Mathematical reliability : an expository perspective

Title:

Series:

Kluwer's international series

Publication Information:

Boston : Kluwer Academic Publishers, 2004

ISBN:

9781402076978

Subject Term:

Reliability (Engineering)

Mathematical optimization

Added Author:

Soyer, Refik

Mazzuchi, Thomas A.

Singpurwalla, Nozer D.

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010046538	TS173 M37 2004	Open Access Book	Book	Searching... Unknown

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.

Philip J. Boland and Francisco J. SamaniegoWay Kuo and Rajendra PrasadAndrew W. SwiftElja Arjas and Madhuchhanda BhattacharjeeKjell A. Doksum and Lancelot F. JamesEdsel A. Pena and Myles HollanderNader Ebrahimi and Ehsan S. SoofiVijay N. Nair and Luis A. Escobar and Michael S. HamadaAlyson G. Wilson and C. Shane Reese and Michael S. Hamada and Harry F. MartzHenry W. Block and Thomas H. SavitsUwe Jensen and Fabio SpizzichinoI. Robert Chiang and Lynn KuoSuleyman Ozekici and Refik SoyerJ. D. Lynch and W. J. PadgettSimon P. WilsonNicholas James LynnNozer D. Singpurwalla

Preface	p. ix
Contributing Authors	p. xiii
Part I Networks and Systems
1 The Signature of a Coherent System	p. 3
1.1 Introduction	p. 3
1.2 Related Concepts	p. 10
1.3 Comparison of Systems - Theory	p. 16
1.4 Comparison of Systems - Applications	p. 18
1.5 Discussion and Conclusions	p. 25
2 System Reliability Optimization: An Overview	p. 31
2.1 Introduction	p. 32
2.2 Redundancy Allocation	p. 34
2.3 Optimal Reliability-Redundancy Allocation	p. 41
2.4 Multi-Objective Optimization in Reliability System Design	p. 43
2.5 Optimal Assignment of Components in Coherent Systems	p. 45
2.6 Discussion	p. 47
3 Methods for Assessing Network Reliability	p. 55
3.1 Introduction	p. 55
3.2 Notation and Preliminaries	p. 55
3.3 Probability Measures for Component Reliability	p. 57
3.4 Identical Components and Borel's Paradox	p. 60
3.5 Calculating the Reliability of Networks with Unknown Structures	p. 61
3.6 Networks with Cascading Failures	p. 65
Part II Recurrent Events
4 Modelling Heterogeneity: Hierarchical Bayesian Approach	p. 71
4.1 Introduction	p. 72
4.2 Illustration 1: Valve Failures in Nuclear Power Plants	p. 74
4.3 Illustration 2: Repeated Occurrence of Relapses	p. 79
4.4 Concluding Remarks	p. 82
5 Spatial Neutral to the Right Processes	p. 87
5.1 Introduction	p. 88
5.2 NTR, Levy and Other Processes	p. 88
5.3 Spatial Neutral to the Right Process	p. 91
5.4 Total Time on Test Transform	p. 99
6 Models for Recurrent Events in Reliability and Survival Analysis	p. 105
6.1 Introduction	p. 105
6.2 Mathematical Framework	p. 107
6.3 Existing Models	p. 108
6.4 A New Class of Models	p. 112
6.5 Statistical Identifiability Issue	p. 118
Part III Information and Design
7 Information Functions for Reliability	p. 127
7.1 Introduction	p. 127
7.2 Discrimination Information Function	p. 128
7.3 Entropy	p. 137
7.4 Mutual Information	p. 141
7.5 Information in Residual Lifetime	p. 147
7.6 Information Statistics	p. 150
8 Experiments for Reliability Assessment and Improvement	p. 161
8.1 Introduction	p. 162
8.2 Accelerated Testing for Reliability Assessment	p. 163
8.3 Reliability Improvement	p. 168
8.4 Reliability Assessment and Improvement with Degradation Data	p. 174
9 Analysis of Computer and Physical Experimental Life Time Data	p. 183
9.1 Introduction	p. 184
9.2 The Basics of Data Integration Using RBHM	p. 186
9.3 Ball Bearing Example	p. 189
9.4 Conclusions	p. 190
Part IV The Failure Rate Function and Burn-in
10 The Shape of Failure Rate Mixtures	p. 197
10.1 Introduction	p. 197
10.2 Limiting Failure Rates of Mixtures	p. 199
10.3 Limiting Monotonicities of Failure Rates of Mixtures	p. 200
10.4 Anomalies	p. 202
10.5 Mixtures of Linear Failure Rates	p. 203
10.6 Mixtures of Additive and Multiplicative Failure Rates	p. 204
10.7 Related Results on Bathtub Shape	p. 204
11 Burn-in-Sequential Stop and Go Strategies	p. 207
11.1 Introduction	p. 207
11.2 Sequential Burn-in for Different Components with Independent Life-times	p. 210
11.3 Sequential Burn-in for Similar Components with Dependent Life-times	p. 218
Part V Software Reliability and Random Environments
12 Managing Software Development Process	p. 233
12.1 Introduction	p. 233
12.2 Background	p. 235
12.3 Incremental Development Concept	p. 235
12.4 Derivation of the Basic Coordination Policy	p. 236
12.5 Incremental Development under the Effect of System Size Growth	p. 240
12.6 Conclusion	p. 244
13 Reliability Modeling and Analysis in Random Environments	p. 249
13.1 Introduction and Overview	p. 249
13.2 Continuous Time Models with Intrinsic Aging	p. 252
13.3 Continuous Time Models in Software Reliability Engineering	p. 255
13.4 Discrete Time Models	p. 262
Part VI Reliability in Composites and Orthopedics
14 Failure of Brittle Fibers and Composites	p. 277
14.1 Introduction	p. 277
14.2 Failure Rate Properties of Strength Distributions of Load-Sharing Systems	p. 279
14.3 Cumulative Damage Models and Inference Procedures	p. 281
14.4 Examples: Tensile Strength of Materials	p. 285
15 Modeling the Reliability of Hip Replacements	p. 291
15.1 Introduction	p. 291
15.2 Data and a Model	p. 292
15.3 Model Fitting and Checking	p. 293
15.4 Reliability Prediction	p. 296
15.5 Conclusions	p. 299
Part VII Reliability in Finance and Forensics
16 The Price of Failure	p. 303
16.1 Introduction	p. 303
16.2 Financial Fundamentals	p. 304
16.3 Parameter Estimation	p. 306
16.4 Derivatives	p. 307
16.5 Application of Reliability Models	p. 311
17 Warranty: A Surrogate of Reliability	p. 317
17.1 Introduction: Terminology	p. 317
17.2 Equilibrium Probabilities and "Just" Warranties	p. 318
17.3 Failure Models Indexed by Time and Usage	p. 324
17.4 Forecasting Financial Reserves for Warranty Claims	p. 327
17.5 Summary and Conclusions	p. 330

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