Table Of ContentDesign and
Analysis
of Accelerated
Tests for
Mission Critical
Reliability
Michael J. LuValle
Bruce G. Lefevre
SriRaman Kannan
CHAPMAN & HALL/CRC
A CRC Press Company
Boca Raton London New York Washington, D.C.
© 2004 by CRC Press, LLC
C4711_C00.fm Page ii Monday, March 29, 2004 10:54 AM
Library of Congress Cataloging-in-Publication Data
LuValle, Michael.
Design and analysis of accelerated tests for mission critical reliability / by Michael
LuValle, Bruce G. Lefevre, SriRaman Kannan.
p. cm.
Includes bibliographical references and index.
ISBN 1-58488-471-1 (alk. paper)
1. Accelerated life testing. 2. Reliability (Engineering) I. Lefevre, Bruce G. II. Kannan,
SriRaman. III. Title.
TA169.3.L88 2004
620'.00452--dc22
2003069580
This book contains information obtained from authentic and highly regarded sources. Reprinted material
is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable
efforts have been made to publish reliable data and information, but the author and the publisher cannot
assume responsibility for the validity of all materials or for the consequences of their use.
Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic
or mechanical, including photocopying, microfilming, and recording, or by any information storage or
retrieval system, without prior permission in writing from the publisher.
The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for
creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC
for such copying.
Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are
used only for identification and explanation, without intent to infringe.
Visit the CRC Press Web site at www.crcpress.com
© 2004 by CRC Press LLC
No claim to original U.S. Government works
International Standard Book Number 1-58488-471-1
Library of Congress Card Number 2003069580
Printed in the United States of America 1 2 3 4 5 6 7 8 9 0
Printed on acid-free paper
© 2004 by CRC Press, LLC
C4711_C00.fm Page iii Monday, March 29, 2004 10:54 AM
Preface
In the early days of accelerated testing, the method was touted as a way to
compress years of use into days of testing. The practitioner subjected the
device to “higher” stress than it would see in operation, and time was
compressed in a nice, predictable fashion, with the parameters the only thing
left to be determined. Most statistical theory for accelerated testing is built
around this kind of assumption.
Although the simplest physical model does have this form, the simplest
physical model does not always hold. Thus, we need to understand what
the more complex physical models may look like and how to model them.
Further, with the direction certain branches of engineering are taking, new
devices made from new materials are being put in mission-critical applica-
tions. Failure is not tolerable over a 20-year life, so what can an accelerated
test say in such a situation?
The purpose of this book is to provide theory and tools necessary to attack
these problems. The theory is an integration of chemical kinetics and statis-
tics aimed particularly at designing accelerated tests and modeling the
results (sudden failure, smooth degradation, and no response at all). The
tools include both general approaches that can be implemented in the vari-
ous computational tools available and an explicit computing environment
written in Splus®.
The theory and tools we provide here are not the final word; however,
they are useful, and have been used for years by one author to support
mission-critical application. They are an opening salvo in an attack on the
problem of extrapolation.
For the practitioner, there are several practical tools and examples pro-
vided. For the teacher and student, exercises are scattered throughout the
text. For researchers, open questions abound and the software (provided as
free source code in Splus) can certainly be improved.
We wish you luck and hope you find this as useful as we have.
© 2004 by CRC Press, LLC
C4711_C00.fm Page v Monday, March 29, 2004 10:54 AM
Authors
Michael J. LuValle, Ph.D., received his doctorate from the Division of Sta-
tistics at the University of California at Davis and started his professional
career as an assistant professor at Kansas State University. He moved to
AT&T Bell Laboratories in 1984, which is where he started seriously address-
ing the problem of extrapolation of acceleration tests. He is at present a
member of OFS Laboratories in the materials, processes, and reliability
research group. His formal background is in mathematical statistics, but he
has worked primarily at the interface of statistics and the physical sciences.
He has authored or co-authored a number of publications and invited talks
in this area.
Dr. LuValle, through the graces of Dr. Lefevre, has recently become
involved in the development of standards for reliability.
Bruce G. Lefevre, Ph.D., received his doctorate from the University of Flor-
ida and is a former professor on the faculty of the Georgia Institute of
Technology. He has served on the technical staff of Bell Laboratories, AT&T,
and Lucent Technologies and is at present a consultant to OFS on fiber-optic
passive components. His technical background is in materials and passive
optical component design, testing, reliability, and standards. He has
authored or co-authored more than 30 technical publications and articles on
these subjects.
Dr. Lefevre is Chairman of IEC SC86B (Fiber Optic Interconnecting Devices
and Passive Components), Co-chair of TIA FO-4.3.3 (Working Group on
Reliability of Fiber Optic Interconnecting Devices and Passive Components),
and a member of the U.S. Technical Advisory Groups to IEC TC86 (Fiber
Optics) and SC86B. He has participated in the drafting, editing, and publi-
cation of numerous standards on design, testing, and performance of passive
fiber optic components.
SriRaman Kannan, Ph.D., obtained his Bachelor of Technology from the
Indian Institute of Technology (IIT–Bombay) in 1988 and Ph.D. from Rutgers
University in 1994. Following a year of U.S. Department of Energy post-
doctoral fellowship (1994–1995), he joined AT&T Bell Labs in 1995. Dr. Kan-
nan has since held the positions of Member of Technical Staff and Technical
Manager. At present he is a reliability specialist at the Government Commu-
nications Division of Bell Laboratories, Lucent Technologies.
Over the years, Dr. Kannan has worked on diverse issues pertaining to
optical fibers, components, and devices such as thermal stability of fiber
gratings, radiation effects on glasses, and hydrogen-induced effects in rare
© 2004 by CRC Press, LLC
C4711_C00.fm Page vi Monday, March 29, 2004 10:54 AM
earth-doped fibers. He has developed and executed qualification plans for
several state-of-the-art telecommunication components and devices, includ-
ing different types of specialty fibers, gratings, fiber lasers and amplifiers,
Raman resonators, and optical channel monitors.
Dr. Kannan has authored more than 25 publications and has made extensive
presentations including invited talks in industry forums. He is also involved
with standards work as a participant of IEC 86B, working group 5 (Reliability
of Fiber Optic Interconnecting Devices and Passive Components).
© 2004 by CRC Press, LLC
C4711_C00.fm Page vii Monday, March 29, 2004 10:54 AM
Acknowledgments
To my twin boys, Brian and Connor, whose impending birth has certainly
presented an immovable deadline for finishing this work, my wife Rosemarie
DiDomenico, who has supported me throughout the long years of this work,
Aspen LuValle for his sage counsel, and my management and colleagues
who have provided encouragement and an environment in which the
research presented here could be done: J.P. Mitchell, T.L. Welsher, K. Svo-
boda, H.M. Cohen, W. Lambert, P. Ward, L. Hines, L. Chan, D. Klinger, V.N.
Nair, J. Chambers, C. Mallows, W. Joyce, F. Nash, R.L. Easton, J. Hooper, M.
Carey, M. Tortorella, J. Aspell, P. Lemaire, D. Sinclair, R. Opila, R. Fran-
kenthal, B. Eggleton, K. Walker, D. DiGiovanni, J. Abate, R. Ahrens, J. Jacques,
J. LeGrange, L. Reith, L. Braun, E. Vogel, L. Copeland, and J. Mrotek, all from
the Bell Labs/OFS Labs in its various incarnations; and W.Q. Meeker, J.
Lawless, W. Nelson, and C.J. Wu, who have provided encouragement from
outside.
Michael J. LuValle
To my wife, Sandy, who has indulged me in all manner of things including
this enterprise.
Bruce G. Lefevre
To my supportive family, fellow authors, and numerous colleagues who
rendered work fun over the years.
SriRaman Kannan
© 2004 by CRC Press, LLC
C4711_C00.fm Page ix Monday, March 29, 2004 10:54 AM
Contents
1. Background
1.1 Introduction
1.2 Other Approaches
1.3 Foundation of Our Approach
1.4 A Simple Example
1.5 Organization of This Book
1.6 Complement: Background Kinetics and Statistics
1.6.1 Arrhenius and Relative Humidity Models
1.6.2 First-Order Kinetics
1.6.3 Binomial Distribution and Its Role in Reliability
1.6.4 Inference for the Binomial Distribution
1.6.5 Splus Source Code for Matrix Exponentiation
2. Demarcation Mapping: Initial Design of Accelerated Tests
2.1 Analytical Theory of Thermal Demarcation Maps
2.2 Designing an Acceptance Test for a Purely Thermal Process
2.3 Simple Temperature/Humidity Models
2.4 Designing an Acceptance Test for a Temperature/Humidity
Model
2.5 Mechanical Cycling Models
2.6 Acceptance Testing for Mechanical Cycling Induced
by Thermal Cycling
2.7 Computational Demarcation Mapping
2.8 Beta Binomial Interpretation of 0 Failures
2.9 An Extrapolation Theorem
2.10 Summary
2.11 Complements to Chapter 2
2.11.1 Demarcation Maps for Multiple Experiments
2.11.2 Using the Freeware
2.11.2.1 Thermal Demarcation Maps
2.11.2.2 Temperature/Humidity Demarcation Maps
2.11.2.3 Mechanical Cycling Demarcation Maps
3. Interface for Building Kinetic Models
3.1 Description and Concepts behind the Interface
3.2 Complement to Chapter 3: Our Interface in Splus, Kinetic
Data Objects, and the GUIs to Create Them
3.2.1 Creating Components of the Kinetic Model
3.2.1.1 Discrete Diffusion
© 2004 by CRC Press, LLC
C4711_C00.fm Page x Monday, March 29, 2004 10:54 AM
3.2.1.2 Creep
3.2.1.3 Stress Voiding
3.2.1.4 One-Step Process
3.2.1.5 One Step with Second Variable
3.2.1.6 One Step with Stress
3.2.1.7 One Step with Second Variable and Stress
3.2.1.8 Glassy One Step
3.2.2 Combining Submodels
3.2.2.1 Competing Reactions
3.2.2.2 Mixing Reactions
3.2.2.3 Reversible Reactions
3.2.2.4 Rejoining Reactions
3.2.2.5 Sequential Reactions
3.2.2.6 Simple Connection of Internal States
3.2.3 Computational Demarcation Map Example
from Chapter 2
4. Evanescent Process Mapping
4.1 Building Blocks for the Theory
4.1.1 Model Neighborhoods
4.1.2 Risk Orthogonality
4.1.3 Model Enumeration
4.1.4 Integrating the Theory
4.2 Identifying Neighborhoods of Models, Sampling, and
“Chunking”
4.3 Example
4.4 Summary, Limitations of Accelerated Testing
4.5 Complement to Chapter 4: Using the Evanescent Process
Mapping Interface to Duplicate Example 4.3
5. Data Analysis for Failure Time Data
5.1 A Simple Data Set
5.2 Adding Physical Sense to the Model
5.3 Analysis of a Real Data Set
5.3.1 Summary
5.4 Complement: Maximum Likelihood Analysis
5.4.1 Law of Large Numbers
5.4.2 Central Limit Theorem
5.4.3 Proof of Consistency of Maximum Likelihood
5.4.4 Derivation of the Distribution of the Maximum
Likelihood Estimator
5.4.5 Splus Source Code
5.5 Complement: Statistical Estimation of Kinetics from
Failure Time Data
5.6 Complement: Pseudo-Maximum Likelihood Estimation
5.7 Complement: The Kaplan–Meier Estimate
© 2004 by CRC Press, LLC
C4711_C00.fm Page xi Monday, March 29, 2004 10:54 AM
5.8 Complement: Printed Wiring Board Data
5.9 Complement: Using the Interface
5.10 Complement: Exercises to Explore Some Questions
in Experiment Design
Problem 5.10.1
Problem 5.10.2
Problem 5.10.3
Hints for Problem 5.10.1
Hint for Problem 5.10.2
Hints for Problem 5.10.3
6. Data Analysis for Degradation Data
6.1 Motivation and Models
6.2 Background for the Example
6.3 Data Analysis for the Example
6.4 Complement: Background Statistical Theory
6.4.1 Linear Regression and Results
6.4.2 Extension to Nonlinear Regression
6.4.3 Extension to an Uncertain Starting Time Model
6.4.4 Prediction Uncertainty and Asymptotic Relative
Efficiency
6.5 Complement: Using the Software to Analyze the Example
Data
6.6 Complement: Exercises for Data Analysis and Experiment
Design
References
Appendix: Installing the Software
© 2004 by CRC Press, LLC
