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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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    References listed on IDEAS

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    1. Kim, Heungseob, 2017. "Optimal reliability design of a system with k-out-of-n subsystems considering redundancy strategies," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 572-582.
    2. Wang, Hongzhou, 2002. "A survey of maintenance policies of deteriorating systems," European Journal of Operational Research, Elsevier, vol. 139(3), pages 469-489, June.
    3. Zhao, Xufeng & Qian, Cunhua & Nakagawa, Toshio, 2013. "Optimal policies for cumulative damage models with maintenance last and first," Reliability Engineering and System Safety, Elsevier, vol. 110(C), pages 50-59.
    4. Wang, Yong & Li, Lin & Huang, Shuhong & Chang, Qing, 2012. "Reliability and covariance estimation of weighted k-out-of-n multi-state systems," European Journal of Operational Research, Elsevier, vol. 221(1), pages 138-147.
    5. Yamamoto, Hisashi & Akiba, Tomoaki & Nagatsuka, Hideki & Moriyama, Yurie, 2008. "Recursive algorithm for the reliability of a connected-(1, 2)-or-(2, 1)-out-of-(m, n):F lattice system," European Journal of Operational Research, Elsevier, vol. 188(3), pages 854-864, August.
    6. Xiang, Yanping & Levitin, Gregory, 2012. "Combined m-consecutive and k-out-of-n sliding window systems," European Journal of Operational Research, Elsevier, vol. 219(1), pages 105-113.
    7. Zhao, Xufeng & Nakagawa, Toshio, 2012. "Optimization problems of replacement first or last in reliability theory," European Journal of Operational Research, Elsevier, vol. 223(1), pages 141-149.
    8. Xie, Wei & Liao, Haitao & Jin, Tongdan, 2014. "Maximizing system availability through joint decision on component redundancy and spares inventory," European Journal of Operational Research, Elsevier, vol. 237(1), pages 164-176.
    9. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2014. "Cold vs. hot standby mission operation cost minimization for 1-out-of-N systems," European Journal of Operational Research, Elsevier, vol. 234(1), pages 155-162.
    10. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, January.
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    Cited by:

    1. 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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    3. 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).

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