Hostname: page-component-76c49bb84f-lvxqv Total loading time: 0 Render date: 2025-07-13T02:53:52.589Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 386 - 393
Copyright
Copyright © Applied Probability Trust 1985 

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.)

Article purchase

Temporarily unavailable

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
Feller, W. (1967) An Introduction to Probability Theory and its Applications, Vol. 1, 3rd edn. Wiley, New York.Google Scholar
Marshall, A. W. and Olkin, I. (1979) Inequalities: Theory of Majorization and its Applications. Academic Press, New York.Google Scholar
Olmstead, P. S. (1940) Note on theoretical and observed distributions of repetitive occurrences. Ann. Math. Statist. 11, 363–366.Google Scholar
Tong, Y. L. (1980) Probability Inequalities in Multivariate Distributions. Academic Press, New York.Google Scholar