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Complex multi-state systems modelled through marked Markovian arrival processes

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  • Ruiz-Castro, Juan Eloy

Abstract

Complex multi-state warm standby systems subject to different types of failures and preventive maintenance are modelled by considering discrete marked Markovian arrival processes. The system is composed of K units, one online and the rest in warm standby and by an indefinite number of repairpersons, R. The online unit passes through several performance states, which are partitioned into two types: minor and major. This unit can fail due to wear or to external shock. In both cases of failures, the failure can be repairable or non-repairable. Warm standby units can only undergo repairable failures due to wear. Derived systems are modelled from the basic one according to the type of the failure; repairable or non-repairable, and preventive maintenance. When a unit undergoes a repairable failure, it goes to the repair facility for corrective repair, and if it is non-repairable, it is replaced by a new, identical one. Preventive maintenance is carried out in response to random inspections. When an inspection takes place, the online unit is observed and if the performance state is major, the unit is sent to the repair facility for preventive maintenance. Preventive maintenance and corrective repair times follow different distributions according to the type of failure. The systems are modelled in transient regime, relevant performance measures are obtained, and rewards and costs are calculated. All results are expressed in algorithmic form and implemented computationally with Matlab. A numerical example shows the versatility of the model presented.

Suggested Citation

  • Ruiz-Castro, Juan Eloy, 2016. "Complex multi-state systems modelled through marked Markovian arrival processes," European Journal of Operational Research, Elsevier, vol. 252(3), pages 852-865.
    • Handle: RePEc:eee:ejores:v:252:y:2016:i:3:p:852-865
    DOI: 10.1016/j.ejor.2016.02.007
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    References listed on IDEAS

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    Cited by:

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    3. Wu, Hui & Li, Yan-Fu & Bérenguer, Christophe, 2020. "Optimal inspection and maintenance for a repairable k-out-of-n: G warm standby system," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    4. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2018. "Heterogeneous standby systems with shocks-driven preventive replacements," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1189-1197.
    5. 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.
    6. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Mission abort and rescue for multistate systems operating under the Poisson process of shocks," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    7. 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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    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. 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).
    11. Li, Yan & Cui, Lirong & Lin, Cong, 2017. "Modeling and analysis for multi-state systems with discrete-time Markov regime-switching," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 41-49.
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