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On the limiting distribution of the failure time of fibrous materials
Published online by Cambridge University Press: 01 July 2016
Abstract
A large deviation theorem of the Cramér–Petrov type and a ranking limit theorem of Loève are used to derive an approximation for the statistical distribution of the failure time of fibrous materials. For that, fibrous materials are modeled as a series of independent and identical bundles of parallel filaments and the asymptotic distribution of their failure time is determined in terms of statistical characteristics of the individual filaments, as both the number of filaments in each bundle and the number of bundles in the chain grow large simultaneously. While keeping the number n of filaments in each bundle fixed and increasing only the chain length k leads to a Weibull limiting distribution for the failure time, letting both increase in such a way that log k(n) = o(n), we show that the limit distribution is for . Since fibrous materials which are both long and have many filaments prevail, the result is of importance in the materials science area since refined approximations to failure-time distributions can be achieved.
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- Copyright © Applied Probability Trust 1983
Footnotes
Research partly carried out while the author was visiting the University of Pittsburgh.
Supported in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), processo n°. 200175-81.
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