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Optimal design of k-out-of-n system under first and last replacement in reliability theory

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Abstract

In various critical applications of many systems, economic use has been an essential architectural attribute for achieving high performance. A k-out-of-n system, which consists of n components and fails if at least \(n-k+1\) of the n components fail, is one of the most important systems in practice. Several researchers have shown that, there is an optimal design of such a system, so that the expected total cost of the system is minimized. The present paper aims to find the best compromise between age replacement and system configuration to design a k-out-of-n system when replacement first and last are applied i.e. the system undergoes preventive maintenances before failure at a planned time T or at a random working cycle Y whichever occurs first or last. Expected cost rates for the first and last replacement are formulated. Case studies are provided to illustrate the applications of the theoretical results developed and a numerical algorithm is made to obtain optimal k-out-of-n system configuration.

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Authors and Affiliations

  1. Polytechnic School of Tunisia, University of Carthage, 2078, La Marsa, Tunisia

    Nizar Mannai

  2. Tunis National Higher School of Engineering, University of Tunis, Avenue Taha Hussein Montfleury, 1008, Tunis, Tunisia

    Soufiane Gasmi

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  1. Nizar Mannai
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  2. Soufiane Gasmi
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Correspondence to Soufiane Gasmi.

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Mannai, N., Gasmi, S. Optimal design of k-out-of-n system under first and last replacement in reliability theory. Oper Res Int J 20, 1353–1368 (2020). https://doi.org/10.1007/s12351-018-0375-4

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  • DOI: https://doi.org/10.1007/s12351-018-0375-4

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