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

### From inside the book

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Page 122

A

exponential distribution by its mean rate parameter , a Poisson distribution by the

mean number of events expected , etc . The first step in any estimate of reliability

...

A

**normal**distribution is characterized by its center and its width or variance , anexponential distribution by its mean rate parameter , a Poisson distribution by the

mean number of events expected , etc . The first step in any estimate of reliability

...

Page 137

( Since , for a

theorem is exact for a

which all the measurements are drawn from the same distribution 1 P ( S ) = – ak

exp [ ik8 ] ...

( Since , for a

**normal**distribution , the higher semi - invariants vanish , thetheorem is exact for a

**normal**distribution . ) In the special limit important case inwhich all the measurements are drawn from the same distribution 1 P ( S ) = – ak

exp [ ik8 ] ...

Page 244

In view of the above , if we , therefore , define Z ; = In n ; + y ( np ) – Y , , we may

then hypothesize that , for sufficient large nj , Z ; is approximately

mean In 0 ; and variance yl ( ny ) . We now have as our observation equation Z ; =

ln ...

In view of the above , if we , therefore , define Z ; = In n ; + y ( np ) – Y , , we may

then hypothesize that , for sufficient large nj , Z ; is approximately

**normal**withmean In 0 ; and variance yl ( ny ) . We now have as our observation equation Z ; =

ln ...

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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