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Reliability modeling of coherent systems with shared components based on sequential order statistics

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  16 November 2018

S. Ashrafi ,
S. Zarezadeh  and
M. Asadi
S. Ashrafi*
Affiliation:
University of Isfahan
S. Zarezadeh*
Affiliation:
Shiraz University
M. Asadi*
Affiliation:
University of Isfahan
*
* Postal address: Department of Statistics, University of Isfahan, Isfahan, 81744, Iran.
*** Postal address: Department of Statistics, Shiraz University, Shiraz, 71454, Iran. Email address: [email protected]
* Postal address: Department of Statistics, University of Isfahan, Isfahan, 81744, Iran.
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Abstract

In this paper we are concerned with the reliability properties of two coherent systems having shared components. We assume that the components of the systems are two overlapping subsets of a set of n components with lifetimes X1,...,Xn. Further, we assume that the components of the systems fail according to the model of sequential order statistics (which is equivalent, under some mild conditions, to the failure model corresponding to a nonhomogeneous pure-birth process). The joint reliability function of the system lifetimes is expressed as a mixture of the joint reliability functions of the sequential order statistics, where the mixing probabilities are the bivariate signature matrix associated to the structures of systems. We investigate some stochastic orderings and dependency properties of the system lifetimes. We also study conditions under which the joint reliability function of systems with shared components of order m can be equivalently written as the joint reliability function of systems of order n (n>m). In order to illustrate the results, we provide several examples.

Keywords

Bivariate signature matrixpositive quadrant dependentnonhomogeneous pure-birth processstochastic orderingequivalent systems

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 3 , September 2018 , pp. 845 - 861
Copyright
Copyright © Applied Probability Trust 2018 

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