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On the optimal redundancy allocation for multi-state series–parallel systems under epistemic uncertainty

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  • Sun, Mu-Xia
  • Li, Yan-Fu
  • Zio, Enrico

Abstract

In this paper, we study the redundancy allocation problem (RAP) for multi-state series–parallel systems (MSSPSs). For each multi-state component, the exact values of its state probabilities are assumed to be unknown, due to epistemic uncertainty (EU), and only conservative lower and upper bounds of them are given. The objective of the RAP is to simultaneously maximize the supremum and infimum of the system's uncertain availability, under a cost constraint. The problem is two-stage and multi-objective. In this work, we: 1. provide a linear-time algorithm to obtain the component state distribution, under which the uncertain system availability will be at its supremum or infimum; 2. show that the problem is reducible to one-stage; 3. analyze the landscape of MSSPS RAP under EU and propose a modified NSGA-II, with targeted designs of repair and local search operation. The proposed algorithm is compared with standard NSGA-II on multiple benchmarks. The results show that the proposed algorithm significantly outperforms the standard NSGA-II in both optimality and time efficiency.

Suggested Citation

  • Sun, Mu-Xia & Li, Yan-Fu & Zio, Enrico, 2019. "On the optimal redundancy allocation for multi-state series–parallel systems under epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:reensy:v:192:y:2019:i:c:s0951832016310080
    DOI: 10.1016/j.ress.2017.11.025
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    References listed on IDEAS

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    1. Ouzineb, Mohamed & Nourelfath, Mustapha & Gendreau, Michel, 2008. "Tabu search for the redundancy allocation problem of homogenous series–parallel multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 93(8), pages 1257-1272.
    2. Rashika Gupta & Manju Agarwal, 2006. "Penalty guided genetic search for redundancy optimization in multi-state series-parallel power system," Journal of Combinatorial Optimization, Springer, vol. 12(3), pages 257-277, November.
    3. Jaszkiewicz, Andrzej, 2002. "Genetic local search for multi-objective combinatorial optimization," European Journal of Operational Research, Elsevier, vol. 137(1), pages 50-71, February.
    4. Li, Chun-yang & Chen, Xun & Yi, Xiao-shan & Tao, Jun-yong, 2010. "Heterogeneous redundancy optimization for multi-state series–parallel systems subject to common cause failures," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 202-207.
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    Citations

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    Cited by:

    1. Enrico Zio & Hadi Gholinezhad, 2023. "Redundancy Allocation of Components with Time-Dependent Failure Rates," Mathematics, MDPI, vol. 11(16), pages 1-27, August.
    2. Li, Yan-Fu & Zhang, Hanxiao, 2022. "The methods for exactly solving redundancy allocation optimization for multi-state series–parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    3. Xu, Yue & Pi, Dechang & Yang, Shengxiang & Chen, Yang, 2021. "A novel discrete bat algorithm for heterogeneous redundancy allocation of multi-state systems subject to probabilistic common-cause failure," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    4. Sharifi, Mani & Taghipour, Sharareh, 2024. "Redundancy allocation problem with a mix of components for a multi-state system and continuous performance level components," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    5. Narayanaswamy Balakrishnan & Ghobad Saadat Kia (Barmalzan) & Aliakbar Hosseinzadeh & Mostafa Sattari, 2023. "Optimal Grouping of Dependent Components in Parallel-Series and Series-Parallel Systems with Independent Subsystems Equipped with Starting Devices," Mathematics, MDPI, vol. 11(17), pages 1-19, August.
    6. Kowal, Karol, 2022. "Lifetime reliability and availability simulation for the electrical system of HTTR coupled to the electricity-hydrogen cogeneration plant," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    7. Yeh, Wei-Chang & Zhu, Wenbo & Tan, Shi-Yi & Wang, Gai-Ge & Yeh, Yuan-Hui, 2022. "Novel general active reliability redundancy allocation problems and algorithm," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).

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