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

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Page 27

of the indicator process I ( t ) would have the form shown in fig . 3 . ilw , t ) 13 Fig .

3 . At the epochs T , 21 , 2 , . . . , the generator has just been repaired and is as ...

**Renewal**theory . In the power generator model discussed above , a sample pathof the indicator process I ( t ) would have the form shown in fig . 3 . ilw , t ) 13 Fig .

3 . At the epochs T , 21 , 2 , . . . , the generator has just been repaired and is as ...

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1 ) H ( t ) = 24 k 1 le can This infinite series for the

always summable . Indeed one can show that , for Az ( 0 + ) = 0 , H ( w , t ) = { w

Ams " ( t ) has an infinite radius of convergence , so that E [ N ( t ) ] < for all

positive ...

1 ) H ( t ) = 24 k 1 le can This infinite series for the

**renewal**function F ( t ) isalways summable . Indeed one can show that , for Az ( 0 + ) = 0 , H ( w , t ) = { w

Ams " ( t ) has an infinite radius of convergence , so that E [ N ( t ) ] < for all

positive ...

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At each

reverting to age 0 . Let F ( x , t ) = P [ X ( t ) < « ] and let the associated density of

the age process be f ( x , t ) . If the lifetime distribution Af ( x ) is absolutely

continuous ...

At each

**renewal**epoch Tx the age process X ( t ) regenerates or renews byreverting to age 0 . Let F ( x , t ) = P [ X ( t ) < « ] and let the associated density of

the age process be f ( x , t ) . If the lifetime distribution Af ( x ) is absolutely

continuous ...

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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