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

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Page 18

that the class of increasing failure rate on the average (

closed under the formation of coherent systems. A distribution F(t) with failure rate

r(t) is said to have an increasing failure t rate average if (l/<)Jr(«)dw is monotonic

...

that the class of increasing failure rate on the average (

**IFEA**) life distributions isclosed under the formation of coherent systems. A distribution F(t) with failure rate

r(t) is said to have an increasing failure t rate average if (l/<)Jr(«)dw is monotonic

...

Page 20

By the

i-i i i WIU II (-1 WlU II w « The first inequality in (8) follows from the

and the second by the Minkowski inequality. Theorem 3.5 follows by the ...

By the

**IFEA**definition, \l{'l*)\m>\I(')\,^. and (8) M-)IU= 2 ||»,I4(- )IUi< I ' <*^n| <|| = □i-i i i WIU II (-1 WlU II w « The first inequality in (8) follows from the

**IFEA**definitionand the second by the Minkowski inequality. Theorem 3.5 follows by the ...

Page 21

Proof. Let I be an increasing indicator function. By definition of

only show El p(Tl'T^-'Tn)] > {BIUWn ... , r,)]}« , V 0 <«<1 . But -g(xT1,...,ocTn)>g(T1,

...,T„) implies where T* — <xTt, i = 1, 2,... , n, implies m >EI S)]>2S (£, .... &)]>[£2.w

...

Proof. Let I be an increasing indicator function. By definition of

**IFEA**, we needonly show El p(Tl'T^-'Tn)] > {BIUWn ... , r,)]}« , V 0 <«<1 . But -g(xT1,...,ocTn)>g(T1,

...,T„) implies where T* — <xTt, i = 1, 2,... , n, implies m >EI S)]>2S (£, .... &)]>[£2.w

...

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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