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On the mean residual life of a k-out-of-n:G system with a single cold standby component

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  • Eryilmaz, Serkan

Abstract

The concept of mean residual life is one of the most important characteristics that has been widely used in dynamic reliability analysis. It is a useful tool for investigating ageing properties of technical systems. In this paper, we define and study three different mean residual life functions for k-out-of-n:G system with a single cold standby component. In particular, we obtain explicit expressions for the corresponding functions using distributions of order statistics. We also provide some stochastic ordering results associated with the lifetime of a system. We illustrate the results for various lifetime distributions.

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  • Eryilmaz, Serkan, 2012. "On the mean residual life of a k-out-of-n:G system with a single cold standby component," European Journal of Operational Research, Elsevier, vol. 222(2), pages 273-277.
    • Handle: RePEc:eee:ejores:v:222:y:2012:i:2:p:273-277
    DOI: 10.1016/j.ejor.2012.05.012
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    Cited by:

    1. Longlong Liu & Xiaochuan Ai & Jun Wu, 2024. "Reliability and Residual Life of Cold Standby Systems," Mathematics, MDPI, vol. 12(10), pages 1-22, May.
    2. Frank PA Coolen & Tahani Coolen-Maturi & Abdullah H Al-nefaiee, 2014. "Nonparametric predictive inference for system reliability using the survival signature," Journal of Risk and Reliability, , vol. 228(5), pages 437-448, October.
    3. Krzysztof Jasiński, 2021. "Some conditional reliability properties of k-out-of-n system composed of different types of components with discrete independent lifetimes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1241-1251, November.
    4. Navarro, Jorge & Pellerey, Franco & Di Crescenzo, Antonio, 2015. "Orderings of coherent systems with randomized dependent components," European Journal of Operational Research, Elsevier, vol. 240(1), pages 127-139.
    5. 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.
    6. Jorgen Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2021. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Papers 2112.10672, arXiv.org.
    7. Aboalkhair, Ahmad M. & Coolen, Frank P.A. & MacPhee, Iain M., 2013. "Nonparametric predictive reliability of series of voting systems," European Journal of Operational Research, Elsevier, vol. 226(1), pages 77-84.
    8. Finkelstein, Maxim & Cha, Ji Hwan & Langston, Amy, 2022. "Optimal preventive switching of components in degrading systems," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    9. Xiaojun Liang & Yinghui Tang, 2019. "The improvement upon the reliability of the k-out-of-n:F system with the repair rates differentiation policy," Operational Research, Springer, vol. 19(2), pages 479-500, June.
    10. Zohreh Pakdaman & Jafar Ahmadi, 2019. "Switching time of the standby component to the k-out-of-n:G system in the stress–strength setup," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 225-248, March.
    11. Mohamed Kayid & Mashael A. Alshehri, 2023. "Stochastic Comparisons of Lifetimes of Used Standby Systems," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    12. Jørgen Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03634370, HAL.
    13. Gupta, Nitin & Misra, Neeraj & Kumar, Somesh, 2015. "Stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components," European Journal of Operational Research, Elsevier, vol. 240(2), pages 425-430.
    14. Jørgen Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Post-Print hal-03634370, HAL.
    15. Zarezadeh, S. & Asadi, M. & Balakrishnan, N., 2014. "Dynamic network reliability modeling under nonhomogeneous Poisson processes," European Journal of Operational Research, Elsevier, vol. 232(3), pages 561-571.
    16. Jørgen Vitting Andersen & Roy Cerqueti & Giulia Rotundo, 2017. "Rational expectations and stochastic systems," Documents de travail du Centre d'Economie de la Sorbonne 17060, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2019.
    17. Li, Chen & Li, Xiaohu, 2023. "On k-out-of-n systems with homogeneous components and one independent cold standby redundancy," Statistics & Probability Letters, Elsevier, vol. 203(C).
    18. Li, Xiaohu & Fang, Rui & Mi, Jie, 2015. "On the timing to switch on the standby in k-out-of-n:G redundant systems," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 10-20.
    19. Eryilmaz, Serkan, 2017. "The effectiveness of adding cold standby redundancy to a coherent system at system and component levels," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 331-335.
    20. Roy Cerqueti, 2022. "A new concept of reliability system and applications in finance," Annals of Operations Research, Springer, vol. 312(1), pages 45-64, May.
    21. Zhang, Nan & Fouladirad, Mitra & Barros, Anne, 2019. "Reliability-based measures and prognostic analysis of a K-out-of-N system in a random environment," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1120-1131.
    22. Zhao, Fei & Peng, Rui & Zhang, Nan, 2023. "Inspection policy optimization for a k-out-of-n/Cl(k′,n′;F) system considering failure dependence: a case study," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    23. Jia, Xiang & Chen, Hao & Cheng, Zhijun & Guo, Bo, 2016. "A comparison between two switching policies for two-unit standby system," Reliability Engineering and System Safety, Elsevier, vol. 148(C), pages 109-118.
    24. Achintya Roy & Nitin Gupta, 2020. "Reliability of a coherent system equipped with two cold standby components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 677-697, August.
    25. Jorgen-Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Annals of Operations Research, Springer, vol. 326(1), pages 295-316, July.

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