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

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Page 23

Most of elementary probability theory and statistics deals with probabilistic statics,

i.e. sets of

Most of elementary probability theory and statistics deals with probabilistic statics,

i.e. sets of

**random variables**and their correlation, with the order of these**random****variables**unimportant. The study of the failure of random systems is concerned ...Page 113

Time-association of random processes. Beal

associated if (3.1) Gov[f(Tu Tn),g(T„ Tn)]>0 for each pair of increasing functions f,

g\R"^-R, for which the covariance in (3.1) does exist. The fundamental properties

of ...

Time-association of random processes. Beal

**random variables**Tlf Tn areassociated if (3.1) Gov[f(Tu Tn),g(T„ Tn)]>0 for each pair of increasing functions f,

g\R"^-R, for which the covariance in (3.1) does exist. The fundamental properties

of ...

Page 388

To prove theorem 3.5, we need assumption A6, which is a generalization of

assumption A3, obtained by considering a nondecreasing positive real valued

function h defined on (0, oo), and a sequence of i.i.d.

To prove theorem 3.5, we need assumption A6, which is a generalization of

assumption A3, obtained by considering a nondecreasing positive real valued

function h defined on (0, oo), and a sequence of i.i.d.

**random variables**Vt ...### What people are saying - Write a review

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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