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

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Page 20

The first inequality in ( 8 ) follows from the IFRA definition and the second by the

Minkowski inequality .

convergence

generalization ...

The first inequality in ( 8 ) follows from the IFRA definition and the second by the

Minkowski inequality .

**Theorem**3 . 5 follows by the Lebesgue monotoneconvergence

**theorem**. Another key fact is that**theorem**3 . 5 has a vectorgeneralization ...

Page 145

A key

provides a method for computing the probability density of the random variable

expressing our uncertainty concerning the parameter conditioned on the ...

A key

**theorem**based on this point of view is the fundamental Bayes '**theorem**. Itprovides a method for computing the probability density of the random variable

expressing our uncertainty concerning the parameter conditioned on the ...

Page 176

Since Ly ( 0 ) increases in h , we have proved

X ) = EF ( X ) = 0 , then Lp , ( 0 ) < ( > ) Lp , ( O ) , O < ( > ) s , and Lp , ( 0 ) = Lr , ( 0

) , 0 = 8 . Analogous to corollary 3 . 3 and

Since Ly ( 0 ) increases in h , we have proved

**Theorem**3 . 6 . If F , < F , and Ep . (X ) = EF ( X ) = 0 , then Lp , ( 0 ) < ( > ) Lp , ( O ) , O < ( > ) s , and Lp , ( 0 ) = Lr , ( 0

) , 0 = 8 . Analogous to corollary 3 . 3 and

**theorem**3 . 4 , we have the following ...### What people are saying - Write a review

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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