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Mathematical Reliability : An Expository Perspective - Refik Soyer

Mathematical Reliability

An Expository Perspective

By: Refik Soyer (Editor), Thomas A. Mazzuchi (Editor), Nozer D. Singpurwalla (Editor)

Hardcover Published: 31st December 2003
ISBN: 9781402076978
Number Of Pages: 333

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In this volume consideration was given to more advanced theoretical approaches and novel applications of reliability to ensure that topics having a futuristic impact were specifically included. Topics like finance, forensics, information, and orthopedics, as well as the more traditional reliability topics were purposefully undertaken to make this collection different from the existing books in reliability. The entries have been categorized into seven parts, each emphasizing a theme that seems poised for the future development of reliability as an academic discipline with relevance. The seven parts are networks and systems; recurrent events; information and design; failure rate function and burn-in; software reliability and random environments; reliability in composites and orthopedics, and reliability in finance and forensics. Embedded within the above are some of the other currently active topics such as causality, cascading, exchangeability, expert testimony, hierarchical modeling, optimization and survival analysis. These topics, when linked with utility theory, constitute the science base of risk analysis.

Prefacep. ix
Contributing Authorsp. xiii
Networks and Systems
The Signature of a Coherent Systemp. 3
Introductionp. 3
Related Conceptsp. 10
Comparison of Systems - Theoryp. 16
Comparison of Systems - Applicationsp. 18
Discussion and Conclusionsp. 25
System Reliability Optimization: An Overviewp. 31
Introductionp. 32
Redundancy Allocationp. 34
Optimal Reliability-Redundancy Allocationp. 41
Multi-Objective Optimization in Reliability System Designp. 43
Optimal Assignment of Components in Coherent Systemsp. 45
Discussionp. 47
Methods for Assessing Network Reliabilityp. 55
Introductionp. 55
Notation and Preliminariesp. 55
Probability Measures for Component Reliabilityp. 57
Identical Components and Borel's Paradoxp. 60
Calculating the Reliability of Networks with Unknown Structuresp. 61
Networks with Cascading Failuresp. 65
Recurrent Events
Modelling Heterogeneity: Hierarchical Bayesian Approachp. 71
Introductionp. 72
Illustration 1: Valve Failures in Nuclear Power Plantsp. 74
Illustration 2: Repeated Occurrence of Relapsesp. 79
Concluding Remarksp. 82
Spatial Neutral to the Right Processesp. 87
Introductionp. 88
NTR, Levy and Other Processesp. 88
Spatial Neutral to the Right Processp. 91
Total Time on Test Transformp. 99
Models for Recurrent Events in Reliability and Survival Analysisp. 105
Introductionp. 105
Mathematical Frameworkp. 107
Existing Modelsp. 108
A New Class of Modelsp. 112
Statistical Identifiability Issuep. 118
Information and Design
Information Functions for Reliabilityp. 127
Introductionp. 127
Discrimination Information Functionp. 128
Entropyp. 137
Mutual Informationp. 141
Information in Residual Lifetimep. 147
Information Statisticsp. 150
Experiments for Reliability Assessment and Improvementp. 161
Introductionp. 162
Accelerated Testing for Reliability Assessmentp. 163
Reliability Improvementp. 168
Reliability Assessment and Improvement with Degradation Datap. 174
Analysis of Computer and Physical Experimental Life Time Datap. 183
Introductionp. 184
The Basics of Data Integration Using RBHMp. 186
Ball Bearing Examplep. 189
Conclusionsp. 190
The Failure Rate Function and Burn-in
The Shape of Failure Rate Mixturesp. 197
Introductionp. 197
Limiting Failure Rates of Mixturesp. 199
Limiting Monotonicities of Failure Rates of Mixturesp. 200
Anomaliesp. 202
Mixtures of Linear Failure Ratesp. 203
Mixtures of Additive and Multiplicative Failure Ratesp. 204
Related Results on Bathtub Shapep. 204
Burn-in-Sequential Stop and Go Strategiesp. 207
Introductionp. 207
Sequential Burn-in for Different Components with Independent Life-timesp. 210
Sequential Burn-in for Similar Components with Dependent Life-timesp. 218
Software Reliability and Random Environments
Managing Software Development Processp. 233
Introductionp. 233
Backgroundp. 235
Incremental Development Conceptp. 235
Derivation of the Basic Coordination Policyp. 236
Incremental Development under the Effect of System Size Growthp. 240
Conclusionp. 244
Reliability Modeling and Analysis in Random Environmentsp. 249
Introduction and Overviewp. 249
Continuous Time Models with Intrinsic Agingp. 252
Continuous Time Models in Software Reliability Engineeringp. 255
Discrete Time Modelsp. 262
Reliability in Composites and Orthopedics
Failure of Brittle Fibers and Compositesp. 277
Introductionp. 277
Failure Rate Properties of Strength Distributions of Load-Sharing Systemsp. 279
Cumulative Damage Models and Inference Proceduresp. 281
Examples: Tensile Strength of Materialsp. 285
Modeling the Reliability of Hip Replacementsp. 291
Introductionp. 291
Data and a Modelp. 292
Model Fitting and Checkingp. 293
Reliability Predictionp. 296
Conclusionsp. 299
Reliability in Finance and Forensics
The Price of Failurep. 303
Introductionp. 303
Financial Fundamentalsp. 304
Parameter Estimationp. 306
Derivativesp. 307
Application of Reliability Modelsp. 311
Warranty: A Surrogate of Reliabilityp. 317
Introduction: Terminologyp. 317
Equilibrium Probabilities and "Just" Warrantiesp. 318
Failure Models Indexed by Time and Usagep. 324
Forecasting Financial Reserves for Warranty Claimsp. 327
Summary and Conclusionsp. 330
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9781402076978
ISBN-10: 1402076975
Series: International Operations Research & Management Science
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 333
Published: 31st December 2003
Publisher: SPRINGER VERLAG GMBH
Country of Publication: US
Dimensions (cm): 24.23 x 16.36  x 2.69
Weight (kg): 0.75

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