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

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Page 139

We then seek an estimator P(n2, t2: n,, tj where the Poisson probability is f(n,t) = (

pt)"exp[— pt]ln\ and the condition for lack of bias is ti)P(nt, t.2; nu

Substituting for /(wl5 <i) this leads to exp — 12)] = -j - 2 —V p(m*> <*; wm *i) □ \

Pl2) ...

We then seek an estimator P(n2, t2: n,, tj where the Poisson probability is f(n,t) = (

pt)"exp[— pt]ln\ and the condition for lack of bias is ti)P(nt, t.2; nu

**tt**) = f(nu t2) .Substituting for /(wl5 <i) this leads to exp — 12)] = -j - 2 —V p(m*> <*; wm *i) □ \

Pl2) ...

Page 203

under the IFR assumption and (3.4) 0<

These restrictions must be reflected in the prior joint distribution of the «, in order

to represent informed opinion. This may be accomplished by using a Dirichlet ...

under the IFR assumption and (3.4) 0<

**tt**,<**tt**,<...<«t<l under the DFR assumption.These restrictions must be reflected in the prior joint distribution of the «, in order

to represent informed opinion. This may be accomplished by using a Dirichlet ...

Page 437

This gives a time-varying Poisson process in which the failure rate decreases

from an initial rate of 1.0 towards an ultimate rate of 0.2, with a time constant of y-

1 = 20 time units. - •-

-* ...

This gives a time-varying Poisson process in which the failure rate decreases

from an initial rate of 1.0 towards an ultimate rate of 0.2, with a time constant of y-

1 = 20 time units. - •-

**tt**-**tttt**-**tt**-**tt tt**--tt»**tt tt***»*-* * * K 1* * * *** ** *-tt*-tt H H »-« * _*--*-* ...

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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