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

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Page 156

Thus, if the successive failure ages actually observed are denoted by y1} yz, the

probability that N = n units have to be tested in order to observe k actual failures

is ...

Thus, if the successive failure ages actually observed are denoted by y1} yz, the

**corresponding**conditional joint density is given by # , • « A Aexp[-^] **«P Theprobability that N = n units have to be tested in order to observe k actual failures

is ...

Page 158

We, therefore, assume a rectangular prior density on 8: n{8) = M-1 for 0<8<M,

where M is large (*). The

approximately, by Bayes' theorem (theorem 1.2), as (3.2) n{8\x^, xn) = exp [- &/0]//

» ...

We, therefore, assume a rectangular prior density on 8: n{8) = M-1 for 0<8<M,

where M is large (*). The

**corresponding**posterior density for 8 may be computedapproximately, by Bayes' theorem (theorem 1.2), as (3.2) n{8\x^, xn) = exp [- &/0]//

» ...

Page 273

2 then shows the actual treaties y{(x) vs. x,

the constrained Pareto-optimal treaties consist of layered, nonlinear functions

determined parametrically as follows: 1) Given the Pareto multipliers {&,} and the

...

2 then shows the actual treaties y{(x) vs. x,

**corresponding**to fig. 1. To summarize,the constrained Pareto-optimal treaties consist of layered, nonlinear functions

determined parametrically as follows: 1) Given the Pareto multipliers {&,} and the

...

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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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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