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Limit theorems and approximations for the reliability of load-sharing systems

Published online by Cambridge University Press:  01 July 2016

Richard L. Smith
Richard L. Smith*
Affiliation:
Imperial College, London
*
∗Postal address: Imperal College of Science and Technology, Department of Mathematics, Huxley Building, Queens' Gate, London SW7 2BZ, U.K.
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Abstract

Techniques for studying the reliability of simple series or parallel systems are well known. This paper is concerned with more complicated systems in which the load on failed elements is transmitted to unfailed elements according to some load-sharing rule. The emphasis is on local load sharing, and in particular on a specific load-sharing rule introduced by Harlow and Phoenix for fibrous composites. Earlier results are reviewed and improved techniques for approximating the probability of failure and the size effect are derived.

Keywords

BUNDLES OF FIBRESSERIES–PARALLEL SYSTEMSLOCAL LOAD SHARINGSIZE EFFECTEXTREME-VALUE THEORY
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 2 , June 1983 , pp. 304 - 330
Copyright
Copyright © Applied Probability Trust 1983 

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References

Daniels, H. E. (1945) The statistical theory of the strength of bundles of threads I. Proc. R. Soc. London A 183, 404–435.Google Scholar
Fukuda, H. and Kawata, K. (1976) On the stress concentration factor in fibrous composites. Fibre Sci. Technol. 9, 189–203.CrossRefGoogle Scholar
De Haan, L. (1970) On Regular Variation and its Application to the Weak Convergence of Sample Extremes. Mathematisch Centrum, Amsterdam.Google Scholar
Harlow, D. G. and Phoenix, S. L. (1978a) The chain-of-bundles probability model for the strength of fibrous materials I: Analysis and conjectures. J. Composite Materials 12, 195–214.Google Scholar
Harlow, D. G. and Phoenix, S. L. (1978b) The chain-of-bundles probability model for the strength of fibrous materials II: A numerical study of convergence. J. Composite Materials 12, 314–334.Google Scholar
Harlow, D. G. and Phoenix, S. L. (1981a) Probability distributions for the strength of composite materials I: Two-level bounds. Internat. J. Fracture 17, 347–372.Google Scholar
Harlow, D. G. and Phoenix, S. L. (1981b) Probability distributions for the strength of composite materials II: A convergent sequence of tight bounds. Internat. J. Fracture 17, 601–630.Google Scholar
Harlow, D. G. and Phoenix, S. L. (1982) Probability distributions for the strength of fibrous materials under local load sharing I: Two level failure. Adv. Appl. Prob. 14, 68–94.CrossRefGoogle Scholar
Harlow, D. G., Smith, R. L. and Taylor, H. M. (1983) Lower tail analysis of the distribution of the strength of load-sharing systems. J. Appl. Prob. 20, 358–367.Google Scholar
Hedgepeth, J. M. and Van Dyke, P. (1967) Local stress concentrations in imperfect filamentary composite materials. J. Composite Materials 1, 294–309.Google Scholar
Loynes, R. M. (1965) Extreme value in uniformly mixing stationary stochastic procèsses. Ann. Math. Statist. 36, 993–999.CrossRefGoogle Scholar
Seneta, E. (1976) Regularly Varying Functions. Lecture Notes in Mathematics 508, Springer-Verlag, Berlin.CrossRefGoogle Scholar
Smith, R. L. (1980) A probability model for fibrous materials with local load sharing. Proc. R. Soc. London A 372, 539–553.Google Scholar
Smith, R. L. (1982) A note on a probability model for fibrous composites. Proc. R. Soc. London A 382, 179–182.Google Scholar
Tierney, L. J. (1982) Asymptotic bounds on the time to fatigue failure of bundles of fibers under local load-sharing. Adv. Appl. Prob. 14, 95–121.Google Scholar
Watson, G. S. (1954) Extreme values in samples from M-dependent stationary stochastic processes. Ann. Math. Statist. 25, 798–800.CrossRefGoogle Scholar