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A dynamic bounding algorithm for approximating multi-state two-terminal reliability

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  • Jane, Chin-Chia
  • Laih, Yih-Wenn

Abstract

This paper modifies Jane and Laih's (2008) exact and direct algorithm to provide sequences of upper bounds and lower bounds that converge to the NP-hard multi-state two-terminal reliability. Advantages of the modified algorithm include (1) it does not require a priori the lower and/or upper boundary points of the network, (2) it derives a series of increasing lower bounds and a series of decreasing upper bounds simultaneously, guaranteed to enclose the exact reliability value, and (3) trade-off between accuracy and execution time can be made to ensure an exact difference between the upper and lower bounds within an acceptable time. Examples are analyzed to illustrate the bounding algorithm, and to compare the bounding algorithm with existing algorithms. Computational experiments on a large network are conducted to realize the performance of the bounding algorithm.

Suggested Citation

  • Jane, Chin-Chia & Laih, Yih-Wenn, 2010. "A dynamic bounding algorithm for approximating multi-state two-terminal reliability," European Journal of Operational Research, Elsevier, vol. 205(3), pages 625-637, September.
    • Handle: RePEc:eee:ejores:v:205:y:2010:i:3:p:625-637
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    References listed on IDEAS

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    1. Jane, Chin-Chia & Yuan, John, 2001. "A sum of disjoint products algorithm for reliability evaluation of flow networks," European Journal of Operational Research, Elsevier, vol. 131(3), pages 664-675, June.
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    6. BALL, Michael O., 1979. "Computing network reliability," LIDAM Reprints CORE 377, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    8. Ahuja, Ravindra K. & Kodialam, Murali & Mishra, Ajay K. & Orlin, James B., 1997. "Computational investigations of maximum flow algorithms," European Journal of Operational Research, Elsevier, vol. 97(3), pages 509-542, March.
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    Cited by:

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    2. 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.
    3. Byun, Ji-Eun & Zwirglmaier, Kilian & Straub, Daniel & Song, Junho, 2019. "Matrix-based Bayesian Network for efficient memory storage and flexible inference," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 533-545.
    4. Schneider, Kellie & Rainwater, Chase & Pohl, Ed & Hernandez, Ivan & Ramirez-Marquez, Jose Emmanuel, 2013. "Social network analysis via multi-state reliability and conditional influence models," Reliability Engineering and System Safety, Elsevier, vol. 109(C), pages 99-109.
    5. Xu, Bei & Liu, Tao & Bai, Guanghan & Tao, Junyong & Zhang, Yun-an & Fang, Yining, 2022. "A multistate network approach for reliability evaluation of unmanned swarms by considering information exchange capacity," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    6. Wang, Yong & Li, Lin & Huang, Shuhong & Chang, Qing, 2012. "Reliability and covariance estimation of weighted k-out-of-n multi-state systems," European Journal of Operational Research, Elsevier, vol. 221(1), pages 138-147.
    7. 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).
    8. Forghani-elahabad, Majid & Kagan, Nelson & Mahdavi-Amiri, Nezam, 2019. "An MP-based approximation algorithm on reliability evaluation of multistate flow networks," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    9. Jane, Chin-Chia & Laih, Yih-Wenn, 2017. "Distribution and reliability evaluation of max-flow in dynamic multi-state flow networks," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1045-1053.
    10. 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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