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Modeling and analysis for multi-state systems with discrete-time Markov regime-switching

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  • Li, Yan
  • Cui, Lirong
  • Lin, Cong

Abstract

The main focus of this paper is on the development of reliability measures for a repairable multi-state system which operates under dynamic regimes under the discrete-time hypothesis. The switching process of regimes is governed by a Markov chain, and the functioning process of the system follows another Markov chain with different transition probability matrices under different regimes. In terms of two chains as above, a new Markov chain is constructed to depict the evolution process of the dynamic system. For the regime consideration, some novel reliability indices are essential and firstly introduced in this paper. By means of hierarchical partitions for the new state space, Ion-Channel modeling theory and discrete-time Markov chain, the traditional and novel reliability and availability functions for the system under random regimes are easily obtained with the closed form solutions, such as two types of system reliabilities, two types of system point availabilities, two types of system multiple-point availabilities and the associated system multi-interval availabilities and so on. In addition, some probability distributions of sojourn times we are interested in are discussed and computed here. Finally, a numerical example is given to illustrate the results obtained in the paper.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:166:y:2017:i:c:p:41-49
    DOI: 10.1016/j.ress.2017.03.024
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    References listed on IDEAS

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    4. Li, Yan & Zhang, Wei & Liu, Baoliang & Wang, Xiaofeng, 2024. "Availability and maintenance strategy under time-varying environments for redundant repairable systems with PH distributions," Reliability Engineering and System Safety, Elsevier, vol. 246(C).
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    6. Mateusz Oszczypała & Jarosław Ziółkowski & Jerzy Małachowski, 2022. "Analysis of Light Utility Vehicle Readiness in Military Transportation Systems Using Markov and Semi-Markov Processes," Energies, MDPI, vol. 15(14), pages 1-24, July.
    7. Yi, He & Cui, Lirong & Shen, Jingyuan & Li, Yan, 2018. "Stochastic properties and reliability measures of discrete-time semi-Markovian systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 162-173.
    8. McNelles, Phillip & Renganathan, Guna & Zeng, Zhao Chang & Chirila, Marius & Lu, Lixuan, 2019. "A comparison of fault trees and the Dynamic Flowgraph Methodology for the analysis of FPGA-based safety systems part 2: Theoretical investigations," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 60-83.
    9. 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.
    10. Yong-Hua Li & Fu-Yu Zhao & Yue-Hua Gao & Peng-Peng Zhi, 2022. "Importance analysis of underframe connection system for the pantograph lower arm rod," Annals of Operations Research, Springer, vol. 311(1), pages 211-223, April.
    11. Luo, Yi & Zhao, Xiujie & Liu, Bin & He, Shuguang, 2024. "Condition-based maintenance policy for systems under dynamic environment," Reliability Engineering and System Safety, Elsevier, vol. 246(C).

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