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A rearrangement inequality for the longest run, with an application to network reliability

Published online by Cambridge University Press:  14 July 2016

Y. L. Tong
Y. L. Tong*
Affiliation:
Georgia Institute of Technology
*
∗Postal address: School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA.
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Abstract

Let Xl, · ··, Χ n be independent binary variables with parameters θl, · ··, θ n respectively, and let R denote the length of the longest run of 1's. This note concerns a new expression for and a rearrangement inequality. The inequality is applied to solve an optimal permutation problem for consecutive-k-out-of-n: F networks, and its implications on a recent conjecture of Derman et al. (1982) are discussed.

Keywords

LONGEST RUNREARRANGEMENT INEQUALITYRELIABILITY OF CONSECUTIVE-k-OUT-OF-n: F NETWORKS
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 386 - 393
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

This work was partially supported by NSF Grant MCS81-00775, A01.

References

Derman, C., Lieberman, G. J. and Ross, S. M. (1982) On the consecutive-k-out-of-n: F system. IEEE Trans. Reliability R-31, 57–63.CrossRefGoogle Scholar
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