## 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 random

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 96

Suppose the pdf f(t) of a random

either type (5.1) ^(f(t)) = f*(s) = hj^T or type (5.2) m*)) = f*(»)=i~j, where -2?(*) is

the Laplace transform of the function in brackets, k4, w{ are positive, real and

such ...

Suppose the pdf f(t) of a random

**variable**T has a rational Laplace transform ofeither type (5.1) ^(f(t)) = f*(s) = hj^T or type (5.2) m*)) = f*(»)=i~j, where -2?(*) is

the Laplace transform of the function in brackets, k4, w{ are positive, real and

such ...

Page 113

Beal random

each pair of increasing functions f,g\R"^-R, for which the covariance in (3.1) does

exist. The fundamental properties of associated random

Beal random

**variables**Tlf Tn are associated if (3.1) Gov[f(Tu Tn),g(T„ Tn)]>0 foreach pair of increasing functions f,g\R"^-R, for which the covariance in (3.1) does

exist. The fundamental properties of associated random

**variables**, proved in [3], ...### 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