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

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Page 48

that Z ( t ) is a probability density function . This arises from the fact that Poolt ) is a

positive mixture of decreasing exponentials . To see this , one

**Note**that ( 4 . 22 ) 5 ( 8 ) = L { _ dpoo ( t ) / dt ) _ } = L { Z ( t ) } 11 – Pool00 ) andthat Z ( t ) is a probability density function . This arises from the fact that Poolt ) is a

positive mixture of decreasing exponentials . To see this , one

**notes**from the ...Page 157

far considered ! ( Compare ( 2 . 8 ) , ( 2 . 6 ) and ( 2 . 3 ) . ) Remarks . In the three

sampling plans considered so far , the number k of observed failures and the total

...

**Note**that the posterior densities are identical under the three sampling plans sofar considered ! ( Compare ( 2 . 8 ) , ( 2 . 6 ) and ( 2 . 3 ) . ) Remarks . In the three

sampling plans considered so far , the number k of observed failures and the total

...

Page 384

As a justification for the above ,

denotes the probability that j inputs ( shocks ) are received in time t , and the

second term inside the summation sign denotes the probability that all j inputs do

not ...

As a justification for the above ,

**note**that the first term inside the summation signdenotes the probability that j inputs ( shocks ) are received in time t , and the

second term inside the summation sign denotes the probability that all j inputs do

not ...

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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