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

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Page 122

The characteristic of all these, as mentioned before, is width, and that means that

the characterization of a reliability

« mean time between failures » or any other single parameter is inappropriate.

The characteristic of all these, as mentioned before, is width, and that means that

the characterization of a reliability

**problem**in terms of « mean time to failure » or« mean time between failures » or any other single parameter is inappropriate.

Page 230

F,3 &f)\ to obtain the latter one, Ave would have to compute the conditional mean

As a conclusion, computing the intensity with respect to the internal history might

call for the solution of a conditional mean

F,3 &f)\ to obtain the latter one, Ave would have to compute the conditional mean

As a conclusion, computing the intensity with respect to the internal history might

call for the solution of a conditional mean

**problem**(filtering**problem**, see sect.Page 231

The filtering

following: Let Xt be a semi-martingale adapted to a history {^i}: (5.1) X, = X0 + at+

mt, where a, is predictable, bounded variation and adapted to {J^} (compensator),

...

The filtering

**problem**. A fairly general, common and relevant**problem**is thefollowing: Let Xt be a semi-martingale adapted to a history {^i}: (5.1) X, = X0 + at+

mt, where a, is predictable, bounded variation and adapted to {J^} (compensator),

...

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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