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New interval availability indexes for Markov repairable systems

Author

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  • Cui, Lirong
  • Chen, Jianhui
  • Wu, Bei

Abstract

In maintenance field, there are many indexes such as instantaneous availability, steady state availability, interval availability and others, which have been widely used to describe the various properties and performance of repairable systems on maintenance. However, all the present availability indexes still cannot cover some situations which people are interested in. In the paper, two new interval availability indexes are introduced for Markov repairable systems, which is named as an availability with a given window length and containing a specified point or interval. The new interval availability is the probability that the system is working during a given window length and this window must contains a specified point or interval. Their calculation formulas are presented in matrix forms by using the Laplace transform. Some properties on the two indexes are discussed briefly, and numerical examples are shown to illustrate the features of the two new indexes, finally conclusions are given. These two new indices can become the conventional interval availability when the given window length is zero or equal to the specified interval length. The results in the paper may be used to measure the performance of repairable system more deeply and detail.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:168:y:2017:i:c:p:12-17
    DOI: 10.1016/j.ress.2017.03.016
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    References listed on IDEAS

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    2. Lirong Cui & Shijia Du & Aofu Zhang, 2014. "Reliability measures for two-part partition of states for aggregated Markov repairable systems," Annals of Operations Research, Springer, vol. 212(1), pages 93-114, January.
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    5. 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.
    6. 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.
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    8. 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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    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. D’Amico, Guglielmo & Petroni, Filippo, 2023. "ROCOF of higher order for semi-Markov processes," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    3. Fang, Chen & Cui, Lirong, 2021. "Balanced Systems by Considering Multi-state Competing Risks Under Degradation Processes," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    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. Gao, Hongda & Cui, Lirong & Yi, He, 2019. "Availability analysis of k-out-of-n: F repairable balanced systems with m sectors," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    6. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2018. "Constructing a Markov process for modelling a reliability system under multiple failures and replacements," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 34-47.
    7. Fang, Chen & Cui, Lirong, 2021. "Reliability evaluation for balanced systems with auto-balancing mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    8. Vahid Andalib & Jyotirmoy Sarkar, 2022. "A System with Two Spare Units, Two Repair Facilities, and Two Types of Repairers," Mathematics, MDPI, vol. 10(6), pages 1-13, March.
    9. 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.
    10. Jingyuan Shen & Alaa Elwany & Lirong Cui, 2018. "Reliability modeling for systems degrading in K cyclical regimes based on gamma processes," Journal of Risk and Reliability, , vol. 232(6), pages 754-765, December.
    11. Wu, Bei & Cui, Lirong & Fang, Chen, 2020. "Multi-state balanced systems with multiple failure criteria," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    12. Wu, Shaomin & Do, Phuc, 2017. "Editorial," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 1-3.
    13. He Yi & Lirong Cui & Narayanaswamy Balakrishnan & Jingyuan Shen, 2022. "Multi-Point and Multi-Interval Bounded-Covering Availability Measures for Aggregated Markovian Repairable Systems," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2427-2453, December.
    14. Guglielmo D’Amico & Raimondo Manca & Filippo Petroni & Dharmaraja Selvamuthu, 2021. "On the Computation of Some Interval Reliability Indicators for Semi-Markov Systems," Mathematics, MDPI, vol. 9(5), pages 1-23, March.
    15. Yi, He & Cui, Lirong & Balakrishnan, Narayanaswamy, 2021. "New reliability indices for first- and second-order discrete-time aggregated semi-Markov systems with an application to TT&C system," Reliability Engineering and System Safety, Elsevier, vol. 215(C).

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