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

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Page 404

However, the main results are not these point estimators, but in the fact that the

full

density obtained at the start of the experiment {t — 0) ; for our parameters the

initial ...

However, the main results are not these point estimators, but in the fact that the

full

**predictive**density can be obtained from (4.6). Figure 3 shows the (Pascal)density obtained at the start of the experiment {t — 0) ; for our parameters the

initial ...

Page 414

If the

estimator », y — y(@v), formed from the data, 3>v, then we refer to the formula for

the

If the

**predictive**mean of some random variable y is a linear function of a « naturalestimator », y — y(@v), formed from the data, 3>v, then we refer to the formula for

the

**predictive**mean as a « credibility estimator », because it generally has the ...Page 420

As in (6.15), the

+l\2>*)= 1 a'+n'p'( + n0^ [ □ ' p(n0\®*) n,+ l b' Uy't + n. = ,TTI h(n* + n"' x» *> Q h ((i

- ~Vo) ; "T + y.) • Numerical computation is very efficient; by setting = 1, one in ...

As in (6.15), the

**predictive**density can be put into recurrence form as r«201 p(n0+l\2>*)= 1 a'+n'p'( + n0^ [ □ ' p(n0\®*) n,+ l b' Uy't + n. = ,TTI h(n* + n"' x» *> Q h ((i

- ~Vo) ; "T + y.) • Numerical computation is very efficient; by setting = 1, one in ...

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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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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