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The Role of a Group of Modules in the Failure of Systems

Published online by Cambridge University Press:  27 July 2009

A. M. Abouammoh ,
Emad El-Neweihi  and
Jayaram Sethuraman
A. M. Abouammoh
Affiliation:
Vice Dean, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Emad El-Neweihi
Affiliation:
Department of Mathematics, University of Illinois at Chicago, Chicago, Illinois 60558
Jayaram Sethuraman
Affiliation:
Department of Statistics, Florida State University, Tallahassee, Florida 32306-3033
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Abstract

Consider a system consisting of a number of modules. The probability that a particular module is among the ones that have already failed by the time of system failure can be used as a measure of the importance of that module. In El-Neweihi and Sethuraman [6], this probability was called the role of a module in the failure of a system and its properties were developed. In this article we propose the number of failed modules from among a particular subgroup of modules as the basis for measuring the role of that subgroup of modules. We study some monotonicity properties of the distribution of that random variable, in some second order r-out-of-k systems. We illustrate the possible extensions of these results to multistate systems. Yet another measure of the role of a particular subgroup of modules can be based on the number of failed components from this subgroup by the time of system failure. We derive some monotonicity properties of the expected value of the number of such failed components.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 1 , January 1994 , pp. 89 - 101
Copyright
Copyright © Cambridge University Press 1994

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