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Pseudo-modular decompositions and ‘refined bounds’ for the interval reliability and the availability for binary coherent systems

Published online by Cambridge University Press:  01 July 2016

N. Mazars
N. Mazars*
Affiliation:
University of Oslo
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Abstract

‘Divide and conquer’ is a traditional approach in various fields of applied mathematics. In reliability, only modules have been proposed to decompose complex coherent systems. However, a system may include no modules, except ‘trivial’ ones. This paper is the second step of a study concerned with module generalizations : in the first step, pseudo-modules have been retained as the most general coherent subsystems which can yield a complete extension of the fundamental results concerning modules; in addition, it has been proved that they concern any binary coherent system; in this paper, it is shown that pseudo-modular decompositions are the most general coherent decompositions which can yield a complete extension of all the ‘refined bounds’ for the interval reliability and the availability currently proposed in terms of modular decompositions.

This study also yields some fundamental results to extend all the ‘refined bounds’ currently proposed for multistate coherent systems, using an easier approach.

Keywords

MODULESCOHERENT SUBSYSTEMSPSEUDO-MODULESQUASI-MODULESPERFORMANCE FUNCTIONPOSITIVE ASSOCIATION
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 1 , March 1989 , pp. 91 - 122
Copyright
Copyright © Applied Probability Trust 1989 

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