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Research on the model of a multistate aggregated Markov repairable system

Author

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  • Quan Zhang
  • Shihang Yu
  • Yang Han
  • Yanjun Li

Abstract

In theory and practice, system performance is one of the most important issues. Therefore, a series of indexes has been proposed for evaluating the system performance, such as availability. However, these indexes still cannot meet the variant requirements in the reliability and other fields. The purpose of the article is to develop some theoretical results that may be used in modeling the evolution of system performance. So, based on the aggregated stochastic process theory, some new indexes are introduced and established in Markov repairable systems. In this model, the state space is partitioned into working subset W and failure subset F . The system is regarded as stable if the state of system enters one subset, either W or F , at any instance and sojourns within the subset exceeding a given non-negative threshold Ï„ . Otherwise, the system is regarded as unstable. Under these assumptions, the concepts of point-wise and interval-wise are proposed, and the computation formulae of two types of indexes are derived in the theory. Finally, a special case and a few of numerical examples are given to illustrate the results obtained in the paper.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:risrel:v:236:y:2022:i:2:p:266-276
    DOI: 10.1177/1748006X19887651
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    References listed on IDEAS

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    1. 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.
    2. Baoliang Liu & Lirong Cui & Yanqing Wen, 2014. "Interval reliability for aggregated Markov repairable system with repair time omission," Annals of Operations Research, Springer, vol. 212(1), pages 169-183, January.
    3. 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.
    4. Zhigang Tian & Ming Zuo & Richard Yam, 2009. "Multi-state systems and their performance evaluation," IISE Transactions, Taylor & Francis Journals, vol. 41(1), pages 32-44.
    5. Liying Wang & Lirong Cui, 2013. "Performance Evaluation Of Aggregated Markov Repairable Systems With Multi-Operating Levels," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-27.
    6. 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.
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