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A new algorithm for generating minimal cut sets in k-out-of-n networks

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  • Yeh, Wei-Chang

Abstract

Evaluating the network reliability is an important topic in the planning, designing, and control of systems. A k-out-of-n network is a special network in that some nodes must receive at least k (>1) flows from all of their input edges (n). In real-life cases, many networks such as computer and telecommunications include k-out-of-n nodes for redundancy. The minimal-cut-node-set (MCN) is the major and fundamental tools for evaluating the k-out-of-n network reliability. In this study, a very simple algorithm based on some intuitive theorems that characterize the structure of the MCN is developed to solve the k-out-of-n network reliability. Compared to the existing algorithms, the proposed algorithm generates all k-out-of-n MCs without duplication based on fewer MCNs and fewer (k-out-of-n MC) candidates. The proposed algorithm is not only easier to understand and implement, but is also better than the existing algorithms. The correctness of the proposed algorithm will be analyzed and proven. One example is illustrated to show how all k-out-of-n MCs are generated, verified, and implemented to evaluate the k-out-of-n network reliability using the proposed algorithm.

Suggested Citation

  • Yeh, Wei-Chang, 2006. "A new algorithm for generating minimal cut sets in k-out-of-n networks," Reliability Engineering and System Safety, Elsevier, vol. 91(1), pages 36-43.
    • Handle: RePEc:eee:reensy:v:91:y:2006:i:1:p:36-43
    DOI: 10.1016/j.ress.2004.11.020
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    Cited by:

    1. Yeh, Wei-Chang, 2020. "A new method for verifying d-MC candidates," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    2. Yeh, Wei-Chang, 2022. "Novel direct algorithm for computing simultaneous all-level reliability of multistate flow networks," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    3. Miroslav Kvassay & Vitaly Levashenko & Elena Zaitseva, 2016. "Analysis of minimal cut and path sets based on direct partial Boolean derivatives," Journal of Risk and Reliability, , vol. 230(2), pages 147-161, April.
    4. Tien, Iris & Der Kiureghian, Armen, 2016. "Algorithms for Bayesian network modeling and reliability assessment of infrastructure systems," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 134-147.

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