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Optimal allocation of active redundancies in weighted k-out-of-n systems

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  • Zhang, Yiying

Abstract

This paper investigates optimal allocation of active redundancies for weighted k-out-of-n systems. Optimal allocation policies are presented for the case of one, two and multiple active redundancies in the sense of the usual stochastic order when the system is comprised of independent and heterogeneous components having different weights. Some allocation policies known for the k-out-of-n system in the literature are generalized to the weighted k-out-of-n system. Numerical examples and applications are provided to highlight these theoretical findings as well.

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  • 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.
    • Handle: RePEc:eee:stapro:v:135:y:2018:i:c:p:110-117
    DOI: 10.1016/j.spl.2017.12.002
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    References listed on IDEAS

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    1. Yinping You & Rui Fang & Xiaohu Li, 2016. "Allocating active redundancies to k‐out‐of‐n reliability systems with permutation monotone component lifetimes," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(5), pages 607-620, September.
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    4. 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.
    5. Samaniego, Francisco J. & Shaked, Moshe, 2008. "Systems with weighted components," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 815-823, April.
    6. Kundu, Pradip & Hazra, Nil Kamal & Nanda, Asok K., 2016. "Reliability study of a coherent system with single general standby component," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 25-33.
    7. Eryilmaz, Serkan, 2013. "Mean instantaneous performance of a system with weighted components that have arbitrarily distributed lifetimes," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 290-293.
    8. 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.
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    Cited by:

    1. Yiying Zhang & Peng Zhao, 2019. "Optimal allocation of minimal repairs in parallel and series systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(6), pages 517-526, September.
    2. 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.
    3. 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.
    4. 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).
    5. Serkan Eryilmaz & Ali Riza Bozbulut, 2019. "Reliability analysis of weighted- k -out-of- n system consisting of three-state components," Journal of Risk and Reliability, , vol. 233(6), pages 972-977, December.
    6. Hamideh Jeddi & Mahdi Doostparast, 2022. "Allocation of redundancies in systems: a general dependency-base framework," Annals of Operations Research, Springer, vol. 312(1), pages 259-273, May.
    7. Eryilmaz, Serkan & Devrim, Yilser, 2019. "Reliability and optimal replacement policy for a k-out-of-n system subject to shocks," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 393-397.
    8. 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.
    9. Oszczypała, Mateusz & Konwerski, Jakub & Ziółkowski, Jarosław & Małachowski, Jerzy, 2024. "Reliability analysis and redundancy optimization of k-out-of-n systems with random variable k using continuous time Markov chain and Monte Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    10. Shekhar, Chandra & Kumar, Amit & Varshney, Shreekant, 2020. "Load sharing redundant repairable systems with switching and reboot delay," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    11. 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).
    12. 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.
    13. 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).
    14. Ioannis S. Triantafyllou, 2024. "A Probabilistic Approach for Threshold Reliability Structures with Three Different Types of Components," Mathematics, MDPI, vol. 12(21), pages 1-14, October.
    15. 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.
    16. 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).

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