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COMBINATORIAL APPROACH TO COMPUTING COMPONENT IMPORTANCE INDEXES IN COHERENT SYSTEMS

Published online by Cambridge University Press:  25 November 2011

Ilya B. Gertsbakh  and
Yoseph Shpungin
Ilya B. Gertsbakh
Affiliation:
Department of Mathematics, Ben-Gurion University, Beer-Sheva, 84105, Israel. E-mail: [email protected]
Yoseph Shpungin
Affiliation:
Software Engineering Department, Sami Shamoon College of Engineering, Beer Sheva, 84100, Israel. E-mail: [email protected]
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Abstract

We consider binary coherent systems with independent binary components having equal failure probability q. The system DOWN probability is expressed via its signature's combinatorial analogue, the so-called D-spectrum. Using the definition of the Birnbaum importance measure (BIM), we introduce for each component a new combinatorial parameter, so-called BIM-spectrum, and develop a simple formula expressing component BIM via the component BIM-spectrum. Further extension of this approach allows obtaining a combinatorial representation for the joint reliability importance (JRI) of two components. To estimate component BIMs and JRIs, there is no need to know the analytic formula for system reliability. We demonstrate how our method works using the Monte Carlo approach. We present several examples of estimating component importance measures in a network when the DOWN state is defined as the loss of terminal connectivity.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 1 , January 2012 , pp. 117 - 128
Copyright
Copyright © Cambridge University Press 2011

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References

1.Barlow, R. & Proschan, F. (1975). Statistical theory of reliability and life testing. New York: Holt, Rinehart and Winston.Google 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.Gertsbakh, I. & Shpungin, Y. (2009). Models of network reliability: Analysis, combinatorics and Monte Carlo. Boca Raton, FL: CRC Press.Google Scholar
4.Gao, X., Cui, L., & Li, J. (2007). Analysis for joint importance of components in a coherent system. European Journal of Operational Research 182: 282–299.Google Scholar
5.Hong, J.S. & Lie, C.H. (1993). Joint reliability importance of two edges in an undirected network. IEEE Transactions on Reliability 42(1): 17–23.CrossRefGoogle Scholar
6.Samaniego, F. (2007). System signatures and their application in engineering reliability. New York: Springer.CrossRefGoogle Scholar
7.Spizzichino, F. & Navarro, J. (2011). Signatures and symmetry properties of coherent systems. In Frenkel, I. & Lisniansky, A. (eds.), Advances in reliability. New York: Springer, 33–48.Google Scholar