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Optimal Consecutive-k−Out−of−n Systems under a Fixed Budget

Published online by Cambridge University Press:  27 July 2009

G. J. Chang  and
F. K. Hwang
G. J. Chang
Affiliation:
Department ofMathematics Central University Chungli, Taiwan
F. K. Hwang
Affiliation:
Department of Discrete Mathematics AT&T Bell Laboratories Murray. Hill, New Jersey07974
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Abstract

A consecutive-k−out−of−n system is a graph with n vertices where the system fails if and only if some path of k consecutive vertices all fail. The assumption is made that qi, is the failing probability of the ith vertex and the states of the vertices are statistically independent. The problem is to find the best system, i.e., a set {q1, …,qn}, and its assignment to the vertices of the system graph that maximizes the reliability of the system, under the constraint that the product of qi's is a constant. We solve the problem for all lines and some cycles. We then extend our results to trees and show that for given n and k the best tree is a star and the worst is a line.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 1 , January 1988 , pp. 63 - 73
Copyright
Copyright © Cambridge University Press 1988

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