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A simple minimal path method for estimating the weighted multi-commodity multistate unreliable networks reliability

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  • Yeh, Wei-Chang

Abstract

The weighted multicommodity multistate unreliable network (WMMUN) is a novel network composed of multistate unreliable components (arcs and nodes) capable of transmitting different types of commodities in which capacity weight varies with components. It is an extension of the multistate network. The current method for evaluating the directed WMMUN reliability has been derived from minimal cut (MC) based algorithm. The existing best-known method needed extensive comparison and verification, and failed to find the real directed WMMUN reliability. A very simple algorithm based on minimal paths (MPs) is developed for the WMMUN reliability problem. The correctness and computational complexity of the proposed algorithm will be analyzed and proven. An example is given to illustrate how the WMMUN reliability is evaluated using the proposed algorithm. The relationships among all different versions of MPs are also clarified.

Suggested Citation

  • Yeh, Wei-Chang, 2008. "A simple minimal path method for estimating the weighted multi-commodity multistate unreliable networks reliability," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 125-136.
    • Handle: RePEc:eee:reensy:v:93:y:2008:i:1:p:125-136
    DOI: 10.1016/j.ress.2006.11.004
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    References listed on IDEAS

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    1. T. C. Hu, 1963. "Multi-Commodity Network Flows," Operations Research, INFORMS, vol. 11(3), pages 344-360, June.
    2. Yeh, Wei-Chang, 2004. "Multistate network reliability evaluation under the maintenance cost constraint," International Journal of Production Economics, Elsevier, vol. 88(1), pages 73-83, March.
    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, January.
    4. Yeh, Wei-Chang, 2007. "An improved sum-of-disjoint-products technique for the symbolic network reliability analysis with known minimal paths," Reliability Engineering and System Safety, Elsevier, vol. 92(2), pages 260-268.
    5. Yeh, Wei-Chang, 2006. "The k-out-of-n acyclic multistate-node networks reliability evaluation using the universal generating function method," Reliability Engineering and System Safety, Elsevier, vol. 91(7), pages 800-808.
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    Citations

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    Cited by:

    1. Yi-Kuei Lin & Cheng-Fu Huang, 2016. "Reliability evaluation according to a routing scheme for multi-state computer networks under assured accuracy rate," Annals of Operations Research, Springer, vol. 244(1), pages 221-240, September.
    2. Yeh, Wei-Chang, 2021. "A quick BAT for evaluating the reliability of binary-state networks," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    3. Yeh, Wei-Chang, 2020. "A new method for verifying d-MC candidates," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
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    6. Tina Song, Wheyming & Lin, Peisyuan, 2018. "System reliability of stochastic networks with multiple reworks," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 258-268.
    7. Yun Zhang & Zhengguo Xu & Xinli Wang & Jiangang Lu & Youxian Sun, 2014. "Single minimal path based backup path for multi-state network," Journal of Risk and Reliability, , vol. 228(2), pages 152-165, April.
    8. Yeh, Wei-Chang, 2023. "Novel recursive inclusion-exclusion technology based on BAT and MPs for heterogeneous-arc binary-state network reliability problems," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    9. Yu-Cheng Chou & Po Ting Lin, 2015. "An efficient and robust design optimisation of multi-state flow network for multiple commodities using generalised reliability evaluation algorithm and edge reduction method," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(14), pages 2659-2672, October.
    10. Yeh, Wei-Chang, 2023. "QB-II for evaluating the reliability of binary-state networks," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    11. Lin, Yi-Kuei, 2010. "Reliability evaluation of a revised stochastic flow network with uncertain minimum time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(6), pages 1253-1258.
    12. Ji Hwan Cha & Maxim Finkelstein, 2019. "On some characteristics of quality for systems operating in a random environment," Journal of Risk and Reliability, , vol. 233(2), pages 257-267, April.
    13. Ji Hwan Cha & Maxim Finkelstein, 2019. "Optimal preventive maintenance for systems having a continuous output and operating in a random environment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 327-350, July.
    14. Lin, Shuai & Jia, Limin & Zhang, Hengrun & Zhang, Pengzhu, 2022. "Reliability of high-speed electric multiple units in terms of the expanded multi-state flow network," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    15. Lin, Yi-Kuei & Huang, Cheng-Fu & Chang, Ping-Chen, 2013. "System reliability evaluation of a touch panel manufacturing system with defect rate and reworking," Reliability Engineering and System Safety, Elsevier, vol. 118(C), pages 51-60.
    16. Khodakaram Salimifard & Sara Bigharaz, 2022. "The multicommodity network flow problem: state of the art classification, applications, and solution methods," Operational Research, Springer, vol. 22(1), pages 1-47, March.
    17. Lin, Yi-Kuei & Chang, Ping-Chen, 2012. "Evaluate the system reliability for a manufacturing network with reworking actions," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 127-137.
    18. Lin, Yi-Kuei, 2010. "Calculation of minimal capacity vectors through k minimal paths under budget and time constraints," European Journal of Operational Research, Elsevier, vol. 200(1), pages 160-169, January.
    19. George-Williams, Hindolo & Patelli, Edoardo, 2016. "A hybrid load flow and event driven simulation approach to multi-state system reliability evaluation," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 351-367.
    20. Hao, Zhifeng & Yeh, Wei-Chang & Zuo, Ming & Wang, Jing, 2020. "Multi-distribution multi-commodity multistate flow network model and its reliability evaluation algorithm," Reliability Engineering and System Safety, Elsevier, vol. 193(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. Ji Hwan Cha & Maxim Finkelstein, 2020. "Stochastic modelling of operational quality of k-out-of-n systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 424-441, July.
    23. Lin, Yi-Kuei, 2010. "System reliability of a stochastic-flow network through two minimal paths under time threshold," International Journal of Production Economics, Elsevier, vol. 124(2), pages 382-387, April.

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