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A weibull limit for the reliability of a consecutive k-within-m-out-of-n system

Published online by Cambridge University Press:  01 July 2016

Stavros G. Papastavridis
Stavros G. Papastavridis*
Affiliation:
University of Patras
*
∗ Postal address: Department of Mathematics, University of Patras, 261 10 Patras, Greece.
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Abstract

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A consecutive k-within-m-out-of-n system consists of n identical and stochastically independent components arranged on a line. The system will fail if and only if within m consecutive components, there are at least k failures. Let Tn be the system's lifetime. Then, under quite general conditions we prove that there is a positive constant a such that the random variable n1/kaTn converges to a Weibull distribution as n →∞.

Keywords

WEIBULL DISTRIBUTION

Information

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 20 , Issue 3 , September 1988 , pp. 690 - 692
Copyright
Copyright © Applied Probability Trust 1988 

Footnotes

This paper was written while the author was visiting Bell Laboratories (MH), in the fall of 1987–88.

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