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Multi-state systems and their performance evaluation

Author

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  • Zhigang Tian
  • Ming Zuo
  • Richard Yam

Abstract

The k-out-of-n system structure is a very popular type of redundancy in fault-tolerant systems, with wide applications in both industrial and military systems. In this paper, the modeling, application and reliability evaluation of k-out-of-n systems are studied for the case where the components and the system have multiple performance levels. A multi-state k-out-of-n system model is proposed that allows different requirements on the number of components for different state levels, and, very importantly, more practical engineering systems can fit into this model. The multiple states in the model can be interpreted in two ways: (i) multiple levels of capacity; and (ii) multiple failure modes. Application examples of the proposed multi-state k-out-of-n system model are given under each of the interpretations. An approach is presented for efficient reliability evaluation of multi-state k-out-of-n systems with identically and independently distributed components. A recursive algorithm is proposed for reliability evaluation of multi-state k-out-of-n systems with independent components. Efficiency investigations show that both of the reliability evaluation approaches are efficient. The multi-state k-out-of-n system model with a constant k value, which is a special case of the general multi-state k-out-of-n system model, has been studied for a long time, but only on the theoretical stage. A practical application of this model is presented in this paper as well.

Suggested Citation

  • Zhigang Tian & Ming Zuo & Richard Yam, 2009. "Multi-state systems and their performance evaluation," IISE Transactions, Taylor & Francis Journals, vol. 41(1), pages 32-44.
    • Handle: RePEc:taf:uiiexx:v:41:y:2009:i:1:p:32-44
    DOI: 10.1080/07408170802322655
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    Citations

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    Cited by:

    1. Wang, Chaonan & Xing, Liudong & Amari, Suprasad V. & Tang, Bo, 2020. "Efficient reliability analysis of dynamic k-out-of-n heterogeneous phased-mission systems," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    2. Ruiz-Castro, Juan Eloy & Li, Quan-Lin, 2011. "Algorithm for a general discrete k-out-of-n: G system subject to several types of failure with an indefinite number of repairpersons," European Journal of Operational Research, Elsevier, vol. 211(1), pages 97-111, May.
    3. Sheng, Yuhong & Ke, Hua, 2020. "Reliability evaluation of uncertain k-out-of-n systems with multiple states," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    4. Coit, David W. & Chatwattanasiri, Nida & Wattanapongsakorn, Naruemon & Konak, Abdullah, 2015. "Dynamic k-out-of-n system reliability with component partnership," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 82-92.
    5. Funda Iscioglu, 2017. "Dynamic performance evaluation of multi – state systems under non – homogeneous continuous time Markov process degradation using lifetimes in terms of order statistics," Journal of Risk and Reliability, , vol. 231(3), pages 255-264, June.
    6. Faghih-Roohi, Shahrzad & Xie, Min & Ng, Kien Ming & Yam, Richard C.M., 2014. "Dynamic availability assessment and optimal component design of multi-state weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 57-62.
    7. Wang, Guanjun & Peng, Rui & Xing, Liudong, 2018. "Reliability evaluation of unrepairable k-out-of-n: G systems with phased-mission requirements based on record values," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 191-197.
    8. Quan Zhang & Shihang Yu & Yang Han & Yanjun Li, 2022. "Research on the model of a multistate aggregated Markov repairable system," Journal of Risk and Reliability, , vol. 236(2), pages 266-276, April.
    9. Mo, Yuchang & Xing, Liudong & Amari, Suprasad V. & Bechta Dugan, Joanne, 2015. "Efficient analysis of multi-state k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 95-105.
    10. Yin, Juan & Cui, Lirong & Sun, Yudao & Balakrishnan, Narayanaswamy, 2022. "Reliability modelling for linear and circular k-out-of-n: F systems with shared components," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    11. 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.
    12. S K Chaturvedi & S H Basha & S V Amari & M J Zuo, 2012. "Reliability analysis of generalized multi-state k-out-of-n systems," Journal of Risk and Reliability, , vol. 226(3), pages 327-336, June.
    13. Su, Peng & Wang, Guanjun & Duan, Fengjun, 2020. "Reliability evaluation of a k-out-of-n(G)-subsystem based multi-state system with common bus performance sharing," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    14. Xiaogang Song & Zhengjun Zhai & Yangming Guo & Peican Zhu & Jie Han, 2017. "Approximate Analysis of Multi-State Weighted k -Out-of- n Systems Applied to Transmission Lines," Energies, MDPI, vol. 10(11), pages 1-16, October.

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