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On the limiting distribution of the failure time of fibrous materials

Published online by Cambridge University Press:  01 July 2016

Wagner De Souza Borges
Wagner De Souza Borges*
Affiliation:
Universidade de São Paulo
*
∗Postal address: Instituto de Matemática e Estatistica, Universidade de São Paulo, Caixa Postal 20570, Ag lguatemi, 05508 São Paulo SP, Brazil.
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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.

Keywords

MECHANICAL SYSTEMSFIBER BUNDLESRELIABILITYLIFE DISTRIBUTION
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 2 , June 1983 , pp. 331 - 348
Copyright
Copyright © Applied Probability Trust 1983 

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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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