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

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Page 89

(u, m( = 0): specification of times since system components are functioning; the

ages of components other than component i are the same as prescribed by the

vector u, the age of component i is

operation.

(u, m( = 0): specification of times since system components are functioning; the

ages of components other than component i are the same as prescribed by the

vector u, the age of component i is

**zero**because it has been just put intooperation.

Page 90

Let px(u;v;t) denote the joint probability of the discrete state * and probability

density function of uu w„, vlt v„ at time t, with the understanding that, if x{ = 0 (xt =

1), ut is certainly

Let px(u;v;t) denote the joint probability of the discrete state * and probability

density function of uu w„, vlt v„ at time t, with the understanding that, if x{ = 0 (xt =

1), ut is certainly

**zero**(«t is certainly**zero**). Denning px(u; v;t) in formulae in the ...Page 125

Finally, when the number of failures in the allotted test time becomes small, like

power plant, what does one learn about the probability of core melt (the ultimate ...

Finally, when the number of failures in the allotted test time becomes small, like

**zero**or one, the analysis becomes questionable. For example, in a nuclearpower plant, what does one learn about the probability of core melt (the ultimate ...

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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