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A complex multi-state k-out-of-n: G system with preventive maintenance and loss of units

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  • Ruiz-Castro, Juan Eloy

Abstract

In this study, a multi-state k-out-of-n: G system subject to multiple events is modeled through a Markovian Arrival Process with marked arrivals. The system is composed initially of n units and is active when at least k units are operational. Each unit is multi-state, each of which is classified as minor or major according to the level of degradation presented. Each operational unit may undergo internal repairable or non-repairable failures, external shocks and/or random inspections. An external shock can provoke extreme failure, while cumulative external damage can deteriorate internal performance. This situation can produce repairable and non-repairable failures. When a repairable failure occurs the unit is sent to a repair facility for corrective repair. If the failure is non-repairable, the unit is removed. When the system has insufficient units with which to operate, it is restarted. Preventive maintenance is employed in response to random inspection. The system is modeled in an algorithmic and computational form. Several interesting measures of performance are considered. Costs and rewards are included in the system. All measures are obtained for transient and stationary regimes. A numerical example is analyzed to determine whether preventive maintenance is profitable, financially and in terms of performance.

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  • Ruiz-Castro, Juan Eloy, 2020. "A complex multi-state k-out-of-n: G system with preventive maintenance and loss of units," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:reensy:v:197:y:2020:i:c:s0951832019301024
    DOI: 10.1016/j.ress.2020.106797
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    References listed on IDEAS

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    12. Ruiz-Castro, Juan Eloy & Dawabsha, Mohammed & Alonso, Francisco Javier, 2018. "Discrete-time Markovian arrival processes to model multi-state complex systems with loss of units and an indeterminate variable number of repairpersons," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 114-127.
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    17. Juan Eloy Ruiz-Castro, 2015. "A preventive maintenance policy for a standby system subject to internal failures and external shocks with loss of units," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(9), pages 1600-1613, July.
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    Citations

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    Cited by:

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    2. Juan Eloy Ruiz-Castro, 2021. "Optimizing a Multi-State Cold-Standby System with Multiple Vacations in the Repair and Loss of Units," Mathematics, MDPI, vol. 9(8), pages 1-29, April.
    3. Alkaff, Abdullah, 2021. "Discrete time dynamic reliability modeling for systems with multistate components," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    4. Delia Montoro-Cazorla & Rafael Pérez-Ocón, 2022. "Optimizing Costs in a Reliability System under Markovian Arrival of Failures and Reposition by K -Policy Inspection," Mathematics, MDPI, vol. 10(11), pages 1-21, June.
    5. Delia Montoro-Cazorla & Rafael Pérez-Ocón, 2022. "Analysis of k-Out-of-N-Systems with Different Units under Simultaneous Failures: A Matrix-Analytic Approach," Mathematics, MDPI, vol. 10(11), pages 1-13, June.
    6. Zhang, Ning & Qi, Faqun & Zhang, Chengjie & Zhou, Hongming, 2022. "Joint optimization of condition-based maintenance policy and buffer capacity for a two-unit series system," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    7. Safaei, Fatemeh & Ahmadi, Jafar & Taghipour, Sharareh, 2022. "A maintenance policy for a k-out-of-n system under enhancing the system’s operating time and safety constraints, and selling the second-hand components," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    8. Juan E. Ruiz-Castro & Christian Acal & Ana M. Aguilera & Juan B. Roldán, 2021. "A Complex Model via Phase-Type Distributions to Study Random Telegraph Noise in Resistive Memories," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
    9. Juybari, Mohammad N. & Hamadani, Ali Zeinal & Ardakan, Mostafa Abouei, 2023. "Availability analysis and cost optimization of a repairable system with a mix of active and warm-standby components in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    10. Cheng, Dawei & Lu, Zhong & Zhou, Jia & Liang, Xihui, 2023. "An optimizing maintenance policy for airborne redundant systems operating with faults by using Markov process and NSGA-II," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    11. Levitin, Gregory & Finkelstein, Maxim & Xiang, Yanping, 2021. "Optimal mission abort policies for repairable multistate systems performing multi-attempt mission," Reliability Engineering and System Safety, Elsevier, vol. 209(C).

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