Reliability, Life Testing and the Prediction of Service Lives: For Engineers and Scientists
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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. Yet tutorial problems of this nature are virtually never encountered in coursework. 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.Most reliability practitioners will be employed where personal interaction between disciplines is a necessity. A section is included on communication skills to facilitate model selection and formulation based on verifiable assumptions, rather than favorable conclusions. However, whether the answer is "right" can never be ascertained.Past and current applications of stochastic modeling to life-length can only be a guide for future adaptations under different conditions, with new materials in unknown usages. This book unifies the study of cumulative-damage distributions, namely, Wald and Tweedie (i.e., inverse-Gaussian and its reciprocal) with "fatigue-life." These distributions are most useful when the coefficient-of-variation is more appropriate than is the variance as a measure of dispersion. It is shown, uniquely, that the same hyperbolic-sine transformation of each life length variate has a Chi-square one-df distribution. This property is useful in the sample statistics. These IHRA distributions realistically model life-length, strength or duration of load under linear cumulative damage and can be combined as approximations in non-linear situations.Sam C. Saunders has served as a research engineer for 17 years at the Boeing Scientific Research Laboratories, 20 years as a consultant to the Advisory Committee for Nuclear Safeguards, 10 years as a consultant to NIST, was a principal in the consulting firms Mathematical Analysis Research Corporation and Scientific Consulting Service; and was for 26 years a professor of Applied Mathematics/Statistics at Washington State University. He is a Fellow of the American Statistical Association and a former editor of Technometrics.
Preface vAcknowledgements viiGlossary viiiAdmonitions ixRequisites 1Why Reliability Is Important 1Valuable Concepts 3Elements of Reliability 10Properties of Life Distributions 10Useful Parametric Life Distributions 14Partitions and Selection 26Binomial Coefficients and Sterling Numbers 26Lotteries and Coupon Collecting 30Occupancy and Allocations 34Related Concepts 39Coherent Systems 44Functional Representation 44Event-Tree Depiction 50Evaluation of Reliability 53Use of Association to Bound Reliability 60Shape of the Reliability Function 63Diagnostics and Importance of System Components 66Hazard Rates and Polya Frequency Functions 68Closure Properties 69Applicable Life Distributions 75The Gaussian or Normal Distribution 75Epstein's Distribution 77The Galton and Fatigue-Life Distributions 78Discovery and Rediscovery 80Extreme Value Theory and Association 82Philosophy, Science, and Sense 89Likelihood without Priors 89Likelihood for Complete Samples 92Properties of the Likelihood 94Types of Censoring of Data 101Generation of Ordered Observations 105A Parametric Model of Censoring 108The Empirical Cumulative Distribution 111Nonparametric Life Estimators 114The Empiric Survival Distribution 114Expectation and Bias of the K-M Estimator 117The Variance and Mean-Square Error 122The Nelson-Aalen Estimator 124Weibull Analysis 128Distribution of Failure Times for Systems 128Estimation for the Weibull Distribution 128Competing Risks 130Analysis of Censored Data 131Change Points and Multiple Failure Mechanisms 139Examine Data, Diagnose and Consult 148Scientific Idealism 148Consultation and Diagnosis 149Datasets in Service-Life Prediction 151Data, Consulting, and Modeling 157Cumulative Damage Distributions 160The Past as Prologue 160The Fatigue-Life Distribution 162The Mixed Class of Cumulative Damage Distributions 164Elementary Derivation of Means and Variances 166Behavior of the Hazard Rate 168Mixed Variate Relationships 172Estimation for Wald's Distributions 176Estimation for the FL-Distribution 182Estimation for Tweedie's Distribution 187Cases of Misidentification 189Analysis of Dispersion 194Applicability 194Schrodinger's Distribution 195Sample Distributions under Consonance 195Classifications for Dispersion Analysis 206Damage Processes 214The Poisson Process 214Damage Due to Intermittant Shocks 216Renewal Processes 219Shock Models with Varying Intensity 224Stationary Renewal Processes 227The Miner-Palmgren Rule and Additive Damage 229Other Cumulative Damage Processes 232When Linear Cumulative Damage Fails 235Service Life of Structures 240Wear under Spectral Loading 240Multivariate Fatigue Life 241Correlations between Component Damage 248Implementation 253Strength and Durability 258Range of Applicability 258Accelerated Tests for Strength 262Danger of Extrapolation from Tests 266Fracture Mechanics and Stochastic Damage 270Maintenance of Systems 273Introduction 273Availability 273Age Replacement with Renewal 277The Inversion of Transforms 281Problems in Scheduled Maintenance 284Mathematical Appendix 289Integration 289Probability and Measure 291Distribution Transforms 293A Compendium of Discrete Distributions 297A Compendium of Continuous Distributions 298Bibliography 299Index 305
