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P1: OTA/XYZ JWBS068-fm P2: ABC JWBS068-Noorossana May 10, 2011 10:7 Printer Name: Yet to Come Statistical Analysis of Proﬁle Monitoring i

P1: OTA/XYZ JWBS068-fm P2: ABC JWBS068-Noorossana May 10, 2011 10:7 Printer Name: Yet to Come WILEY SERIES IN PROBABILITY AND STATISTICS Established by WALTER A. SHEWHART and SAMUEL S. WILKS Editors: David J. Balding, Noel A. C. Cressie, Garrett M. Fitzmaurice, Harvey Goldstein, Iain M. Johnstone, Geert Molenberghs, David W. Scott, Adrian F. M. Smith, Ruey S. Tsay, Sanford Weisberg Editors Emeriti: Vic Barnett, J. Stuart Hunter, Joseph B. Kadane, Jozef L. Teugels A complete list of the titles in this series appears at the end of this volume. ii

P1: OTA/XYZ JWBS068-fm P2: ABC JWBS068-Noorossana May 10, 2011 10:7 Printer Name: Yet to Come Statistical Analysis of Proﬁle Monitoring RASSOUL NOOROSSANA Industrial Engineering Department Iran University of Science and Technology Tehran, Iran ABBAS SAGHAEI Industrial Engineering Department Islamic Azad University – Science and Research Branch Tehran, Iran AMIRHOSSEIN AMIRI Industrial Engineering Department Shahed University Tehran, Iran A JOHN WILEY & SONS, INC., PUBLICATION iii

P1: OTA/XYZ JWBS068-fm P2: ABC JWBS068-Noorossana May 10, 2011 10:7 Printer Name: Yet to Come Copyright C 2011 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. 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, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax˜(978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and speciﬁcally disclaim any implied warranties of merchantability or ﬁtness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of proﬁt or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com Library of Congress Cataloging-in-Publication Data Noorossana, Rassoul, 1959– Statistical analysis of proﬁle monitoring / Rassoul Noorossana, Abbas Saghaei, Amirhossein Amiri. p. cm. Includes bibliographical references and index. ISBN 978-0-470-90322-3 (cloth) 1. Process control–Statistical methods. 2. Quality control–Statistical methods. 1972– II. Amiri, Amirhossein, 1979– III. Title. TS156.8.N656 2011 658.5–dc22 I. Saghaei, Abbas, 2011002197 Printed in Singapore oBook ISBN: 9781118071984 ePDF ISBN: 9781118071960 ePub ISBN: 9781118071977 10 9 8 7 6 5 4 3 2 1 iv

P1: OTA/XYZ JWBS068-fm P2: ABC JWBS068-Noorossana May 10, 2011 10:7 Printer Name: Yet to Come Contents Preface Contributors 1 Introduction to Proﬁle Monitoring Introduction, 1 1.1 Functional Relationships Qualiﬁed as Proﬁles, 6 1.2 Functional Relationships not Qualiﬁed as Proﬁles, 13 1.3 Structure of This Book, 15 References, 19 2 Simple Linear Proﬁles Introduction, 21 2.1 Phase I Simple Linear Proﬁle, 22 2.2 Phase II Simple Linear Proﬁle, 53 2.3 Special Cases and an Important Application, 74 2.4 Diagnostic Statistics, 77 2.5 Violation of the Model Assumptions, 81 Appendix, 83 References, 89 3 Multiple Linear and Polynomial Proﬁles Introduction, 93 3.1 Monitoring Multiple Linear Proﬁles, 94 3.2 Monitoring Polynomial Proﬁles, 108 References, 116 v ix xi 1 21 93

P1: OTA/XYZ JWBS068-fm P2: ABC JWBS068-Noorossana May 10, 2011 10:7 Printer Name: Yet to Come vi 4 Binary Response Proﬁles Introduction, 117 4.1 Model Setting and Parameter Estimation, 118 4.2 Phase I Control, 120 4.3 Phase II Monitoring, 122 4.4 Applications, 123 4.5 Conclusions, 126 References, 128 5 Parametric Nonlinear Proﬁles Introduction, 129 5.1 Nonlinear Model Estimation, 130 5.2 Phase I Methods, 132 5.3 Phase II Methods, 142 5.4 Variance Proﬁles, 145 Appendix, 154 References, 155 6 Nonparametric Nonlinear Proﬁles Introduction, 157 6.1 Model Formulation and Nonparametric Example, 159 6.2 Splines, 162 6.3 Component Analysis, 170 6.4 Wavelets, 174 References, 187 7 Multivariate Linear Proﬁles Monitoring Introduction, 189 7.1 Monitoring Multivariate Simple Linear Proﬁles, 190 7.2 Monitoring Multivariate Multiple Linear Proﬁles, 204 References, 216 CONTENTS 117 129 157 189 8 Statistical Process Control for Geometric Speciﬁcations 217 Introduction, 217 8.1 Examples of Geometric Feature Concerning Circularity, 221 8.2 Control Charts for Proﬁle Monitoring, 224 8.3 Simple Approaches for Monitoring Manufactured Proﬁles: The Industrial Practice, 233

P1: OTA/XYZ JWBS068-fm P2: ABC JWBS068-Noorossana May 10, 2011 10:7 Printer Name: Yet to Come CONTENTS vii 8.4 Performance Comparison, 237 8.5 Moving from 2D Proﬁles to 3D Surfaces, 245 8.6 Concluding Remarks, 249 Acknowledgments, 250 References, 250 9 Correlation and Autocorrelation in Proﬁles 253 Introduction, 253 9.1 Methods for WPA for Linear Models, 255 9.2 Methods for BPC for Linear Models, 257 9.3 Methods for WPA and BPC for Other (Nonlinear) Models, 258 9.4 Phase I Analysis, 259 9.5 Phase II Analysis, 262 9.6 Related Issues: Rational Subgrouping and Random Effects, 263 9.7 Discussion and Open Questions, 266 Acknowledgment, 267 References, 267 10 Nonparametric Proﬁle Monitoring 269 Introduction, 269 10.1 Monitoring Proﬁles Based on Nonparametric Regression, 270 10.2 Nonparametric Proﬁle Monitoring Using Change-Point Formulation and Adaptive Smoothing, 281 10.3 Nonparametric Proﬁle Monitoring by Mixed-Effects Modeling, 288 Appendix A: Approximate the Distributions of Quadratic Forms Like zT Az, 299 Appendix B: The Expression of lrt,k in Model (10.8), 300 References, 301 Index 303

P1: OTA/XYZ JWBS068-PREFACE P2: ABC JWBS068-Noorossana April 25, 2011 19:7 Printer Name: Yet to Come Preface The aim of this book is to summarize major achievements in statistical proﬁle moni- toring methods. Statistical proﬁle monitoring can be considered as a potential subarea of statistical quality control that has recently attracted attention of many researchers and practitioners. One major reason behind this attractiveness is the wide range of applications that one can identify for the concept of proﬁle monitoring in different service and manufacturing settings. It should not be too long before the concept, methods, and issues related to statistical proﬁle monitoring and its related analy- ses are introduced in different engineering and statistical textbooks and software packages. It is well known that, in standard statistical process control applications, one is traditionally concerned with monitoring performance of a process or product using measurements on a single quality characteristic or a vector of quality characteristics at a given time or space. However, in many applications of statistical process control, quality of a process or product is best characterized and summarized by a functional relationship. In the literature of proﬁle monitoring, this functional relationship is usually referred to as proﬁle, signature, or waveform. Fortunately, advances in tech- nology have made it possible for process or statistical engineers and practitioners to collect a large number of process or product measurements to reconstruct this functional relationship with the aim of understanding and evaluating its stability over time using statistical methods. This book addresses the fundamental concepts, methods, and issues related to statistical proﬁle monitoring. The book begins with an introduction to the concept of proﬁle monitoring and its applications in practice, and then throughout the remain- ing nine chapters, issues related to simple linear proﬁles, complex nonlinear pro- ﬁles, and roundness proﬁles or proﬁles associated with geometric speciﬁcations are discussed. This book can be used as a major reference or textbook for researchers, engineers, and statisticians who are interested in advanced topics in statistical process control. In ix

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