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

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Page 23

Stochastic models. l'l.

familiar with elementary probability theory as represented in any introductory text

[1, 2]. It is also assumed that the reader is familiar with the elementary

classification ...

Stochastic models. l'l.

**Stochastic processes**. - It is assumed that the reader isfamiliar with elementary probability theory as represented in any introductory text

[1, 2]. It is also assumed that the reader is familiar with the elementary

classification ...

Page 24

The totality of all such realizations constitutes the «

) where the index set {1,2, N} is finite. Actually, the situation discussed above is

simple in that the number of tosses is finite. There are occasions, however, when

...

The totality of all such realizations constitutes the «

**stochastic process**» (X1,...,X!I) where the index set {1,2, N} is finite. Actually, the situation discussed above is

simple in that the number of tosses is finite. There are occasions, however, when

...

Page 26

All four

easy to see how the random number generator of a computer could be used to

generate sample paths for the process I(t) which could be used to simulate all

four ...

All four

**stochastic processes**have their setting in the same probability space. It iseasy to see how the random number generator of a computer could be used to

generate sample paths for the process I(t) which could be used to simulate all

four ...

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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