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Optimal redundancy allocation in coherent systems with heterogeneous dependent components

Part of: Operations research and management science Special processes Survival analysis and censored data

Published online by Cambridge University Press:  25 August 2022

Maryam Kelkinnama  and
Majid Asadi Open the ORCID record for Majid Asadi [Opens in a new window]
Maryam Kelkinnama*
Affiliation:
Isfahan University of Technology
Majid Asadi*
Affiliation:
University of Isfahan
*
*Postal address: Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran. Email address: m.kelkinnama@iut.ac.ir
**Postal address: Department of Statistics, University of Isfahan, Isfahan 81744, Iran, & School of Mathematics, Institute of Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran, Iran. Email address: m.asadi@sci.ui.ac.ir
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Abstract

This paper is concerned with the optimal number of redundant allocation to n-component coherent systems consisting of heterogeneous dependent components. We assume that the system is built up of L groups of different components, $L\geq 1$ , where there are $n_i$ components in group i, and $\sum_{i=1}^{L}n_i=n$ . The problem of interest is to allocate $v_i$ active redundant components to each component of type i, $i=1,\dots, L$ . To get the optimal values of $v_i$ we propose two cost-based criteria. One of them is introduced based on the costs of renewing the failed components and the costs of refreshing the alive ones at the system failure time. The other criterion is proposed based on the costs of replacing the system at its failure time or at a predetermined time $\tau$ , whichever occurs first. The expressions for the proposed functions are derived using the mixture representation of the system reliability function based on the notion of survival signature. We assume that a given copula function models the dependency structure between the components. In the particular case that the system is a series-parallel structure, we provide the formulas for the proposed cost-based functions. The results are discussed numerically for some specific coherent systems.

Keywords

Reliabilitycost optimalitysystem maintenancesurvival signatureactive redundancyexchangeability

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K10: Applications (reliability, demand theory, etc.) 62N05: Reliability and life testing
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 4 , December 2022 , pp. 1144 - 1177
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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