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Performance analysis and optimization of a cold standby system subject to δ-shocks and imperfect repairs

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  • Zhao, Bing
  • Yue, Dequan
  • Liao, Haitao
  • Liu, Yuanhui
  • Zhang, Xiaohong

Abstract

This paper analyzes and optimizes the economic performance of a cold standby system subject to δ-shocks and imperfect repairs. Specially, the system consists of two components with different reliability characteristics. It is assumed that shocks arrive according to a Poisson process. When a component is active during operation, it will fail whenever the interarrival time between successive shocks is less than a threshold influenced by the number of repairs performed on this component. For reliability analysis, geometric process models are utilized to characterize the lifetime and repair time of the active component subject to δ-shocks and imperfect repairs. Using the supplementary variable method, some reliability measures of the system are obtained. Moreover, an explicit expression for the long-run cost per unit time is derived to quantify the system's economic performance. Finally, the optimal repair policy is determined based on this economic performance measure, and a sensitivity analysis is conducted to provide managerial insights for the efficient operation of such a system.

Suggested Citation

  • Zhao, Bing & Yue, Dequan & Liao, Haitao & Liu, Yuanhui & Zhang, Xiaohong, 2021. "Performance analysis and optimization of a cold standby system subject to δ-shocks and imperfect repairs," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:reensy:v:208:y:2021:i:c:s0951832020308231
    DOI: 10.1016/j.ress.2020.107330
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    References listed on IDEAS

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    6. Yeh Lam & Yuan Lin Zhang, 1996. "Analysis of a two‐component series system with a geometric process model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(4), pages 491-502, June.
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    Cited by:

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    2. Chadjiconstantinidis, Stathis & Eryilmaz, Serkan, 2024. "On δ-shock model with a change point in intershock time distribution," Statistics & Probability Letters, Elsevier, vol. 208(C).
    3. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2023. "Co-optimizing component allocation and activation sequence in heterogeneous 1-out-of-n standby system exposed to shocks," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    4. Eryilmaz, Serkan & Unlu, Kamil Demirberk, 2023. "A new generalized δ-shock model and its application to 1-out-of-(m+1):G cold standby system," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    5. Wu, Bei & Wei, Xiaohua & Zhang, Yamei & Bai, Sijun, 2023. "Modeling dynamic environment effects on dependent failure processes with varying failure thresholds," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    6. Wei, Xiaohua & Bai, Sijun & Wu, Bei, 2023. "A novel shock-dependent preventive maintenance policy for degraded systems subject to dynamic environments and N-critical shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    7. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2021. "Optimal shock-driven switching strategies with elements reuse in heterogeneous warm-standby systems," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    8. Chadjiconstantinidis, Stathis & Eryilmaz, Serkan, 2023. "Reliability of a mixed δ-shock model with a random change point in shock magnitude distribution and an optimal replacement policy," Reliability Engineering and System Safety, Elsevier, vol. 232(C).

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