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

### From inside the book

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Page 23

Most of elementary probability theory and statistics deals with probabilistic statics

, i . e . sets of

Most of elementary probability theory and statistics deals with probabilistic statics

, i . e . sets of

**random variables**and their correlation , with the order of these**random variables**unimportant . The study of the failure of random systems is ...Page 113

Time - association of random processes . Real

associated if ( 3 . 1 ) Cov [ f ( T , , . . . , Tn ) , g ( T1 , . . . , Tn ) ] > 0 for each pair of

increasing functions f , g : R " →R , for which the covariance in ( 3 . 1 ) does exist .

Time - association of random processes . Real

**random variables**T1 , . . . , T , areassociated if ( 3 . 1 ) Cov [ f ( T , , . . . , Tn ) , g ( T1 , . . . , Tn ) ] > 0 for each pair of

increasing functions f , g : R " →R , for which the covariance in ( 3 . 1 ) does exist .

Page 388

For k = 1 , 2 , . . . , the conditional

> N , ( Tx | N , 1 ) = 1 ( A ( N – k + 1 ) ) V , k < N ... Furthermore , let U1 , U2 , . . . be

independent and exponentially distributed

For k = 1 , 2 , . . . , the conditional

**random variable**( Tx | N , 4 ) is such that Joo , k> N , ( Tx | N , 1 ) = 1 ( A ( N – k + 1 ) ) V , k < N ... Furthermore , let U1 , U2 , . . . be

independent and exponentially distributed

**random variables**with mean 1 .### 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