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

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Page 32

The process J ( t ) is said to be semi - Markov . When all the transition rate

functions Nik ( x ) are constants , i . e . independent of x , the process J ( t ) is

Markov . The process J ( t ) is then said to be a finite Markov chain in

time , and ...

The process J ( t ) is said to be semi - Markov . When all the transition rate

functions Nik ( x ) are constants , i . e . independent of x , the process J ( t ) is

Markov . The process J ( t ) is then said to be a finite Markov chain in

**continuous**time , and ...

Page 221

Decomposition for

. – Let us now go back to the

said to be predictable with respect to a given history { F } if , for each t , X , is F ...

Decomposition for

**continuous**- time processes . 31 . More on counting processes. – Let us now go back to the

**continuous**case . A**continuous**- time process X , issaid to be predictable with respect to a given history { F } if , for each t , X , is F ...

Page 226

A. Serra, Richard E. Barlow. Because of ( 3 . 13 ) , continuity properties of

compensator and jumping time distributions are intimately related . Indeed ,

Theorem 3 . 4 . A , is ( a . s . , almost surely )

distributions Fj , j = 1 ...

A. Serra, Richard E. Barlow. Because of ( 3 . 13 ) , continuity properties of

compensator and jumping time distributions are intimately related . Indeed ,

Theorem 3 . 4 . A , is ( a . s . , almost surely )

**continuous**if and only if thedistributions Fj , j = 1 ...

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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