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System reliability analysis of retrial machine repair systems with warm standbys and a single server of working breakdown and recovery policy

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  • Wu‐Lin Chen

Abstract

Reliability analysis plays an important role in the machine repair systems. The purpose of this study is to propose reliability analysis of retrial machine repair systems with M operating units, W warm standby units, and a single repair server with recovery policy. Failure times, repair times, and retrial times for all units are assumed to follow exponential distributions. The single repair server is subject to breakdown, and failure times and repair times for the single server are also assumed to follow exponential distributions. The recovery policy is considered in this study to efficiently utilize the single repair server. Based on the transition rate diagram, the probability differential equations are derived, and Laplace transforms are then taken on these equations to derive system reliability and the mean time to system failure (MTTF). Both sensitivity analyses and relative sensitivity analyses are also performed. Some numerical experiments are designed and executed. The important results are outlined below. The failure rate of an operating unit (λ) significantly influences system reliability. Threshold of the recovery policy (q), the service rate of the working server (μ1), and the breakdown rate of the server (α) affect system reliability moderately. The service rate of the broken down server (μ2), the retrial rate (θ), and the repair rate to repair the broken down server (β) affect system reliability slightly; the failure rate of a standby unit (η) rarely influences system reliability. Furthermore, λ affects MTTF significantly, μ1,α,μ2 influence MTTF moderately, β,θ slightly affect MTTF, and η rarely affects MTTF.

Suggested Citation

  • Wu‐Lin Chen, 2018. "System reliability analysis of retrial machine repair systems with warm standbys and a single server of working breakdown and recovery policy," Systems Engineering, John Wiley & Sons, vol. 21(1), pages 59-69, January.
    • Handle: RePEc:wly:syseng:v:21:y:2018:i:1:p:59-69
    DOI: 10.1002/sys.21420
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    Cited by:

    1. Wang, Kuo-Hsiung & Wu, Chia-Huang & Yen, Tseng-Chang, 2022. "Comparative cost-benefit analysis of four retrial systems with preventive maintenance and unreliable service station," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    2. Li, Mingjia & Hu, Linmin & Wu, Shaomin & Zhao, Bing & Wang, Yan, 2023. "Reliability assessment for consecutive-k-out-of-n: F retrial systems under Poisson shocks," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    3. Gao, Shan & Wang, Jinting, 2021. "Reliability and availability analysis of a retrial system with mixed standbys and an unreliable repair facility," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    4. Miaomiao Yu & Yinghui Tang, 2022. "Analysis of a renewal batch arrival queue with a fault-tolerant server using shift operator method," Operational Research, Springer, vol. 22(3), pages 2831-2858, July.
    5. Wang, Yan & Hu, Linmin & Yang, Li & Li, Jing, 2022. "Reliability modeling and analysis for linear consecutive-k-out-of-n: F retrial systems with two maintenance activities," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    6. Yang, Dong-Yuh & Wu, Chia-Huang, 2021. "Evaluation of the availability and reliability of a standby repairable system incorporating imperfect switchovers and working breakdowns," Reliability Engineering and System Safety, Elsevier, vol. 207(C).

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