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Generalized reliability bounds for coherent structures

Part of: Distribution theory - Probability Special processes

Published online by Cambridge University Press:  14 July 2016

Michael V. Boutsikas  and
Markos V. Koutras
Michael V. Boutsikas*
Affiliation:
University of Athens
Markos V. Koutras*
Affiliation:
University of Athens
*
∗Postal address: Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece
∗Postal address: Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece
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Abstract

In this article we introduce generalizations of several well-known reliability bounds. These bounds are based on arbitrary partitions of the family of minimal path or cut sets of the system and can be used for approximating the reliability of any coherent structure with i.i.d. components. An illustration is also given of how the general results can be applied for a specific reliability structure (two-dimensional consecutive-k1 x k2-out-of-n1x n2 system) along with extensive numerical calculations revealing that, in most cases, the generalized bounds perform better than other available bounds in the literature for this system.

Keywords

Reliability boundscut setspath setsassociationbinary coherent structurestwo-dimensional consecutive-k1 × k2-out-of-n1 × n2 system

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 778 - 794
Copyright
Copyright © Applied Probability Trust 2000 

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Footnotes

∗∗∗

Research supported by the National Scholarship Foundation of Greece.

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