Hostname: page-component-84b7d79bbc-x5cpj Total loading time: 0 Render date: 2024-07-26T02:19:56.788Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Barlow, R.E. & Proschan, F. (1975). Importance of system components and failure tree events. Stochastic Processes and Their Applications 3: 153–173.CrossRefGoogle Scholar
2.Birnbaum, Z.W. (1969). On the importance of different components in a multicomponent system. In Krishnaiah, P.R. (ed.), Multivariate analysis II. New York: Academic Press, pp. 581–592.Google Scholar
3.Boland, P.J. & El-Neweihi, E. (1990). Measures of component importance in reliability theory. Technical Report, University College, Dublin.Google Scholar
4.Boland, P.J., El-Neweihi, E., & Proschan, F. (1988). Active redundancy allocation in coherent systems. Probability in the Engineering and Informational Sciences 2: 343–353.CrossRefGoogle Scholar
5.El-Neweihi, E., Proschan, F., & Sethuraman, J. (1978). A simple model with applications in structural reliability, extinction of species, inventory depletion and urn sampling. Advances in Applied Probability 10: 232–254.CrossRefGoogle Scholar
6.El-Neweihi, E. & Sethuraman, J. (1991). A study of the role of modules in the failure of systems. Probability in the Engineering and Informational Sciences 5: 215–227.CrossRefGoogle Scholar
7.Fussell, J.B. & Vesely, W.E. (1972). A new methodology for obtaining cut sets for fault trees. American Nuclear Society Transactions 15(1): 262–263.Google Scholar
8.Hollander, M., Proschan, F., & Sethuraman, J. (1977). Functions decreasing in transposition and their applications in ranking problems. Annals of Statistics 5: 722–733.CrossRefGoogle Scholar
9.Marshall, A.W. & Olkin, I. (1979). Theory of majorization and its applications. New York: Academic Press.Google Scholar
10.Natvig, B. (1985). New light on measures of importance of system components. Scandinavian Journal of Statistics 12: 43–54.Google Scholar
11.Nevius, S.E., Proschan, F., & Sethuraman, J. (1977). Schur functions in statistics — II, stochastic majorization. Annals of Statistics 5: 263–273.CrossRefGoogle Scholar
12.Pledger, G. & Proschan, F. (1971). Comparisons of order statistics and of spacings from heterogeneous distributions. In Rustagi, J. (ed.), Optimization methods in statistics. New York: Academic Press, pp. 89–113.Google Scholar
13.Proschan, F. & Sethuraman, J. (1977). Schur functions in statistics — I, the preservation theorem. Annals of Statistics 5: 256–262.CrossRefGoogle Scholar