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

### From inside the book

Results 1-3 of 65

Page 149

Since the

Broo ) = 2 : 0 exp [ - 193 ] will override in importance the retangular prior To ( a ) =

M - 1 , 0 < 2CM , when M » Â . From the prior 1 , we calculate the posterior density

...

Since the

**sample**size of 100 is moderately large , the likelihood [ ( 2162 . . . ,Broo ) = 2 : 0 exp [ - 193 ] will override in importance the retangular prior To ( a ) =

M - 1 , 0 < 2CM , when M » Â . From the prior 1 , we calculate the posterior density

...

Page 151

The

outcomes . If we observe the lifetimes of n units , the

, we may just as well consider another

the ...

The

**sample**space . The**sample**space is the space or set of possible**sample**outcomes . If we observe the lifetimes of n units , the

**sample**space is ... However, we may just as well consider another

**sample**space . Suppose we are told onlythe ...

Page 152

For

probability density Jan exp [ - 2 3 . 0 ; ] , , 70 , 1 < i < n , ( 1 . 9 ) p ( x1 , 82 , . . . , xn

| 2 ) = { 10 , otherwise . For this case I ( 2 ] X1 , , . . . , Xn ) = p ( x1 , 62 , . . . , 2 , 12 )

.

For

**sample**space ( 1 . 7 ) and the exponential model we have the joint -probability density Jan exp [ - 2 3 . 0 ; ] , , 70 , 1 < i < n , ( 1 . 9 ) p ( x1 , 82 , . . . , xn

| 2 ) = { 10 , otherwise . For this case I ( 2 ] X1 , , . . . , Xn ) = p ( x1 , 62 , . . . , 2 , 12 )

.

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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