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

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Page 37

It follows that, if the matrix v is irreducible, i.e. if every state can be reached from

every other state, then ar is

for a,, and e*a = eTv. It follows from (3.17) that, when irreducibility is present for v,

...

It follows that, if the matrix v is irreducible, i.e. if every state can be reached from

every other state, then ar is

**ergodic**and aj ->1eJ, where e, is the**ergodic**vectorfor a,, and e*a = eTv. It follows from (3.17) that, when irreducibility is present for v,

...

Page 38

For

are usually easiest (but not always easy) to obtain and of groat practical interest.

In much of the literature of engineering reliability interest focuses largely on the ...

For

**ergodic**Markov chains J(t) in continuous time, the**ergodic**probabilities emare usually easiest (but not always easy) to obtain and of groat practical interest.

In much of the literature of engineering reliability interest focuses largely on the ...

Page 42

The exit time from the good set O when pi = eT0 (case 6) above) will be called the

the sojourn time on G. The sequence of sojourn times (TBi) on the good set are ...

The exit time from the good set O when pi = eT0 (case 6) above) will be called the

**ergodic**exit time [4-6]. The exit time from 0 for weight /»' = 0 of (4.4) will be calledthe sojourn time on G. The sequence of sojourn times (TBi) on the good set are ...

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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