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The asymptotic time to failure of a bundle of fibers with random slacks

Published online by Cambridge University Press:  01 July 2016

L. Tierney
L. Tierney*
Affiliation:
Cornell University
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Abstract

Consider a bundle that has been constructed by placing n fibers in parallel between two clamps. The simplest assumption on fiber load sharing is that all non-failed fibers share the load applied to the bundle equally. Phoenix (1978b) shows that, as n tends to ∞, the time to failure of such a bundle is asymptotically normally distributed under certain assumptions on the stochastic nature of the fibers. In this paper we show that this asymptotic normality is preserved but with changed mean and variance if random slacks are introduced, as caused by random variations in the lengths of the fibers. A theorem on random linear combinations of order statistics, which is given in the appendix, is used to prove the result.

Keywords

FIBER BUNDLETIME TO FAILURELOAD SHARINGWEAK CONVERGENCELINEAR COMBINATIONS OF ORDER STATISTICS
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 3 , September 1981 , pp. 548 - 566
Copyright
Copyright © Applied Probability Trust 1981 

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