Accelerated testing : statistical models, test plans and data analyses

626 Pages·1990·31.115 MB·English

by  Wayne Nelson

Accelerated Testing
Statistical Models, Test Plans,
and Data Analyses
WAYNE NELSON
Consultant, Schenectady, NY

A JOHN WILEY & SONS, INC., PUBLICATION
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Accelerated Testing
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Accelerated Testing
Statistical Models, Test Plans,
and Data Analyses
WAYNE NELSON
Consultant, Schenectady, NY

A JOHN WILEY & SONS, INC., PUBLICATION
Copyright 0 1990,2004 by John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
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ISBN 0-47 1-69736-2

Printed in the United States of America.
I 0 9 8 7 6 5 4 3 2 1
This book is gratefully dedicated to the many clients whose fruitful
collaboration and challenging applications stimulated my interest and
developments in accelerated testing, and to the many colleagues who kindly
provided me with examples, references, suggestions, and encouragement.
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Contents
Preface, xi
1. Introduction and Background, 1
Survey Methodology and Applications, 3
1. of
Types Data,
2. of 12
Types Acceleration and Stress Loading,
3. of 15
Engineering Considerations,
4. 22
Common Accelerated Tests,
5. 37
Statistical Considerations,
6. 43
Problems,
49
2. Models for Ufe Tests with Constant Stress, 51
Introduction,
1. 51
Basic Concepts and the Exponential Distribution,
2. 53
Normal Distribution,
3. 58
Lognormal Distribution, 60
4.
Weibull Distribution,
5. 63
Extreme Value Distribution, 65
6.
Other Distributions,
7. 68
Life-Stress Relationships,
8. 71
9. Arrhenius Life-Temperature Relationship,
75
Inverse Power Relationship, 85
10.
Endurance (Fatigue) Limit Relationships and Distributions,
11. 92
Other Single Stress Relationships, 95
12.
13. Multi variable Relationships, 98
Spread Life Depends on Stress,
14. in Log 105
Problems,
107
3. Graphical Data Analysis, 113
Introduction,
1. 113
Complete Data and Arrhenius-Lognormal Model,
2. 114
Complete Data and Power-Weibull Model,
3. 128
Singly Censored Data,
4. 134
vii
viii CONTENTS
5. Multiply Censored Data, 139
6. Interval (Read-Out) Data, 145
Problems, 154
4. Complete Data and Least Squares Analyses, 167
1. Introduction, 167
2. Least-Squares Methods for Lognormal Life, 170
3. Checks on the Linear-Lognormal Model and Data, 182
4. Least-Squares Methods for Weibull and Exponential Life, 189
5. Checks the Linear-Weibull Model and Data, 203
on
6. Multivariable Relationships, 210
Problems, 229
5. Censored Data and Maximum Ukelihood Methods, 233
1. Introduction to Maximum Likelihood, 234
2. Fit the Simple Model to Right Censored Data, 242
3. Assess the Simple Model and Right Censored Data, 255
4. Other Models and w e so f Data, 265
5. Maximum Likelihood Calculations, 284
Problems, 302
6. Test Plans, 317
1. Plans for the Simple Model and Complete Data, 317
2. Plans for the Simple Model and Singly Censored Data, 328
3. Evaluation of a Test Plan by Simulation, 349
4. Survey of Test Plans, 361
5. ML Theory for Test Plans,
364
Problems, 371
7. Competing Failure Modes and Size Effect, 377
1. Series-System Model, 378
2. Series Systems of Identical Parts, 383
3. Size Effect, 385
4. Nonuniform Stress, 387
5. Graph ical Analysis, 392
6. ML Analysis for Competing Failure Modes, 407
7. ML Theory for Competing Modes, 413
Problems, 417
8. Least-Squares Comparisons for Complete Data, 425
1. Hypothesis Tests and Confidence Intervals, 426
2. Graphical Comparisons, 429
3. Compare Log Standard Deviations, 434
4. Compare Means, 437
(Log)
5. Compare Simple Relationships, 441