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COMPARING BIRNBAUM IMPORTANCE MEASURE OF SYSTEM COMPONENTS

Published online by Cambridge University Press:  16 April 2004

Fan C. Meng
Affiliation:
Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan, E-mail: fcmeng@stat.sinica.edu.tw

Abstract

This article provides us with some simple criteria to compare Birnbaum reliability importance measure of components in a general binary coherent system. Such criteria are particularly useful in the absence of information concerning component reliabilities. We also find several simple (necessary and sufficient) conditions concerning system structure, under which such comparison is possible. Examples are given to illustrate our results.

Type
Research Article
Copyright
© 2004 Cambridge University Press

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References

REFERENCES

Barlow, R.E. & Proschan, F. (1981). Statistical theory of reliability and life testing. Silver Spring, MD: To Begin With.
Birnbaum, Z.W. (1969). On the importance of different components in a multicomponent system. In P.R. Krishnaiah (ed.), Multivariate Analysis II. New York: Academic Press, pp. 581592.
Boland, P.J. & Proschan, F. (1983). The reliability of k out of n systems. Annals of Probability 11: 760764.Google Scholar
Boland, P.J., Proschan, F., & Tong, Y.L. (1989). Optimal arrangement of components via pairwise rearrangements. Naval Research Logistics 36: 807815.Google Scholar
Butler, D.A. (1979). A complete importance ranking for components of binary coherent systems with extensions to multi-state systems. Naval Research Logistics Quarterly 4: 565578.Google Scholar
Marshall, A. & Olkin, I. (1981). Inequalities: Theory of majorization and its applications. New York: Academic Press.
Meng, F.C. (1994). Comparing criticality of nodes via minimal cut (path) sets for coherent systems. Probability in the Engineering and Informational Sciences 8: 7987.Google Scholar
Meng, F.C. (1995). Some further results on ranking the importance of system components. Reliability Engineering and System Safety 47(2): 97101.Google Scholar
Meng, F.C. (1996). Comparing the importance of system components by some structural characteristics. IEEE Transactions on Reliability 45: 5965.Google Scholar
Meng, F.C. (2000). Relationships of Fussell–Vesely and Birnbaum importance to structural importance in coherent systems. Reliability Engineering and System Safety 67(1): 5560.Google Scholar