## Proceedings of the International School of Physics "Enrico Fermi". |

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Page 156

Then, conditional on Y< i„ and <„, the density of Y is

exp [— Xt0]) for 0 < y < <„ . Thus, if the successive failure ages actually observed

are denoted by y1} yz, the corresponding conditional joint density is

Then, conditional on Y< i„ and <„, the density of Y is

**given**by X exp [— Ai/]/(l —exp [— Xt0]) for 0 < y < <„ . Thus, if the successive failure ages actually observed

are denoted by y1} yz, the corresponding conditional joint density is

**given**by # ...Page 206

Under the DFR assumption the posterior distribution of the u{ is

u\s, r) oc (1 - fl (1 - «,)*'«?(«« - u(_xr'-1 . i-i In order to completely specify these

distributions, the constant of integration must be obtained. By expanding the (1 —

« ...

Under the DFR assumption the posterior distribution of the u{ is

**given**by (4.4) fD(u\s, r) oc (1 - fl (1 - «,)*'«?(«« - u(_xr'-1 . i-i In order to completely specify these

distributions, the constant of integration must be obtained. By expanding the (1 —

« ...

Page 218

For instance, we may consider the history generalized by a

denoted by □Ff = a{Xt, 8<i} . We have to be sure which history we refer to, and

explicitly mention it if it is not obvious; for instance,

with ...

For instance, we may consider the history generalized by a

**given**process A',denoted by □Ff = a{Xt, 8<i} . We have to be sure which history we refer to, and

explicitly mention it if it is not obvious; for instance,

**given**a parallel of two items,with ...

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### Contents

System Eeliabujty | 3 |

Statistical Theory of Eeliablitt | 8 |

Definitions and characterizations | 12 |

Copyright | |

39 other sections not shown

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### Common terms and phrases

algorithm approach associated assume assumption Bayesian boundary points chain coherent system complex conjugate prior consider correctness defined denote detected discussed edited equations equivalence class ergodic errors example exponential distribution failure rate Fault Tree Analysis function gamma given human reliability IEEE Trans IFEA implementation increasing independent input domain integration interval likelihood Markov Markov chain matrix mean method modules monotone month2 N. D. Singpurwalla number of failures number of system NUMITEMS observed obtained operational output parameters phase Poisson Poisson process possible predictive prior distribution probability problem procedure Proschan R. E. Barlow random variables reliability growth models reliability theory renewal theory repair requirements sample sect sequence Software Eng software reliability software reliability models specification Stat statistical stochastic stochastic process subsection system failure system reliability techniques theorem tion tt tt values vector zero