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On the calculation of the reliability of general load sharing systems

  • Shiowjen Lee (a1), S. Durham (a2) and J. Lynch (a2)
Abstract

Harlow et al. (1983) have given a recursive formula which is fundamental for computing the bundle strength distribution under a general class of load sharing rules called monotone load sharing rules. As the bundle size increases, the formula becomes prohibitively complex and, by itself, does not give much insight into the relationship of the assumed load sharing rule to the overall strength distribution. In this paper, an algorithm is given which gives some additional insight into this relationship. Here it is shown how to explicitly compute the bundle strength survival distribution by using a new type of graph called the loading diagram. The graph is parallel in structure and recursive in nature and so would appear to lend itself to large-scale computation. In addition, the graph has an interesting property (which we refer to as the cancellation property) which is related to the asymptotics of the Weibull as a minimum stable law.

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Corresponding author
Postal address: Department of Mathematics and Statistics, The University of West Florida, Pensacola, FL 32514-5750, USA.
∗∗ Postal address: Department of Statistics, University of South Carolina, Columbia, SC 29208, USA.
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Research partially supported by an NSF/EPSCOR grant

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References
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Daniels, H. E. (1945) The statistical theory of the strength of bundles of threads 1. Proc. R. Soc. London. A. 83, 405435.
Harlow, D. G. and Phoenix, S. L. (1978) The chain-of-bundles probability model for the strength of fibrous materials 1: Analysis and conjectures. J Composite Materials 12, 195214.
Harlow, D. G. and Phoenix, S. L. (1982) Probability distributions for the strength of fibrous materials under local load sharing 1: Two-level failure and edge effects. Adv. Appl. Prob. 14, 6894.
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, 358367.
Rosen, B. W. (1964) Tensile failure of fibrous composites. AIAA Journal 2, 19851991.
Taylor, H. M. and Karlin, S. (1984) An Introduction to Stochastic Modeling. Academic Press, New York.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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