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A new cut-based algorithm for the multi-state flow network reliability problem

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  • Yeh, Wei-Chang
  • Bae, Changseok
  • Huang, Chia-Ling

Abstract

Many real-world systems can be modeled as multi-state network systems in which reliability can be derived in terms of the lower bound points of level d, called d-minimal cuts (d-MCs). This study proposes a new method to find and verify obtained d-MCs with simple and useful found properties for the multi-state flow network reliability problem. The proposed algorithm runs in O(mσp) time, which represents a significant improvement over the previous O(mp2σ) time bound based on max-flow/min-cut, where p, σ and m denote the number of MCs, d-MC candidates and edges, respectively. The proposed algorithm also conquers the weakness of some existing methods, which failed to remove duplicate d-MCs in special cases. A step-by-step example is given to demonstrate how the proposed algorithm locates and verifies all d-MC candidates. As evidence of the utility of the proposed approach, we present extensive computational results on 20 benchmark networks in another example. The computational results compare favorably with a previously developed algorithm in the literature.

Suggested Citation

  • Yeh, Wei-Chang & Bae, Changseok & Huang, Chia-Ling, 2015. "A new cut-based algorithm for the multi-state flow network reliability problem," Reliability Engineering and System Safety, Elsevier, vol. 136(C), pages 1-7.
    • Handle: RePEc:eee:reensy:v:136:y:2015:i:c:p:1-7
    DOI: 10.1016/j.ress.2014.11.010
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    References listed on IDEAS

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    1. Joseph C. Hudson & Kailash C. Kapur, 1985. "Reliability Bounds for Multistate Systems with Multistate Components," Operations Research, INFORMS, vol. 33(1), pages 153-160, February.
    2. Yan, Zhou & Qian, Meng, 2007. "Improving efficiency of solving d-MC problem in stochastic-flow network," Reliability Engineering and System Safety, Elsevier, vol. 92(1), pages 30-39.
    3. Gregory Levitin, 2005. "The Universal Generating Function in Reliability Analysis and Optimization," Springer Series in Reliability Engineering, Springer, number 978-1-84628-245-4, February.
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    Citations

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    Cited by:

    1. Yeh, Wei-Chang, 2021. "A quick BAT for evaluating the reliability of binary-state networks," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    2. Yeh, Wei-Chang, 2020. "A new method for verifying d-MC candidates," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    3. Lin, Yi-Kuei & Huang, Ding-Hsiang, 2020. "Reliability analysis for a hybrid flow shop with due date consideration," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    4. Paweł Marcin Kozyra, 2020. "Analysis of minimal path and cut vectors in multistate monotone systems and use it for detection of binary type multistate monotone systems," Journal of Risk and Reliability, , vol. 234(5), pages 686-695, October.
    5. Niu, Yi-Feng & Wan, Xiao-Yu & Xu, Xiu-Zhen & Ding, Dong, 2020. "Finding all multi-state minimal paths of a multi-state flow network via feasible circulations," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    6. Niu, Yi-Feng & Gao, Zi-You & Lam, William H.K., 2017. "A new efficient algorithm for finding all d-minimal cuts in multi-state networks," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 151-163.
    7. Kozyra, Paweł Marcin, 2023. "The usefulness of (d,b)-MCs and (d,b)-MPs in network reliability evaluation under delivery or maintenance cost constraints," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    8. Yeh, Wei-Chang, 2021. "Novel binary-addition tree algorithm (BAT) for binary-state network reliability problem," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    9. Yeh, Wei-Chang & Du, Chia-Ming & Tan, Shi-Yi & Forghani-elahabad, Majid, 2023. "Application of LSTM based on the BAT-MCS for binary-state network approximated time-dependent reliability problems," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    10. Niu, Yi-Feng & Zhao, Xia & Xu, Xiu-Zhen & Zhang, Shi-Yun, 2023. "Reliability assessment of a stochastic-flow distribution network with carbon emission constraint," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    11. Barranco, Manuel & Proenza, Julián & Almeida, Luís, 2015. "Quantitative characterization of the reliability of simplex buses and stars to compare their benefits in fieldbuses," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 163-175.
    12. Yeh, Wei-Chang & Tan, Shi-Yi & Zhu, Wenbo & Huang, Chia-Ling & Yang, Guang-yi, 2022. "Novel binary addition tree algorithm (BAT) for calculating the direct lower-bound of the highly reliable binary-state network reliability," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    13. Yeh, Wei-Chang, 2024. "A new hybrid inequality BAT for comprehensive all-level d-MP identification using minimal paths in Multistate Flow Network reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    14. Zhang, Hanxiao & Sun, Muxia & Li, Yan-Fu, 2022. "Reliability–redundancy allocation problem in multi-state flow network: Minimal cut-based approximation scheme," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    15. Niu, Yi-Feng, 2021. "Performance measure of a multi-state flow network under reliability and maintenance cost considerations," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    16. Goharshady, Amir Kafshdar & Mohammadi, Fatemeh, 2020. "An efficient algorithm for computing network reliability in small treewidth," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    17. Liu, Tao & Bai, Guanghan & Tao, Junyong & Zhang, Yun-An & Fang, Yining & Xu, Bei, 2022. "Modeling and evaluation method for resilience analysis of multi-state networks," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    18. Niu, Yi-Feng & Gao, Zi-You & Lam, William H.K., 2017. "Evaluating the reliability of a stochastic distribution network in terms of minimal cuts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 100(C), pages 75-97.
    19. Cheng-Fu Huang, 2022. "System reliability for a multi-state distribution network with multiple terminals under stocks," Annals of Operations Research, Springer, vol. 311(1), pages 117-130, April.
    20. Wei, Wei & Hu, Qiuyuan & Zhang, Qinghui, 2024. "Improving node connectivity by optimized dual tree-based effective node consolidation," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    21. Yeh, Wei-Chang & Hao, Zhifeng & Forghani-elahabad, Majid & Wang, Gai-Ge & Lin, Yih-Lon, 2021. "Novel Binary-Addition Tree Algorithm for Reliability Evaluation of Acyclic Multistate Information Networks," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    22. Bai, Guanghan & Zuo, Ming J. & Tian, Zhigang, 2015. "Search for all d-MPs for all d levels in multistate two-terminal networks," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 300-309.

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