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

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Page 32

If that epoch is in class j, and X(t) = x, there are competing failure rate functions or

epoch in class k. At each epoch the system regenerates in that its statistical future

...

If that epoch is in class j, and X(t) = x, there are competing failure rate functions or

**transition**rate functions {rjik(x), k = 1, 2, ... , K] generating the occurrence of anepoch in class k. At each epoch the system regenerates in that its statistical future

...

Page 39

If all

and the same eT is obtained. This implies that one can never get mean system

failure time from eT. The flow rates imn carry some of the needed information.

If all

**transition**rates vmn are speeded up by a common factor K, Q becomes KQ,and the same eT is obtained. This implies that one can never get mean system

failure time from eT. The flow rates imn carry some of the needed information.

Page 56

binary, i.e. assume they have only two states, « good » and « bad ». Let n be the

number of system components, the number of system states results then to be ...

**Transition**matrix representation and storage. Assume system components to bebinary, i.e. assume they have only two states, « good » and « bad ». Let n be the

number of system components, the number of system states results then to be ...

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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