## Mathematical Models for Systems ReliabilityEvolved from the lectures of a recognized pioneer in developing the theory of reliability, Mathematical Models for Systems Reliability provides a rigorous treatment of the required probability background for understanding reliability theory. This classroom-tested text begins by discussing the Poisson process and its associated probability |

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### Contents

1 | |

Statistical life length distributions | 39 |

Reliability of various arrangements of units | 63 |

Reliability of a oneunit repairable system | 91 |

Reliability of a twounit repairable system | 101 |

Continuoustime Markov chains | 117 |

First passage time for systems reliability | 143 |

Embedded Markov chains and systems reliability | 173 |

Integral equations in reliability theory | 207 |

247 | |

251 | |

### Other editions - View all

Mathematical Models for Systems Reliability Benjamin Epstein,Ishay Weissman No preview available - 2008 |

### Common terms and phrases

active unit assumed Bernoulli trials Chapter common c.d.f. compute conditional probability constant failure rate Continuation of Problem denoted device discrete random variable distributed with mean distributed with p.d.f. duty interval embedded Markov chain event Example exponentially distributed failed unit failure c.d.f. Find follows given hazard function Hence homogeneous Poisson process integral equations Laplace transform Laplace-Stieltjes transform large number length Markov process mean first passage n-unit number of failures o(At observed obtained one-unit repairable system parameter Pi(t Pij(t Problems for Section Prove rates diagram rates matrix readily verified renewal process repair distribution repair rate repairman replaced semi-Markov process series-parallel Show statistic steady-state probabilities stochastic process subsystems sufficient statistic Suppose survives switches system availability system consisting system failure occurs system is initially system reliability T)dt transition probabilities matrix transitions and rates two-unit repairable system UMVUE unbiased estimator variance Weibull distribution