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On reliability analysis of a k-out-of-n system with components having random weights

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  • Eryilmaz, Serkan

Abstract

Consider a system consisting of n components each with its own positive integer-valued random weight (capacity). The system is assumed to have a performance level above c if there are at least k working components, and the total weight of all working components is above c. We study the reliability properties of such a system. A recursive formula is obtained for computing the system state probabilities. We present a Monte-Carlo simulation algorithm to observe the time spent by the system in state c or above. The algorithm is based on the use of ordered lifetimes of components. We illustrate the results with numerical computations.

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  • Eryilmaz, Serkan, 2013. "On reliability analysis of a k-out-of-n system with components having random weights," Reliability Engineering and System Safety, Elsevier, vol. 109(C), pages 41-44.
    • Handle: RePEc:eee:reensy:v:109:y:2013:i:c:p:41-44
    DOI: 10.1016/j.ress.2012.07.010
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    References listed on IDEAS

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    1. Li, Wei & Zuo, Ming J., 2008. "Reliability evaluation of multi-state weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 160-167.
    2. Samaniego, Francisco J. & Shaked, Moshe, 2008. "Systems with weighted components," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 815-823, April.
    3. Li, Wei & Zuo, Ming J., 2008. "Optimal design of multi-state weighted k-out-of-n systems based on component design," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1673-1681.
    4. G.Y. Tütüncü & S. Eryilmaz, 2009. "Reliability evaluation of linear consecutive-weighted-k-out-of-n : F System," Post-Print hal-00569519, HAL.
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    Citations

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    Cited by:

    1. Yiying Zhang & Weiyong Ding & Peng Zhao, 2018. "On total capacity of k‐out‐of‐n systems with random weights," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(4), pages 347-359, June.
    2. Rahmani, Rabi-Allah & Izadi, Muhyiddin & Khaledi, Baha-Eldin, 2016. "Stochastic comparisons of total capacity of weighted-k-out-of-n systems," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 216-220.
    3. Bayramoglu, Ismihan, 2020. "Joint distribution of a random sample and an order statistic: A new approach with an application in reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    4. 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.
    5. Zhang, Yiying, 2021. "Reliability Analysis of Randomly Weighted k-out-of-n Systems with Heterogeneous Components," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    6. 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.
    7. Eryilmaz, Serkan & Ucum, Kaan Ayberk, 2021. "The lost capacity by the weighted k-out-of-n system upon system failure," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    8. Hamdan, K. & Tavangar, M. & Asadi, M., 2021. "Optimal preventive maintenance for repairable weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    9. 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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