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On Optimal Consecutive k-out-of-n: F Systems Subject to a Fixed Product of Failure Probabilities

Published online by Cambridge University Press:  27 July 2009

Y. C. Yao
Y. C. Yao
Affiliation:
Department of Statistics Colorado State University Fort Collins, Colorado 80523
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Extract

A consecutive−k−out−of−n:F system is an n−vertex graph where the system fails if and only if some k consecutive vertices all fail. Assuming that the n vertices have, independently, the respective failure probabilities q1,…, qn, the problem is to find, subject to πqi = Q (a constant), a set of q1,…, qn so as to maximize the system reliability. In the case that the graph is a circle (or cycle), Chang and Hwang [1] conjectured that q1 =… = qn, = Q1/n is optimal if n and k are relatively prime. In this paper, it is shown that the conjecture is true for sufficiently small Q. It is also shown by counterexample that the conjecture is not true in general.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 2 , April 1989 , pp. 165 - 173
Copyright
Copyright © Cambridge University Press 1989

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References

REFERENCES

Chang, G.J. & Hwang, F.K. (1988). Optimal consecutive−k−out−of−n systems under a fixed budget. Probability in the Engineering and Informational Sciences 2: 63–73.CrossRefGoogle Scholar
Chiang, D.T. & Niu, S.C. (1981). Reliability of consecutive−k−out−of−n: F systems. IEEE Transactions on Reliability R-30: 87–89.CrossRefGoogle Scholar
Derman, C., Lieberman, G.J., & Ross, S.M. (1982). On the onsecutive−k−of−n: F system. IEEE Transactions on Reliability R-31: 57–63.Google Scholar
Du, D.Z. & Hwang, F.K. (1986). Optimal consecutive-2-out-of-n systems. Mathematics of Operations Research 11: 187–191.Google Scholar
Hwang, F.K. (1982). Fast solutions for consecutive-k-out-of-n systems. IEEE Transactions on Reliability R-31: 447–448.CrossRefGoogle Scholar
Hwang, F.K. (1986). Simplified reliabilities for consecutive−k−out−of−n systems. SIAM Journal on Algebraic and Discrete Methods 7: 258–264.Google Scholar
Lambiris, M. & Papastavridis, S. (1985). Exact reliability formulas for linear and circular consecutive−k−out−of−n: F systems. IEEE Transactions on Reliobility R-34: 124–126.CrossRefGoogle Scholar
Malon, D.M. (1985). Optimal consecutive−k−out−of−n: F component sequencing. IEEE Transactions on Reliability R-34: 46–49.CrossRefGoogle Scholar
Shanthikumar, J.G. (1982). Recursive algorithm to evaluate the reliability of a consecutive−k− out−of−n: F system. IEEE Transactions on Reliability R-31: 442–443.Google Scholar
Wang, E.T. (1988). Letter to the editor. Mathmedia 12: 106–108 (in Chinese).Google Scholar