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Reliability measures of discrete time k-out-of-n: G retrial systems based on Bernoulli shocks

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  • Yu, Xiaoyun
  • Hu, Linmin
  • Ma, Mengrao

Abstract

Existing reliability studies on k-out-of-n: G systems with retrial characteristics mainly focused on continuous time reliability modeling and evaluation. However, in the real world, it is not always possible to continuously monitor all systems for various reasons, but at some discrete points in time. Based on this practical engineering phenomenon, a discrete time k-out-of-n: G system reliability model with retrial is developed. The system operates in an environment with Bernoulli shocks and the component failure is caused by both its own lifetime and shocks. Two types of reliability shock models are given based on the distributions of the magnitude of the shock and the failure threshold. Other failed components will enter the retrial space and keep retrying according to the first-in-first-out (FIFO) rule while the repairman is busy on a failed component. Discrete time Markov process theory is used to analyze the system steady-state measures, and the system transient-state measures are derived by the multi-step transition probability matrix. Numerical experiments and evaluation of reliability measures are carried out based on the application problem for the cloud data processing center, and numerical results for two types of models are given to exhibit the potential applications of the developed models.

Suggested Citation

  • Yu, Xiaoyun & Hu, Linmin & Ma, Mengrao, 2023. "Reliability measures of discrete time k-out-of-n: G retrial systems based on Bernoulli shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    • Handle: RePEc:eee:reensy:v:239:y:2023:i:c:s0951832023004052
    DOI: 10.1016/j.ress.2023.109491
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    References listed on IDEAS

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    2. Changjiang Lai & Ehmet Kasim & Ahmadjan Muhammadhaji, 2024. "Dynamic Analysis of a Standby System with Retrial Strategies and Multiple Working Vacations," Mathematics, MDPI, vol. 12(24), pages 1-34, December.

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