## Proceedings of the International School of Physics "Enrico Fermi", Volume 94 |

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Page 404

behave more smoothly than the posterior modes and seem to converge towards

the true N for lower values of t . However , the main results are not these point

estimators , but in the fact that the full

behave more smoothly than the posterior modes and seem to converge towards

the true N for lower values of t . However , the main results are not these point

estimators , but in the fact that the full

**predictive**density can be obtained from ( 4 .Page 414

If the

estimator » , ŷ = ż ( D , ) , formed from the data , D , , then we refer to the formula

for the

If the

**predictive**mean of some random variable ō is a linear function of a « naturalestimator » , ŷ = ż ( D , ) , formed from the data , D , , then we refer to the formula

for the

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

15 ) , the

D * ) 1 a ' + no i Bi + no P ( no | D * ) no + 1 b ' + Vķ + no 1 ī fälnr + noi no + 1 " n ( i

) - ) ; nr + no ; ni ) . nt + nol Numerical computation is very efficient ; by setting p ...

15 ) , the

**predictive**density can be put into recurrence form as ( 6 . 20 ) p ( no + 1 |D * ) 1 a ' + no i Bi + no P ( no | D * ) no + 1 b ' + Vķ + no 1 ī fälnr + noi no + 1 " n ( i

) - ) ; nr + no ; ni ) . nt + nol Numerical computation is very efficient ; by setting p ...

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### Contents

STATISTICAL THEORY OF RELIABLITY | 8 |

Definitions and characterizations | 12 |

J KEILSON Stochastic models in reliability theory | 23 |

Copyright | |

37 other sections not shown

### Common terms and phrases

analysis application approach associated assume assumption BARLOW Bayesian calculation called complex components consider constant continuous correctness Course defined density depends derived described detected determine discussed distribution edited epochs equations equivalence ergodic errors estimate example exists expected exponential fact fail failure rate fault function given Hence important increasing independent input integration interest interval known likelihood limit Markov matrix mean measure method modules normal Note observed obtain occur operational parameters performance phase positive possible posterior predictive prior probability problem procedure prove random variables renewal repair requirements rule sample selected sequence simple software reliability space specification statistical stochastic structure Suppose task theorem theory tion transition tree University values York