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

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Page 32

The process [J(t),X(t)] is a bivariate

of the system. The process J(t) is said to be semi-

rate ...

The process [J(t),X(t)] is a bivariate

**Markov**process. The process J(t) is not**Markov**since elapsed-time information is needed to specif y the statistical futureof the system. The process J(t) is said to be semi-

**Markov**. When all the transitionrate ...

Page 55

The

. 0. A. Clarotti ENEA TIB-ISP OBE Oasacda - 8.P. Anguillarese 301, 00100 Roma,

Italia 1. - Introduction. The so-called

The

**Markov**Approach to Calculating System Reliability: Computational Problems. 0. A. Clarotti ENEA TIB-ISP OBE Oasacda - 8.P. Anguillarese 301, 00100 Roma,

Italia 1. - Introduction. The so-called

**Markov**approach to calculating system ...Page 63

If

within reasonable limits, no alternative exists to the highly stable implicit methods

which allow the integration step size to be increased as local error constraints get

...

If

**Markov**equations are to be numerically solved and CPU time is to be keptwithin reasonable limits, no alternative exists to the highly stable implicit methods

which allow the integration step size to be increased as local error constraints get

...

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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