Hostname: page-component-5c6d5d7d68-lvtdw Total loading time: 0 Render date: 2024-08-15T08:26:57.429Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparing Criticality of Nodes via Minimal Cut (Path) Sets for Coherent Systems

Published online by Cambridge University Press:  27 July 2009

Fan Chin Meng
Fan Chin Meng
Affiliation:
Institute of Statistical Science, Academia Sinica Taipei, 11529, Taiwan
Get access Rights & Permissions [Opens in a new window]

Abstract

In 1989, Boland, Proschan, and Tong [2] introduced the notion of criticality ranking among nodes and developed a procedure for obtaining an optimal assignment of components in coherent systems. In this article we obtain characterizations of the criticality ranking in terms of minimal cut (path) sets for coherent systems. Furthermore, utilizing the characterizations, it is shown that the criticality ranking defined by Boland et al. [2] is consistent with the cut-importance ranking introduced by Butler in 1979 [4]. A relationship between the criticality ranking and the well-known and widely used Birnbaum reliability importance measure is also derived.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 1 , January 1994 , pp. 79 - 87
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. (1981). Statistical theory of reliability and life testing: Probability models. Silver Spring, MD: To Begin With.Google Scholar
2.Boland, P.J., Proschan, F., & Tong, Y.L. (1989). Optimal arrangement of components via pair-wise rearrangements. Naval Research Logistics 36: 807–815.3.0.CO;2-I>CrossRefGoogle Scholar
3.Butler, D.A. (1978). An importance ranking for system components based on cuts. Operations Research 25: 874–879.CrossRefGoogle Scholar
4.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: 565–578.CrossRefGoogle Scholar
5.Derman, C., Lieberman, G.J., & Ross, S.M. (1974). Assembly of systems having maximum reliability. Naval Research Logistics Quarterly 21: 1–12.CrossRefGoogle Scholar
6.Derman, C., Lieberman, G.J., & Ross, S.M. (1982). On the consecutive-k-of-n:F system. IEEE Transactions on Reliability R-31: 57–63.CrossRefGoogle Scholar
7.El-Neweihi, E., Proschan, F., & Sethuraman, J. (1986). Optimal allocation of components in parallel-series and series-parallel systems. Journal of Applied Probability 23: 770–777.CrossRefGoogle Scholar