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

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Page 126

Suppose the probability of observing X , given the parameter A , is p ( X | A ) , and

X is the actual

and it ...

Suppose the probability of observing X , given the parameter A , is p ( X | A ) , and

X is the actual

**observation**. X is a surrogate here , as before , for many**observations**. It is fair to ask what value of A maximizes p , given X as**observed**,and it ...

Page 153

Complete

popular plan consists of putting n items ... The likelihood of this

outcome under the exponential model is given by n ! L ( 2D ) = 1 ! a exp [ - - 2x ( o

] exp [ - ( n ...

Complete

**observation**until a specified number of failures have occurred . Apopular plan consists of putting n items ... The likelihood of this

**observed**outcome under the exponential model is given by n ! L ( 2D ) = 1 ! a exp [ - - 2x ( o

] exp [ - ( n ...

Page 157

Remarks . In the three sampling plans considered so far , the number k of

makes this true .

Remarks . In the three sampling plans considered so far , the number k of

**observed**failures and the total time on test T are all that we need from the**observations**in order to complete our data analysis ; the sufficiency of k and Tmakes this true .

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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