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

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Page 37

It follows from (3.17) that, when irreducibility is present for v, p(t) has pmn(t) > 0

for all m, n and any <> 0 no matter how small. Thus p(t) is ergodic and eTrp(t) —

eTr. Since the ergodic vector of p(t) is unique, ef is

be ...

It follows from (3.17) that, when irreducibility is present for v, p(t) has pmn(t) > 0

for all m, n and any <> 0 no matter how small. Thus p(t) is ergodic and eTrp(t) —

eTr. Since the ergodic vector of p(t) is unique, ef is

**independent**of v as it shouldbe ...

Page 96

(-1 If (5.1) holds, then the random variable T is the sum of k

variables T{, i = 1, k; Tt is exponentially distributed with parameter At. A Laplace

transform of type (5.2) entails the random variable T to have a probability wt of ...

(-1 If (5.1) holds, then the random variable T is the sum of k

**independent**randomvariables T{, i = 1, k; Tt is exponentially distributed with parameter At. A Laplace

transform of type (5.2) entails the random variable T to have a probability wt of ...

Page 111

If Tu Tn were stochastically

) = P{T, >t, Tm >t} = Y[R,(t). i-i For general coherent systems, 1\, Tm are not

If Tu Tn were stochastically

**independent**random variables, we should have m R(t) = P{T, >t, Tm >t} = Y[R,(t). i-i For general coherent systems, 1\, Tm are not

**independent**even under the assumption of independence among components, ...### 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