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Reliability for a System with Dependent Components

Published online by Cambridge University Press:  27 July 2009

Cyrus Derman  and
Sheldon Ross
Cyrus Derman
Affiliation:
Department of Industrial Engineering and Operations Research, Columbia University New York, NY 10027
Sheldon Ross
Affiliation:
Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720
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Abstract

A general type of model that results in components having a negative type of dependence is proposed. Specifically, a system of dependent binary components, in which component i is said to function if at least one of a given number of multinomial trials results in that outcome, is considered. The multinomial probabilities that maximize the probability of a k-of-n system are determined. Some approximations for the system reliability are proposed first for a system that functions unless k consecutive components are failed and then for a general system. A simulation method that uses a variance reduction technique to estimate the reliability is presented.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 1 , January 1995 , pp. 59 - 63
Copyright
Copyright © Cambridge University Press 1995

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References

1.Ross, S. (1994). A new simulation estimator of system reliability. Journal of Applied Mathematics and Stochastic Analysis 7(3): 331–336.CrossRefGoogle Scholar