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

### From inside the book

Results 1-3 of 10

Page 146

The prior density. First, we confine our choice of prior densities to proper

densities. A density n(-) is proper if jn(k)dX exists and equals one. Next, to

motivate the concept of a natural

particular ...

The prior density. First, we confine our choice of prior densities to proper

densities. A density n(-) is proper if jn(k)dX exists and equals one. Next, to

motivate the concept of a natural

**conjugate prior**for I, we suppose that, in theparticular ...

Page 158

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

where M is large (*). The corresponding ... Wo assume a rectangular prior for 6

here to motivate the use of a natural

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

where M is large (*). The corresponding ... Wo assume a rectangular prior for 6

here to motivate the use of a natural

**conjugate prior**. (in place of a) and b + T (in ...Page 159

Note that, as k, the number of observed failures, increases, the posterior mean

attaches more weight to the MLB of the true mean and loss weight to the prior

mean. Table 3.1 summarizes the properties of the natural

and ...

Note that, as k, the number of observed failures, increases, the posterior mean

attaches more weight to the MLB of the true mean and loss weight to the prior

mean. Table 3.1 summarizes the properties of the natural

**conjugate prior**densityand ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

System Eeliabujty | 3 |

Statistical Theory of Eeliablitt | 8 |

Definitions and characterizations | 12 |

Copyright | |

39 other sections not shown

### Other editions - View all

### 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