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A study on a single-unit repairable system with state aggregations

Author

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  • Lirong Cui
  • Shijia Du
  • Alan Hawkes

Abstract

This article analyzes a single-unit repairable system consisting of an operating subsystem and a maintenance subsystem that is solely used to repair the operating subsystem in the event of it breaking down. Formulae for reliability indexes such as availability and distributions concerned with visits to certain subsets of states are presented in terms of state aggregations in which two partitions are used. The situation with exponentially distributed operational times is discussed not only as a special case of the approach used in this article but also using a Markov model. A numerical example is given to illustrate the results obtained in this article.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:uiiexx:v:44:y:2012:i:11:p:1022-1032
    DOI: 10.1080/0740817X.2012.662309
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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. Shijia Du & Lirong Cui & Cong Lin, 2016. "Some reliability indexes and sojourn time distributions for a repairable degradation model," Journal of Risk and Reliability, , vol. 230(3), pages 334-349, June.
    3. 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.
    4. 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.
    5. Yi, He & Cui, Lirong, 2017. "Distribution and availability for aggregated second-order semi-Markov ternary system with working time omission," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 50-60.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.

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