## Proceedings of the International School of Physics "Enrico Fermi". |

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Page 13

A useful property holds for distributions with

Let F be IFE. Let J^z) < 1. Then F is absolutely continuous on (— 00,2); that is F

has a probability density on (— 00, z). Proof. Let B(z) = — log F(z) denote the ...

A useful property holds for distributions with

**monotone**failure rate. 1.1. Theorem.Let F be IFE. Let J^z) < 1. Then F is absolutely continuous on (— 00,2); that is F

has a probability density on (— 00, z). Proof. Let B(z) = — log F(z) denote the ...

Page 43

Then from (4.3) with pi = eT, we find that #e(t) = = 1o eDaVaa{r)]<> is completely

hence sr(r) as well. This then implies that for systems with independent

memoryless ...

Then from (4.3) with pi = eT, we find that #e(t) = = 1o eDaVaa{r)]<> is completely

**monotone**. Hence se(t) is completely**monotone**and from (4.5) so is Sr(r) andhence sr(r) as well. This then implies that for systems with independent

memoryless ...

Page 172

the lifetimes of several electronic and mechanical components are better

described by distributions having a

rate, such as the gamma, the Pareto, the Weibull, etc. In consideration of the

above, ...

the lifetimes of several electronic and mechanical components are better

described by distributions having a

**monotone**increasing or decreasing failurerate, such as the gamma, the Pareto, the Weibull, etc. In consideration of the

above, ...

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### Contents

System Eeliabujty | 3 |

Statistical Theory of Eeliablitt | 8 |

Definitions and characterizations | 12 |

Copyright | |

39 other sections not shown

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### Common terms and phrases

algorithm approach associated assume assumption Bayesian boundary points chain coherent system complex conjugate prior consider correctness defined denote detected discussed edited equations equivalence class ergodic errors example exponential distribution failure rate Fault Tree Analysis function gamma given human reliability IEEE Trans IFEA implementation increasing independent input domain integration interval likelihood Markov Markov chain matrix mean method modules monotone month2 N. D. Singpurwalla number of failures number of system NUMITEMS observed obtained operational output parameters phase Poisson Poisson process possible predictive prior distribution probability problem procedure Proschan R. E. Barlow random variables reliability growth models reliability theory renewal theory repair requirements sample sect sequence Software Eng software reliability software reliability models specification Stat statistical stochastic stochastic process subsection system failure system reliability techniques theorem tion tt tt values vector zero