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

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Page 148

This is approximately a

parameter n b = 2xt. i-i Now, suppose we obtain an additional independent

random sample of lifelengths yu yt, yn. Then it is reasonable to use as our new

prior ...

This is approximately a

**gamma**donsity with shape parameter a = n + 1 and scaleparameter n b = 2xt. i-i Now, suppose we obtain an additional independent

random sample of lifelengths yu yt, yn. Then it is reasonable to use as our new

prior ...

Page 154

Using (2.1), we obtain for the posterior (2.3) n(X\D) = [b + T(au*)r**P*~-1 exp [- A[

6 + rQ/A* + •) , also a

replaced by a + A; and the scale parameter b of the prior density replaced by b +

...

Using (2.1), we obtain for the posterior (2.3) n(X\D) = [b + T(au*)r**P*~-1 exp [- A[

6 + rQ/A* + •) , also a

**gamma**, but with the shape parameter a of the prior densityreplaced by a + A; and the scale parameter b of the prior density replaced by b +

...

Page 158

... The density of (3.2), denoted by na „((?), is called the inverted

since, if 8 is a random variable with density na „(0), then 0_1 = 1 has

density (1.5). We may verify readily that, if our initial prior is of the form nah(8) of (

3.2; ...

... The density of (3.2), denoted by na „((?), is called the inverted

**gamma**density,since, if 8 is a random variable with density na „(0), then 0_1 = 1 has

**gamma**density (1.5). We may verify readily that, if our initial prior is of the form nah(8) of (

3.2; ...

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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