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On preventive maintenance of k-out-of-n systems subject to fatal shocks

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  • Somayeh Ashrafi
  • Majid Asadi
  • Razieh Rostami

Abstract

In this paper, we investigate optimal age-based preventive maintenance (PM) policies for an ( n - k + 1)-out-of- n system whose components are exposed to fatal shocks that arrive from various sources. We consider two different scenarios for the system failure. In the first one, it is assumed that the shock process is of the type of Marshall-Olkin where each shock affects one component of the system and puts it down, and one shock affects all components and destroys all of them. In the second scenario, it is assumed that the system is subject to an extended type of Marshall-Olkin shock process where the shocks arriving at random times may cause the breakdown of 1, 2, …, or n components. Under each scenario for the components failure, we investigate an optimal age-based PM model for the system by imposing the related cost function. Then, in each case, we explore the optimal PM time that minimizes the mean cost per unit of time. Some numerical results are presented to illustrate the applications of the proposed models.

Suggested Citation

  • Somayeh Ashrafi & Majid Asadi & Razieh Rostami, 2024. "On preventive maintenance of k-out-of-n systems subject to fatal shocks," Journal of Risk and Reliability, , vol. 238(2), pages 291-303, April.
    • Handle: RePEc:sae:risrel:v:238:y:2024:i:2:p:291-303
    DOI: 10.1177/1748006X221147331
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    References listed on IDEAS

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    1. Toshio Nakagawa, 2014. "Random Maintenance Policies," Springer Series in Reliability Engineering, Springer, edition 127, number 978-1-4471-6575-0, December.
    2. Hongzhou Wang & Hoang Pham, 2006. "Reliability and Optimal Maintenance," Springer Series in Reliability Engineering, Springer, number 978-1-84628-325-3, December.
    3. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2018. "Bivariate preventive maintenance of systems with lifetimes dependent on a random shock process," European Journal of Operational Research, Elsevier, vol. 266(1), pages 122-134.
    4. Maxim Finkelstein & Ilya Gertsbakh, 2016. "Preventive maintenance of multistate systems subject to shocks," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(2), pages 283-291, March.
    5. Marzieh Hashemi & Majid Asadi, 2021. "Optimal preventive maintenance of coherent systems: A generalized Pólya process approach," IISE Transactions, Taylor & Francis Journals, vol. 53(11), pages 1266-1280, November.
    6. Li, Xiaohu & Pellerey, Franco, 2011. "Generalized Marshall-Olkin distributions and related bivariate aging properties," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1399-1409, November.
    7. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
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