Research article

Analysis of two components parallel repairable degenerate system with vacation

  • Received: 29 April 2021 Accepted: 13 July 2021 Published: 22 July 2021
  • MSC : TP391

  • This article studies a parallel repairable degradation system with two similar components and a repairman who can take a single vacation. Suppose that the system consists of two components that cannot be repaired "as good as new" after failures; when the repairman has a single vacation, the fault component of system may not be repaired immediately, namely, if a component fails and the repairman is on vacation, the repair of the component will be delayed, if a component fails and the repairman is on duty, the fault component can be repaired immediately. Under these assumptions, a replacement policy $ N $ based on the failed times of component 1 is studied. The explicit expression of the system average cost rate $ C(N) $ and the optimal replacement policy $ N^{\ast} $ by minimizing the $ C(N) $ are obtained, which means the two components of the system will be replaced at the same time if the failures of component 1 reach $ N^{\ast} $. To show the advantage of a parallel system, a replacement policy $ N $ of the cold standby system consisting of the two similar components is also considered. The numerical results of both systems are given by the numerical analysis. The optimal replacement policy $ N^* $ for both systems are obtained. Finally, the comparison of numerical results shows the advantages of the parallel system.

    Citation: YanLing Li, GenQi Xu, Hao Chen. Analysis of two components parallel repairable degenerate system with vacation[J]. AIMS Mathematics, 2021, 6(10): 10602-10619. doi: 10.3934/math.2021616

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  • This article studies a parallel repairable degradation system with two similar components and a repairman who can take a single vacation. Suppose that the system consists of two components that cannot be repaired "as good as new" after failures; when the repairman has a single vacation, the fault component of system may not be repaired immediately, namely, if a component fails and the repairman is on vacation, the repair of the component will be delayed, if a component fails and the repairman is on duty, the fault component can be repaired immediately. Under these assumptions, a replacement policy $ N $ based on the failed times of component 1 is studied. The explicit expression of the system average cost rate $ C(N) $ and the optimal replacement policy $ N^{\ast} $ by minimizing the $ C(N) $ are obtained, which means the two components of the system will be replaced at the same time if the failures of component 1 reach $ N^{\ast} $. To show the advantage of a parallel system, a replacement policy $ N $ of the cold standby system consisting of the two similar components is also considered. The numerical results of both systems are given by the numerical analysis. The optimal replacement policy $ N^* $ for both systems are obtained. Finally, the comparison of numerical results shows the advantages of the parallel system.



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    [1] J. Cheng, Y. H. Tang, M. M. Yu, Reliability of unidirectional closed three-part series and parallel cold storage repairable system, Mathematica Applicata, 30 (2017), 27–39.
    [2] W. L. Chen, System reliability analysis of retrial machine repair systems with warm standbys and a single server of working breakdown and recovery policy, Systems Eng., 21 (2018), 59–69. doi: 10.1002/sys.21420
    [3] L. M. Hu, D. Q. Yue, Z. Y. Ma, Availability Analysis of a Repairable Series-Parallel System with Redundant Dependency$\ast$, J. Syst. Sci. Complex., 33 (2020), 446–460. doi: 10.1007/s11424-019-8039-x
    [4] J. C. Ke, T. H. Liu, D. Y. Yang, Modelling of Machine Interference Problem with Unreliable Repairman and Standbys Imperfect Switchover, Reliab. Eng. Syst. Safe., 174 (2018), 12–18. doi: 10.1016/j.ress.2018.01.013
    [5] Y. Lam, Geometric processes and replacement problem, Acta Math. Appl. Sin-E, 4 (1988), 366–377. doi: 10.1007/BF02007241
    [6] B. Liu, L. Cui, Y. Wen, F. Guo, A cold standby repairable system with the repairman having multiple vacations and operational, repair, and vacation times following phase-type distributions, Commun. Stat-Theor M., 45 (2016), 850–858. doi: 10.1080/03610926.2013.851239
    [7] X. D. Li, C. Cheng, Reliability Analysis of Three Components with Priority in Repairable Cold Standby System, Journal of Lanzhou Institute of Technology, 25 (2018), 84–87.
    [8] Y. L. Li, G. Q. Xu, Analysis of two components parallel repairable system with vacation, Commun. Stat-Theor M., 32 (2019), 21–26.
    [9] M. A. El-Damcese, N. S. Temraz, Analysis for a parallel repairable system with different failure modes, Journal of Reliability and Statistical Studies, 5 (2012), 95–106.
    [10] W. F. Wu, J. S. Song, K. X. Ling, Maintenance and replacement policy for a repairable multi-state system with regular preventive repairs, Systems Engineering and Electronics, 37 (2015), 1319–1324.
    [11] G. J. Wang, Y. L. Zhang, Optimal replacement policy for a two-dissimilar-component cold standby system with different repair actions, Int. J. Syst. Sci., 47 (2016), 1021–1031. doi: 10.1080/00207721.2014.911387
    [12] W. Z. Yuan, G. Q. Xu, Modeling of a deteriorating system with repair satisfying general distribution, Appl. Math. Comput., 218 (2012), 6340–6350.
    [13] D. Q. Yue, Q. Q. Gao, A geometric process model for deteriorating operating system with periodic and random inspections, Qual. Technol. Quant. M., 14 (2016), 269–279.
    [14] Y. L. Zhang, G. J. Wang, An extended geometric process repair model for a cold standby repairable system with imperfect delayed repair, International Journal of Systems Science: Operations and Logistics, 3 (2016), 163–175. doi: 10.1080/23302674.2015.1074759
    [15] Y. L. Zhang, G. J. Wang, An optimal age-replacement policy for a simple repairable system with delayed repair, Commun. Stat-Theor M., 46 (2017), 2837–2850. doi: 10.1080/03610926.2015.1053930
    [16] Y. G. Zhang, Y. C. Sun, L. B. Li, M. Zhao, Copula-based reliability analysis for a parallel system with a cold standby, Commun. Stat-Theor M., 47 (2018), 562–582. doi: 10.1080/03610926.2017.1309432
    [17] Y. L. Zhang, R. C. Yam, M. J. Zuo, Optimal replacement policy for multistate repairable system, J. Oper. Res. Soc., 53 (2002), 1123–1127.
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