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Lost capacity of the weighted k-out-of-n system with discrete component lifetimes

Author

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  • Goroncy, Agnieszka
  • JasiÅ„ski, Krzysztof
  • Korejwo, Faustyna
  • Rudzate, Marta

Abstract

In this paper we consider a weighted k-out-of-n system. Each component has a positive integer-valued weight assigned interpreted as its total capacity. The system is in a working state if the accumulated weights of all working components are at least k. The component lifetimes may be dependent and non-identically discretely distributed random variables. The primary focus is the capacity lost by the system upon its failure, for which we derive the probability mass function. This quantity has a potential that enables optimal system design. We also provide two numerical examples which give a demonstration of the theoretical results.

Suggested Citation

  • Goroncy, Agnieszka & JasiÅ„ski, Krzysztof & Korejwo, Faustyna & Rudzate, Marta, 2025. "Lost capacity of the weighted k-out-of-n system with discrete component lifetimes," Reliability Engineering and System Safety, Elsevier, vol. 259(C).
    • Handle: RePEc:eee:reensy:v:259:y:2025:i:c:s0951832025001024
    DOI: 10.1016/j.ress.2025.110899
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    References listed on IDEAS

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    1. Cihangir Kan & Serkan Eryilmaz, 2021. "Reliability assessment of a discrete time cold standby repairable system," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 613-628, October.
    2. Eryilmaz, Serkan & Kan, Cihangir, 2020. "Reliability based modeling and analysis for a wind power system integrated by two wind farms considering wind speed dependence," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
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    4. Davies, Katherine & Dembińska, Anna, 2019. "On the number of failed components in a k-out-of-n system upon system failure when the lifetimes are discretely distributed," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 47-61.
    5. Serkan Eryilmaz & Fatih Tank, 2023. "Optimal age replacement policy for discrete time parallel systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 475-490, October.
    6. Eryilmaz, Serkan, 2015. "Capacity loss and residual capacity in weighted k-out-of-n:G systems," Reliability Engineering and System Safety, Elsevier, vol. 136(C), pages 140-144.
    7. 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).
    8. 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.
    9. Eryilmaz, Serkan, 2024. "Reliability and performance evaluation of weighted k-out-of-n:G system consisting of components with discrete lifetimes," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
    10. Eryilmaz, Serkan & Yalcin, Femin, 2022. "The number of failed components upon system failure when the lifetimes are discretely distributed," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
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    13. Zhang, Yiying, 2018. "Optimal allocation of active redundancies in weighted k-out-of-n systems," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 110-117.
    14. Qi, Faqun & Yang, Huaqing & Wei, Lai & Shu, Xinting, 2024. "Preventive maintenance policy optimization for a weighted k-out-of-n: G system using the survival signature," Reliability Engineering and System Safety, Elsevier, vol. 249(C).
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    16. 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.
    17. 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.
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    21. 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).
    22. Yu, Xiaoyun & Hu, Linmin & Ma, Mengrao, 2023. "Reliability measures of discrete time k-out-of-n: G retrial systems based on Bernoulli shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
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    2. Dong, Qinglai & Hou, Le & Gao, Hongda, 2025. "Reliability modeling for linear and circular of Weighted-Consecutive-k Systems with shared components," Reliability Engineering and System Safety, Elsevier, vol. 262(C).

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