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Discrete-time Markovian arrival processes to model multi-state complex systems with loss of units and an indeterminate variable number of repairpersons

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  • Ruiz-Castro, Juan Eloy
  • Dawabsha, Mohammed
  • Alonso, Francisco Javier

Abstract

In this study, three discrete-time multi-state complex systems subject to multiple events are modeled, in a well structured form, as Markovian arrival processes with marked arrivals. The systems, ranked by the number of events affecting the online unit, have multiple and variable repairpersons, and the online unit are partitioned into performance stages. The first system is subject only to internal failures. The second, additionally, considers external shocks, which can produce any of three consequences; extreme failure, degradation of the internal performance of the online unit or cumulative damage. Failure may be repairable or non-repairable. The repair facility is composed of an indeterminate number of repairpersons. When a non-repairable failure occurs, the number of repairpersons may be modified. Finally, the third system includes preventive maintenance in combination with random inspections. Various measures are incorporated, in an algorithmic and computational form, in transient and stationary regimes. Costs and rewards are included in the model to optimize the system from different standpoints. The results of this study are implemented computationally with Matlab, and a numerical example shows the versatility of the modeling.

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  • 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.
    • Handle: RePEc:eee:reensy:v:174:y:2018:i:c:p:114-127
    DOI: 10.1016/j.ress.2018.02.019
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    References listed on IDEAS

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    Cited by:

    1. Ruiz-Castro, Juan E. & Acal, Christian & Aguilera, Ana M. & Aguilera-Morillo, M. Carmen & Roldán, Juan B., 2021. "Linear-Phase-Type probability modelling of functional PCA with applications to resistive memories," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 186(C), pages 71-79.
    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. Jin, Yuxue & Geng, Jie & Lv, Chuan & Chi, Ying & Zhao, Tingdi, 2023. "A methodology for equipment condition simulation and maintenance threshold optimization oriented to the influence of multiple events," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    4. 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).
    5. 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).
    6. Sakurahara, Tatsuya & O'Shea, Nicholas & Cheng, Wen-Chi & Zhang, Sai & Reihani, Seyed & Kee, Ernie & Mohaghegh, Zahra, 2019. "Integrating renewal process modeling with Probabilistic Physics-of-Failure: Application to Loss of Coolant Accident (LOCA) frequency estimations in nuclear power plants," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.

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