experiment 2.2.1 Problem and design 2.2.2 Data analysis 2.3 Peek into the black box 2.3.1 Main-effects models 2.3.2 Models with two-factor interaction effects 2.3.3 Factor scaling 2.3.4 Ordinary least squares estimation 2.3.5 Significance tests and statisticalpower calculations 2.3.6 Variance inflation 2.3.7 Aliasing 2.3.8 Optimal design 2.3.9 Generating optimal experimental designs 2.3.10 The extraction experiment revisited 2.3.11 Principles of successful screening: sparsity, hierarchy, and heredity 2.4 Background reading 2.4.1 Screening 2.4.2 Algorithms for finding optimal designs 2.5 Summary xiii xv 1 1 2 8 9 9 10 10 14 21 21 22 24 24 27 28 29 33 35 4041 44 44 44 45

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CONTENTS

3 Adding runs to a screening experiment 3.1 Key concepts 3.2 Case: an augmented extraction experiment 3.2.1 Problem and design 3.2.2 Data analysis 3.3 Peek into the black box 3.3.1 Optimal selection of a follow-up design 3.3.2 Design construction algorithm 3.3.3 Foldover designs 3.4 Background reading 3.5 Summary 4 A response surface design with a...