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A recursive method for the health assessment of systems using the proportional hazards model

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  • Zheng, Rui
  • Najafi, Seyedvahid
  • Zhang, Yingzhi

Abstract

The failure of many practical systems is dependent on both age and a diagnostic covariate process. Cox's proportional hazards model is widely adopted to describe the failure rate of such systems. If the covariate state space is large, it is computationally not feasible to use an analytical method for health assessment at inspection epochs. Existing approximation methods, although can address the above problem, fail to satisfy the critical requirements of modern health management in terms of accuracy, memory storage, and computational speed. This paper develops a novel recursive method to approximately assess the health indices of the proportional hazards model with a Markovian covariate process. The method discretizes age into equidistant and small subintervals. Over each subinterval, an incomplete state transition matrix is constructed with each element measured by its upper and lower bounds. The consideration of dual bounds makes our model more robust than previous methods considering only an upper bound. Then the recursive formulas of various health indices are derived based on the matrixes of consecutive subintervals. Two practical examples demonstrate that the proposed method can produce accurate assessment results with higher efficiency and less memory compared with existing approximation methods.

Suggested Citation

  • Zheng, Rui & Najafi, Seyedvahid & Zhang, Yingzhi, 2022. "A recursive method for the health assessment of systems using the proportional hazards model," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
  • Handle: RePEc:eee:reensy:v:221:y:2022:i:c:s0951832022000564
    DOI: 10.1016/j.ress.2022.108379
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    References listed on IDEAS

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    Cited by:

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    2. Zhu, Mixin & Zhou, Xiaojun, 2023. "Hierarchical-clustering-based joint optimization of spare part provision and maintenance scheduling for serial-parallel multi-station manufacturing systems," International Journal of Production Economics, Elsevier, vol. 264(C).
    3. Yuyun Hidayat & Sukono & Betty Subartini & Nida Khairunnisa & Aceng Sambas & Titi Purwandari, 2022. "An Estimated Analysis of Willingness to Wait Time to Pay Rice Agricultural Insurance Premiums Using Cox’s Proportional Hazards Model," Mathematics, MDPI, vol. 10(21), pages 1-16, October.
    4. Wang, Jiantai & Zhou, Shihan & Peng, Rui & Qiu, Qingan & Yang, Li, 2023. "An inspection-based replacement planning in consideration of state-driven imperfect inspections," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    5. Wang, Jiantai & Ma, Xiaobing & Yang, Li & Qiu, Qingan & Shang, Lijun & Wang, Jingjing, 2024. "A hybrid inspection-replacement policy for multi-stage degradation considering imperfect inspection with variable probabilities," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    6. Hu, Tao & Guo, Yiming & Gu, Liudong & Zhou, Yifan & Zhang, Zhisheng & Zhou, Zhiting, 2022. "Remaining useful life estimation of bearings under different working conditions via Wasserstein distance-based weighted domain adaptation," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    7. Zheng, Rui & Wang, Jingjing & Zhang, Yingzhi, 2023. "A hybrid repair-replacement policy in the proportional hazards model," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1011-1021.

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