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A performance measure for Markov system with stochastic supply patterns and stochastic demand patterns

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  • Liu, Baoliang
  • Cui, Lirong
  • Wen, Yanqing
  • Shen, Jingyuan

Abstract

A system consisting of supply and demand is considered in this paper. Both the supply patterns and demand patterns are random. Thus, both the supply and the demand are modeled by Markov processes. The performance measure considered here is the probability that the demand is met by the supply during given time interval [0,t]. A close form expression for the performance measure is obtained by using aggregated stochastic process theory and Kronecker matrix operations. In the meanwhile, the performance measures in a general interval [a,b] and multiple intervals [a1,b1],[a2,b2],…,[am,bm] have also been given. Finally, a numerical example is given to illustrate the results obtained in this paper.

Suggested Citation

  • Liu, Baoliang & Cui, Lirong & Wen, Yanqing & Shen, Jingyuan, 2013. "A performance measure for Markov system with stochastic supply patterns and stochastic demand patterns," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 294-299.
    • Handle: RePEc:eee:reensy:v:119:y:2013:i:c:p:294-299
    DOI: 10.1016/j.ress.2013.07.001
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    References listed on IDEAS

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    1. Alan Hawkes & Lirong Cui & Zhihua Zheng, 2011. "Modeling the evolution of system reliability performance under alternative environments," IISE Transactions, Taylor & Francis Journals, vol. 43(11), pages 761-772.
    2. Lirong Cui & Shijia Du & Alan Hawkes, 2012. "A study on a single-unit repairable system with state aggregations," IISE Transactions, Taylor & Francis Journals, vol. 44(11), pages 1022-1032.
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    4. Csenki, Attila, 2007. "Joint interval reliability for Markov systems with an application in transmission line reliability," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 685-696.
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    6. Lisnianski, Anatoly & Ding, Yi, 2009. "Redundancy analysis for repairable multi-state system by using combined stochastic processes methods and universal generating function technique," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1788-1795.
    7. Csenki, Attila, 2009. "Stochastic demand patterns for Markov service facilities with neutral and active periods," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 382-393.
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    Citations

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    Cited by:

    1. Wu, Bei & Cui, Lirong & Fang, Chen, 2019. "Reliability analysis of semi-Markov systems with restriction on transition times," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    2. Zhang, Chao & Chen, Rentong & Wang, Shaoping & Dui, Hongyan & Zhang, Yadong, 2022. "Resilience efficiency importance measure for the selection of a component maintenance strategy to improve system performance recovery," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    3. Yu, Huan & Yang, Jun & Mo, Huadong, 2014. "Reliability analysis of repairable multi-state system with common bus performance sharing," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 90-96.
    4. Cui, Lirong & Wu, Bei, 2019. "Extended Phase-type models for multistate competing risk systems," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 1-16.
    5. Du, Shijia & Zeng, Zhiguo & Cui, Lirong & Kang, Rui, 2017. "Reliability analysis of Markov history-dependent repairable systems with neglected failures," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 134-142.
    6. Fang, Chen & Cui, Lirong, 2021. "Reliability evaluation for balanced systems with auto-balancing mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    7. Cui, Lirong & Chen, Jianhui & Wu, Bei, 2017. "New interval availability indexes for Markov repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 12-17.
    8. Quan Zhang & Shihang Yu & Yang Han & Yanjun Li, 2022. "Research on the model of a multistate aggregated Markov repairable system," Journal of Risk and Reliability, , vol. 236(2), pages 266-276, April.
    9. Dhople, S.V. & DeVille, L. & Domínguez-García, A.D., 2014. "A Stochastic Hybrid Systems framework for analysis of Markov reward models," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 158-170.
    10. Lirong Cui & Quan Zhang & Dejing Kong, 2016. "Some New Concepts and Their Computational Formulae in Aggregated Stochastic Processes with Classifications Based on Sojourn Times," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 999-1019, December.
    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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