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The k-out-of-n acyclic multistate-node networks reliability evaluation using the universal generating function method

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  • Yeh, Wei-Chang

Abstract

In this article, a special node called the k−-out-of-n node, which cannot receive more than a certain amount of flows, is newly introduced. The acyclic multistate-node network (AMNN) that unsatisfied the flow conservation law is then extended to the k-out-of-n AMNN by including the k−-out-of-n and k+-out-of-n nodes. A very simple universal generating function method (UGFM) based on some intuitive properties that characterize the structure of the k-out-of-n AMNN is developed to solve the k-out-of-n AMNN reliability. The correctness of the proposed UGFM will be analyzed and proven. An example with three special cases illustrates how the k-out-of-n AMNN reliability is evaluated using the proposed UGFM. To show that the proposed UGFM can also solve the AMNN reliability, the first case of the example demonstrates that the proposed UGFM without needing to remove redundant terms and collecting like terms is more efficient and reasonable than the best-known UGFM.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:91:y:2006:i:7:p:800-808
    DOI: 10.1016/j.ress.2005.08.002
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    References listed on IDEAS

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    1. 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.
    2. Yeh, Wei-Chang, 2005. "A new approach to evaluate reliability of multistate networks under the cost constraint," Omega, Elsevier, vol. 33(3), pages 203-209, June.
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    Citations

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    Cited by:

    1. 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.
    2. Yeh, Wei-Chang, 2024. "Time-reliability optimization for the stochastic traveling salesman problem," Reliability Engineering and System Safety, Elsevier, vol. 248(C).
    3. Yeh, Wei-Chang, 2021. "Novel binary-addition tree algorithm (BAT) for binary-state network reliability problem," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    4. Y Liu & H-Z Huang & G Levitin, 2008. "Reliability and performance assessment for fuzzy multi-state elements," Journal of Risk and Reliability, , vol. 222(4), pages 675-686, December.
    5. Niu, Yi-Feng & Zhao, Xia & Xu, Xiu-Zhen & Zhang, Shi-Yun, 2023. "Reliability assessment of a stochastic-flow distribution network with carbon emission constraint," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    6. Liu, Baoliang & Cui, Lirong & Wen, Yanqing & Shen, Jingyuan, 2013. "A performance measure for Markov system with stochastic supply patterns and stochastic demand patterns," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 294-299.
    7. Lisnianski, Anatoly & Ding, Yi, 2009. "Redundancy analysis for repairable multi-state system by using combined stochastic processes methods and universal generating function technique," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1788-1795.
    8. Wang, Guanjun & Duan, Fengjun & Zhou, Yifan, 2018. "Reliability evaluation of multi-state series systems with performance sharing," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 58-63.
    9. 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).
    10. Yeh, Wei-Chang, 2017. "Evaluation of the one-to-all-target-subsets reliability of a novel deterioration-effect acyclic multi-state information network," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 132-137.

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