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A new efficient algorithm for finding all d-minimal cuts in multi-state networks

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  • Niu, Yi-Feng
  • Gao, Zi-You
  • Lam, William H.K.

Abstract

Reliability evaluation of multi-state systems gives a reasonable demonstration of system performance, and thus is of great importance to their planning, designing and operation. One of the common methods for reliability evaluation is using d-minimal cuts (d-MCs). This paper proposes a new method to solve the d-MC problem. Specifically, several efforts have been devoted to searching for all d-MCs from two aspects: (i) A new technique is developed to calculate lower capacity bounds of edges which are appropriately used to determine some real d-MCs without any verification, and further to reduce the number of d-MC candidates; (ii) A new approach is put forward to correctly and effectively detect duplicate d-MCs, and the approach brings important insights into the underlying reason why a d-MC derived from one MC can be generated from another MC once again. A simple example and a real case study of the LCD monitor delivery are provided to illustrate the solution procedure, and the utility of the proposed algorithm, respectively. In addition, numerical experiments conducted on four benchmark networks show that the proposed algorithm outperforms a newly developed method in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:166:y:2017:i:c:p:151-163
    DOI: 10.1016/j.ress.2017.05.032
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    3. 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.
    4. 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).
    5. Zhou, Yifan & Liu, Libo & Li, Hao, 2022. "Reliability estimation and optimisation of multistate flow networks using a conditional Monte Carlo method," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    6. Schäfer, Lukas & García, Sergio & Srithammavanh, Vassili, 2018. "Simplification of inclusion–exclusion on intersections of unions with application to network systems reliability," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 23-33.
    7. Huang, Ding-Hsiang & Huang, Cheng-Fu & Lin, Yi-Kuei, 2020. "A novel minimal cut-based algorithm to find all minimal capacity vectors for multi-state flow networks," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1107-1114.
    8. Majid Forghani-elahabad & Omar Mutab Alsalami, 2023. "Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints," Mathematics, MDPI, vol. 11(24), pages 1-15, December.
    9. Niu, Yi-Feng & Song, Yi-Fan & Xu, Xiu-Zhen & Zhao, Xia, 2022. "Efficient reliability computation of a multi-state flow network with cost constraint," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    10. Huang, Cheng-Fu & Huang, Ding-Hsiang & Lin, Yi-Kuei, 2022. "Network reliability evaluation for multi-state computing networks considering demand as the non-integer type," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    11. Forghani-elahabad, Majid & Yeh, Wei-Chang, 2022. "An improved algorithm for reliability evaluation of flow networks," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
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    13. 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).

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