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

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Page 202

When such knowledge is available, it must be incorporated into the

fact, most of the commonly used life distributions have a mouotonically increasing

failure ...

When such knowledge is available, it must be incorporated into the

**prior****distribution**. In reliability theory, monotone ... rate functions play a central role. Infact, most of the commonly used life distributions have a mouotonically increasing

failure ...

Page 203

These restrictions must be reflected in the

to represent informed opinion. This may be accomplished by using a Dirichlet

u3 ...

These restrictions must be reflected in the

**prior**joint**distribution**of the «, in orderto represent informed opinion. This may be accomplished by using a Dirichlet

**distribution**as the**prior**joint**distribution**for the random variables Mi — u.,, m2 —u3 ...

Page 385

Bayesian inference for the unknown parameters N and A involves assigning a

distribution using Tlt Tk and the Bayes theorem. Our uncertainty in knowledge

about N ...

Bayesian inference for the unknown parameters N and A involves assigning a

**prior distribution**to the pair (N, A), and then obtaining the resultant posteriordistribution using Tlt Tk and the Bayes theorem. Our uncertainty in knowledge

about N ...

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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