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An efficient sum of disjoint product method for reliability evaluation of stochastic flow networks using d-MPs

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  • Esha Datta

    (Indian Institute of Technology)

  • Neeraj Goyal

    (Indian Institute of Technology)

Abstract

Stochastic flow network evaluation methods often compute a set of success events as d-MPs and obtain reliability from d-MPs. Both finding d-MPs and obtaining reliability from d-MPs are NP-Hard problems. This work addresses the problem of finding the reliability from d-MPs. In particular, we propose three rules to identify redundant and disjoint d-MPs as well as to disjoint the non-disjointed d-MPs. The non-disjointed d-MPs have shared capacity states which needs to be eliminated while evaluating reliability from the d-MPs. We implemented the proposed method in MATLAB and compared its performance with the existing methods using benchmark networks available in the literature. The experimental results show that the proposed SDP method performs better than the existing methods. This improvement is attributed to avoiding certain redundant computations which are part of the existing methods. We also present some practical applications of the stochastic network reliability analysis.

Suggested Citation

  • Esha Datta & Neeraj Goyal, 2023. "An efficient sum of disjoint product method for reliability evaluation of stochastic flow networks using d-MPs," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(4), pages 1228-1246, August.
    • Handle: RePEc:spr:ijsaem:v:14:y:2023:i:4:d:10.1007_s13198-023-01927-y
    DOI: 10.1007/s13198-023-01927-y
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    References listed on IDEAS

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    1. Yi-Kuei Lin & Cheng-Fu Huang & Cheng-Ta Yeh, 2016. "Assessment of system reliability for a stochastic-flow distribution network with the spoilage property," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(6), pages 1421-1432, April.
    2. Forghani-elahabad, Majid & Mahdavi-Amiri, Nezam, 2015. "An efficient algorithm for the multi-state two separate minimal paths reliability problem with budget constraint," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 472-481.
    3. 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).
    4. Esha Datta & Neeraj Kumar Goyal, 2019. "Evaluation of stochastic flow networks susceptible to demand requirements between multiple sources and multiple destinations," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 1302-1327, October.
    5. Esha Datta & Neeraj Kumar Goyal, 2017. "Sum of disjoint product approach for reliability evaluation of stochastic flow networks," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1734-1749, November.
    6. 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.
    7. Chen, Shin-Guang & Lin, Yi-Kuei, 2020. "A permutation-and-backtrack approach for reliability evaluation in multistate information networks," Applied Mathematics and Computation, Elsevier, vol. 373(C).
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