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On the calculation of the reliability of general load sharing systems

Part of: Distribution theory Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Shiowjen Lee ,
S. Durham  and
J. Lynch
Shiowjen Lee*
Affiliation:
University of West Florida
S. Durham*
Affiliation:
University of South Carolina
J. Lynch*
Affiliation:
University of South Carolina
*
∗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.
∗∗Postal address: Department of Statistics, University of South Carolina, Columbia, SC 29208, USA.
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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.

Keywords

BUNDLE STRENGTHMONOTONE LOAD SHARING RULELOADING DIAGRAMRELIABILITY

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 62E10: Characterization and structure theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 3 , September 1995 , pp. 777 - 792
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research partially supported by an NSF/EPSCOR grant

References

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