## Advances in Mathematical Modeling for ReliabilityAdvances 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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### Contents

Graphical Modeling and Bayesian Networks | 1 |

Repairable Systems Modeling | 32 |

Competing Risks | 63 |

Mixture Failure Rate Modeling | 96 |

Signature | 111 |

Relations Among Aging and Stochastic Dependence | 149 |

Theoretical Advances in Modeling Inference and Computation | 165 |

Recent Advances in Recurrent Event Modeling and Inference | 193 |

Point Estimation of the Transition Intensities for a Markov MultiState System via Output Performance Observation | 227 |

235 | |

237 | |

### Other editions - View all

Advances in Mathematical Modeling for Reliability T. Bedford,J. Quigley,L. Walls Limited preview - 2008 |

### Common terms and phrases

2008 The authors aging notions Applied approach assume assumption asymptotic authors and IOS Bayesian Networks bivariate aging censoring coherent systems competing risks model components computation conditional consecutive k-out-of-n:F system consider copula corresponding defined denote density dependence discrete distribution function estimate example exchangeable exponential exponential discounting exponential distribution failure rate Figure Gaussian process given hazard rate hyperbolic discounting independent inference intensity inter-event IOS Press Kijima Lemma lifetimes likelihood likelihood function lower and upper main effects maintenance actions marginal distributions Markov chain method mixture multivariate node nonparametric observed obtained order statistics oriented matroid paper parameters PDAG Poisson process posterior distribution random variables rank correlation repairable systems respect reversed hazard rate Rychlik Samaniego sample Section sensitivity analysis Spizzichino stochastic precedence survival function testing Theorem tion transition upper probabilities variance virtual age Weibull Weibull distributions