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

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Page 3

The mathematical theory of reliability has grown out of the demands of modern

technology and particularly out of the ... Applications of

replacement problems were discussed as early as 1939 by A. J. Lotka [6], who

also ...

The mathematical theory of reliability has grown out of the demands of modern

technology and particularly out of the ... Applications of

**renewal theory**toreplacement problems were discussed as early as 1939 by A. J. Lotka [6], who

also ...

Page 27

of the indicator process I(t) would have the form shown in fig. 3. 3 I0 t| 12 E3 t Pig.

3. At the epochs tJ, r\, r\, the generator has just been repaired and is as good as ...

**Renewal theory**. In the power generator model discussed above, a sample pathof the indicator process I(t) would have the form shown in fig. 3. 3 I0 t| 12 E3 t Pig.

3. At the epochs tJ, r\, r\, the generator has just been repaired and is as good as ...

Page 30

At each renewal epoch rt the age process X{t) regenerates or renews by reverting

to age 0. Let F(x, t) ... when t is very large. A classical paradox of

1] shows the care needed in the argumentation when T is purely 30 J. KEILSON.

At each renewal epoch rt the age process X{t) regenerates or renews by reverting

to age 0. Let F(x, t) ... when t is very large. A classical paradox of

**renewal theory**[1] shows the care needed in the argumentation when T is purely 30 J. KEILSON.

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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