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

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  • Nizar Mannai

    (University of Carthage)

  • Soufiane Gasmi

    (University of Tunis)

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 $$n-k+1$$ 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.

Suggested Citation

  • Nizar Mannai & Soufiane Gasmi, 2020. "Optimal design of k-out-of-n system under first and last replacement in reliability theory," Operational Research, Springer, vol. 20(3), pages 1353-1368, September.
    • Handle: RePEc:spr:operea:v:20:y:2020:i:3:d:10.1007_s12351-018-0375-4
    DOI: 10.1007/s12351-018-0375-4
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    Cited by:

    1. Zhang, Qin & Fang, Zhigeng & Cai, Jiajia, 2021. "Preventive replacement policies with multiple missions and maintenance triggering approaches," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    2. Sheu, Shey-Huei & Liu, Tzu-Hsin & Sheu, Wei-Teng & Zhang, Zhe-George & Ke, Jau-Chuan, 2021. "Optimal replacement policy with replacement last under cumulative damage models," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    3. Chin-Chih Chang, 2023. "Optimal maintenance policy for a k-out-of-n system with replacement first and last," Annals of Operations Research, Springer, vol. 323(1), pages 31-43, April.

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