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A D-MMAP to Model a Complex Multi-state System with Loss of Units

In: Recent Advances in Multi-state Systems Reliability

Author

Listed:
  • Juan Eloy Ruiz-Castro

    (University of Granada)

Abstract

A complex multi-state system subject to different types of failures and preventive maintenance, with loss of units, is modelled by considering a discrete marked Markovian arrival process. The system is composed of K units, one online and the rest in cold standby. The online unit is submitted to different types of failures and when a non-repairable failure occurs the corresponding unit is removed. Several internal degradation states are considered which are observed when a random inspection occurs. This unit is subject to internal repairable failure, external shocks and preventive maintenance. If one internal repairable failure occurs, the unit goes to the repair facility for corrective repair, if a major degradation level is observed by inspection, the unit goes to preventive maintenance and when one external shock happens, this one may produce an aggravation of the internal degradation level, cumulative external damage or external extreme failure (non-repairable failure). Preventive maintenance and corrective repair times follow different distributions. The system is modelled in transient regime and relevant performance measures are obtained. All results are expressed in algorithmic and computational form and they have been implemented computationally with MATLAB and R. A numerical example shows the versatility of the model.

Suggested Citation

  • Juan Eloy Ruiz-Castro, 2018. "A D-MMAP to Model a Complex Multi-state System with Loss of Units," Springer Series in Reliability Engineering, in: Anatoly Lisnianski & Ilia Frenkel & Alex Karagrigoriou (ed.), Recent Advances in Multi-state Systems Reliability, pages 39-58, Springer.
    • Handle: RePEc:spr:ssrchp:978-3-319-63423-4_3
    DOI: 10.1007/978-3-319-63423-4_3
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    Citations

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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. 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).
    4. 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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