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

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Page 23

A random variable is a well-

precisely, a random variable A' is a function mapping 8 into 0t, the set ... One can

similarly

A random variable is a well-

**defined**function of elementary events co in S. Moreprecisely, a random variable A' is a function mapping 8 into 0t, the set ... One can

similarly

**define**vector- valued random variables X = (Xx, XN) by x(co) = (xx(co), .Page 24

The probability measure P assigns mass 2~K to each elementary event co. Now,

for k = 1,2, N, let xt(co) be the number of heads in the first k places of co. The Xt's

are then well-

The probability measure P assigns mass 2~K to each elementary event co. Now,

for k = 1,2, N, let xt(co) be the number of heads in the first k places of co. The Xt's

are then well-

**defined**random variables on the probability space (S, s/, P).Page 203

... DFR assumption. Specifically, for the IFR assumption

distribution as (3.5) 77,(1*) = 35-*-^- EI - W')""'"1 » imp*,)"1 .» 1 k H where «„ = 1,

uk+l ^ 0, /?>(), a,->0, i = 1, k + 1 and ]Ta( = 1. This distribution is

space ...

... DFR assumption. Specifically, for the IFR assumption

**define**the priordistribution as (3.5) 77,(1*) = 35-*-^- EI - W')""'"1 » imp*,)"1 .» 1 k H where «„ = 1,

uk+l ^ 0, /?>(), a,->0, i = 1, k + 1 and ]Ta( = 1. This distribution is

**defined**over thespace ...

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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