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Accelerated Testing ACCELERATED TESTING A Practitioner’s Guide to Accelerated and Reliability Testing Bryan Dodson Harry Schwab Warrendale, Pa. 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, without the prior written permission of SAE. For permission and licensing requests, contact: SAE Permissions 400 Commonwealth Drive Warrendale, PA 15096-0001 USA E-mail: [email protected] Tel: 724-772-4028 Fax: 724-772-4891 Library of Congress Cataloging-in-Publication Data Dodson, Bryan, 1962- Accelerated testing : a practitioner’s guide to accelerated and reliabil- ity testing / Bryan Dodson, Harry Schwab. p. cm. Includes bibliographical references and index. ISB-10 0-7680-0690-2 ISBN-13 978-0-7680-0690-2 1. Reliability (Engineering). I. Schwab, Harry. II. Title. TS173.D61 2006 620’.00452—dc22 2005057538 SAE International 400 Commonwealth Drive Warrendale, PA 15096-0001 USA E-mail: [email protected] Tel: 877-606-7323 (inside USA and Canada) 724-776-4970 (outside USA) Fax: 724-776-1615 Copyright © 2006 SAE International ISBN-10 0-7680-0690-2 ISBN-13 978-0-7680-0690-2 SAE Order No. R-304 Printed in the United States of America. PREFACE This book presents accelerated testing from a practical viewpoint. The material is presented with the practitioner in mind; thus, proofs and derivations have been omitted, and numerous examples have been included. In addition, most examples have been worked in Microsoft® Excel and are included in the accompanying CD. For those desiring proofs and derivations, references are provided. Our goal is that practicing engineers will be able to apply the methods presented after studying this text. Practitioners will fi nd this text valuable as a comprehensive reference book, but this book is also ideal for use in college courses. In particular, it is recommended that this text be used for one-semester college courses. Students should have a familiarity with basic probability and statistics before attempting this material. The text consists of eight chapters. Chapter 1 provides an introduction and overview of the limitations of accelerated testing. Chapters 2, 3, and 4 describe the fundamentals of statistical distributions, the most commonly used distributions in accelerated testing, and parameter estima- tion methods. Chapter 5 describes test plans for accelerated testing, including reliability growth. Chapter 6 explains models for accelerated aging, along with qualitative methods of accelerated testing. Chapter 7 explains environmental stress screening (ESS), and Chapter 8 presents the equipment and methods used in accelerated testing. Be sure to use the accompanying CD, which contains a website to organize the material. The CD contains the following content: • Examples—The examples presented in the text are worked in Microsoft Excel templates. These templates will be useful when applying the material to real-world problems. • Statistical Tables—The statistical tables included in the appendices of books are holdovers to times when computers were not available. These tables give solutions to closed integrals of functions that could not be solved implicitly and required numerical methods to solve. These functions are now included in electronic spreadsheets. When the text references a value available in Appendix A, use the Microsoft Excel templates included on the CD. • Burn-In Optimization—This is a Microsoft Excel template for determining the optimum burn-in duration based on the cost of burn-in time, burn-in failures, and fi eld failures. • Random Number Generator—This Microsoft Excel template generates random numbers that can be used for simulations. There are random number generators for the Weibull, normal, lognormal, and exponential distributions. –vii– A T • Government Documents—This page contains many documents in PDF format. There are numerous military standards and handbooks related to reliability and accelerated testing. • AMSAA Reliability Growth Handbook—This page provides the AMSAA Reliability Growth Handbook in Microsoft Word format. –viii– CONTENTS Chapter 1—Introduction ........................................................................................................... 1 The Purpose of Accelerated Testing .............................................................................1 Design Life ...................................................................................................................2 Statistical Sample Size Determination ......................................................................... 5 Tolerances in Accelerated Testing ................................................................................5 Financial Considerations ..............................................................................................9 Summary ....................................................................................................................17 Chapter 2—Probability Fundamentals ................................................................................... 19 Sampling ....................................................................................................................19 Probability Density Function ..................................................................................... 21 Cumulative Distribution Function ..............................................................................25 Reliability Function ....................................................................................................27 Hazard Function .........................................................................................................27 Expectation .................................................................................................................29 Summary ....................................................................................................................31 Chapter 3—Distributions........................................................................................................ 33 Continuous Modeling Distributions ........................................................................... 33 Weibull Distribution ............................................................................................33 Normal Distribution ............................................................................................39 Lognormal Distribution .......................................................................................46 Exponential Distribution .....................................................................................50 Discrete Modeling Distributions ................................................................................ 55 Poisson Distribution ............................................................................................55 Binomial Distribution ..........................................................................................56 Hypergeometric Distribution ...............................................................................58 Geometric Distribution ........................................................................................60 Identifying the Correct Discrete Distribution ......................................................61 –ix– A T Sampling Distributions ...............................................................................................61 Chi-Square Distribution ......................................................................................62 t-Distribution ....................................................................................................... 64 F-Distribution ...................................................................................................... 66 Bayes’ Theorem ..........................................................................................................68 Summary ....................................................................................................................71 Chapter 4—Parameter Estimation ..........................................................................................73 Maximum Likelihood Estimation .............................................................................. 73 Probability Plotting ....................................................................................................74 Hazard Plotting ...........................................................................................................74 Exponential Distribution ............................................................................................74 Maximum Likelihood Estimation ....................................................................... 75 Hazard Plotting ....................................................................................................79 Probability Plotting.............................................................................................. 80 Normal Distribution ...................................................................................................83 Maximum Likelihood Estimation ....................................................................... 84 Hazard Plotting ....................................................................................................87 Probability Plotting.............................................................................................. 89 Lognormal Distribution ..............................................................................................91
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