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Economic design of a circular consecutive-k-out-of-n:F system with (k-1)-step Markov dependence

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  • Yun, Won-Young
  • Kim, Gui-Rae
  • Yamamoto, Hisashi

Abstract

A circular consecutive-k-out-of-n:F system consists of n components arranged along a circular path. The system fails if and only if at least k consecutive components in the system fail. The system reliability, the expected system life, and the expected number of failures are obtained under the assumption that the failure rate of a component depends on the number of consecutive failed components that follow it. A procedure to find the optimal k and a simulation procedure to search the near-optimal k are proposed with illustrative numerical examples. An expected cost per unit time is considered as the objective function to be minimized.

Suggested Citation

  • Yun, Won-Young & Kim, Gui-Rae & Yamamoto, Hisashi, 2007. "Economic design of a circular consecutive-k-out-of-n:F system with (k-1)-step Markov dependence," Reliability Engineering and System Safety, Elsevier, vol. 92(4), pages 464-478.
    • Handle: RePEc:eee:reensy:v:92:y:2007:i:4:p:464-478
    DOI: 10.1016/j.ress.2005.12.007
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    References listed on IDEAS

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    1. Lam, Yeh & Ng, Hon Keung Tony, 2001. "A general model for consecutive-k-out-of-n: F repairable system with exponential distribution and (k-1)-step Markov dependence," European Journal of Operational Research, Elsevier, vol. 129(3), pages 663-682, March.
    2. D. Z. Du & F. K. Hwang, 1986. "Optimal Consecutive-2-Out-of- n Systems," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 187-191, February.
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    Cited by:

    1. Won Young Yun & Alfonsus Julanto Endharta, 2016. "A preventive replacement policy based on system critical condition," Journal of Risk and Reliability, , vol. 230(1), pages 93-100, February.
    2. Serkan Eryilmaz & Cihangir Kan & Fatih Akici, 2009. "Consecutive k‐within‐m‐out‐of‐n:F system with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 503-510, September.
    3. Villén-Altamirano, José, 2010. "RESTART simulation of non-Markov consecutive-k-out-of-n: F repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 247-254.
    4. Zhu, Xiaoyan & Boushaba, Mahmoud & Coit, David W. & Benyahia, Azzeddine, 2017. "Reliability and importance measures for m-consecutive-k, l-out-of-n system with non-homogeneous Markov-dependent components," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 1-9.
    5. Levitin, Gregory, 2011. "Linear m-gap-consecutive k-out-of-r-from-n:F systems," Reliability Engineering and System Safety, Elsevier, vol. 96(2), pages 292-298.
    6. Wang, Wei & Fu, Yongnian & Si, Peng & Lin, Mingqiang, 2020. "Reliability analysis of circular multi-state sliding window system with sequential demands," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    7. Endharta, Alfonsus Julanto & Yun, Won Young & Ko, Young Myoung, 2018. "Reliability evaluation of circular k-out-of-n: G balanced systems through minimal path sets," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 226-236.
    8. Wang, Wei & Fang, Chao & Liu, Shan & Xiang, Yisha, 2021. "Reliability analysis and optimization of multi-state sliding window system with sequential demands and time constraints," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    9. Eryılmaz, Serkan, 2009. "Reliability properties of consecutive k-out-of-n systems of arbitrarily dependent components," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 350-356.
    10. Wang, Wei & Fang, Chao & Wang, Yan & Li, Jin, 2022. "Reliability Modeling and Optimization of Circular Multi-State Sliding Time Window System with Sequential Demands," Reliability Engineering and System Safety, Elsevier, vol. 225(C).

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