Reliability, Life Testing and the Prediction of Service Lives: For Engineers and Scientists

Reliability, Life Testing and the Prediction of Service Lives: For Engineers and Scientists

by Sam C. Saunders


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This book is intended for students and practitioners who have had a calculus-based statistics course and who have an interest in safety considerations such as reliability, strength, and duration-of-load or service life. Many persons studying statistical science will be employed professionally where the problems encountered are obscure, what should be analyzed is not clear, the appropriate assumptions are equivocal, and data are scant. In this book there is no disclosure with many of the data sets what type of investigation should be made or what assumptions are to be used.

Product Details

ISBN-13: 9780387325224
Publisher: Springer New York
Publication date: 01/25/2007
Series: Springer Series in Statistics
Edition description: 2007
Pages: 308
Product dimensions: 6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Preface     v
Acknowledgements     vii
Glossary     viii
Admonitions     ix
Requisites     1
Why Reliability Is Important     1
Valuable Concepts     3
Elements of Reliability     10
Properties of Life Distributions     10
Useful Parametric Life Distributions     14
Partitions and Selection     26
Binomial Coefficients and Sterling Numbers     26
Lotteries and Coupon Collecting     30
Occupancy and Allocations     34
Related Concepts     39
Coherent Systems     44
Functional Representation     44
Event-Tree Depiction     50
Evaluation of Reliability     53
Use of Association to Bound Reliability     60
Shape of the Reliability Function     63
Diagnostics and Importance of System Components     66
Hazard Rates and Polya Frequency Functions     68
Closure Properties     69
Applicable Life Distributions     75
The Gaussian or Normal Distribution     75
Epstein's Distribution     77
The Galton and Fatigue-Life Distributions     78
Discovery and Rediscovery     80
Extreme Value Theory and Association     82
Philosophy, Science, and Sense     89
Likelihood without Priors     89
Likelihood for Complete Samples     92
Properties of the Likelihood     94
Types of Censoring of Data     101
Generation of Ordered Observations     105
A Parametric Model of Censoring     108
The Empirical Cumulative Distribution     111
Nonparametric Life Estimators     114
The Empiric Survival Distribution     114
Expectation and Bias of the K-M Estimator     117
The Variance and Mean-Square Error     122
The Nelson-Aalen Estimator     124
Weibull Analysis     128
Distribution of Failure Times for Systems     128
Estimation for the Weibull Distribution     128
Competing Risks     130
Analysis of Censored Data     131
Change Points and Multiple Failure Mechanisms     139
Examine Data, Diagnose and Consult     148
Scientific Idealism     148
Consultation and Diagnosis     149
Datasets in Service-Life Prediction     151
Data, Consulting, and Modeling      157
Cumulative Damage Distributions     160
The Past as Prologue     160
The Fatigue-Life Distribution     162
The Mixed Class of Cumulative Damage Distributions     164
Elementary Derivation of Means and Variances     166
Behavior of the Hazard Rate     168
Mixed Variate Relationships     172
Estimation for Wald's Distributions     176
Estimation for the FL-Distribution     182
Estimation for Tweedie's Distribution     187
Cases of Misidentification     189
Analysis of Dispersion     194
Applicability     194
Schrodinger's Distribution     195
Sample Distributions under Consonance     195
Classifications for Dispersion Analysis     206
Damage Processes     214
The Poisson Process     214
Damage Due to Intermittant Shocks     216
Renewal Processes     219
Shock Models with Varying Intensity     224
Stationary Renewal Processes     227
The Miner-Palmgren Rule and Additive Damage     229
Other Cumulative Damage Processes     232
When Linear Cumulative Damage Fails     235
Service Life of Structures     240
Wear under Spectral Loading     240
Multivariate Fatigue Life     241
Correlations between Component Damage     248
Implementation     253
Strength and Durability     258
Range of Applicability     258
Accelerated Tests for Strength     262
Danger of Extrapolation from Tests     266
Fracture Mechanics and Stochastic Damage     270
Maintenance of Systems     273
Introduction     273
Availability     273
Age Replacement with Renewal     277
The Inversion of Transforms     281
Problems in Scheduled Maintenance     284
Mathematical Appendix     289
Integration     289
Probability and Measure     291
Distribution Transforms     293
A Compendium of Discrete Distributions     297
A Compendium of Continuous Distributions     298
Bibliography     299
Index     305

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