Advances in Mathematical Modeling for Reliability discusses fundamental issues on mathematical modeling in reliability theory and its applications. Beginning with an extensive discussion of graphical modeling and Bayesian networks, the focus shifts towards repairable systems: a discussion about how sensitive availability calculations parameter choices, and emulators provide the potential to perform such calculations on complicated systems to a fair degree of accuracy and in a computationally efficient manner. Another issue that is addressed is how competing risks arise in reliability and maintenance analysis through the ways in which data is censored. Mixture failure rate modeling is also a point of discussion, as well as the signature of systems, where the properties of the system through the signature from the probability distributions on the lifetime of the components are distinguished. The last three topics of discussion are relations among aging and stochastic dependence, theoretical advances in modeling, inference and computation, and recent advances in recurrent event modeling and inference.
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Author(s): Lesley Walls, Babakalli Alkali, Tim Bedford, John Quigley, Alireza Daneshkhah
Publisher: IOS Press
Year: 2008
Language: English
Pages: 249
Cover......Page 1
Title page......Page 2
Introduction......Page 6
Contents......Page 10
Bayesian Networks in Reliability: The Good, the Bad, and the Ugly......Page 12
Mixed Non-Parametric Continuous and Discrete Bayesian Belief Nets......Page 20
A Dynamic Graphical Model to Represent Complex Survival Distributions......Page 28
Network Reliability Evaluation with Propositional Directed Acyclic Graphs......Page 36
Some Properties of Incomplete Repair and Maintenance Models......Page 43
On Models of Degradation and Partial Repairs......Page 50
Sensitivity Analysis of a Reliability System Using Gaussian Processes......Page 57
On Independence of Competing Risks......Page 74
Bivariate Competing Risks Models Under Masked Causes of Failure......Page 83
Competing Risks in Repairable Systems......Page 91
Conditionally Independent Generalized Competing Risks for Maintenance Analysis......Page 99
Asymptotic Properties of Bivariate Competing Risks Models......Page 107
On the Reversed Hazard Rate and Mean Inactivity Time of Mixtures......Page 114
Bounds on Lifetimes of Coherent Systems with Exchangeable Components......Page 122
On the Signature of Coherent Systems and Applications for Consecutive k-out-of-n:F Systems......Page 130
The Use of Stochastic Precedence in the Comparison of Engineered Systems......Page 140
The Role of Signature and Symmetrization for Systems with Non-Exchangeable Components......Page 149
Generalized Marshall-Olkin Models: Aging and Dependence Properties......Page 160
New Multivariate IFR and DMRL Notions for Exchangeable Dependent Components......Page 169
Advances in Bayesian Software Reliability Modeling......Page 176
Signed Domination of Oriented Matroid Systems......Page 188
Nonparametric Predictive Inference for k-out-of-m Systems......Page 196
Some Aspects Pertaining to Recurrent Event Modeling and Analysis......Page 204
Sensitivity Estimates in Dynamic Reliability......Page 219
Renewal Theory with Discounting......Page 228
Point Estimation of the Transition Intensities for a Markov Multi-State System via Output Performance Observation......Page 238
Keyword Index......Page 246
Author Index......Page 248
