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A nonlinear wiener process degradation model with damage resistance for reliability analysis

Author

Listed:
  • Yuhan Hu

    (North Carolina State University)

  • Mengmeng Zhu

    (North Carolina State University
    North Carolina State University)

  • Huizhong Lin

    (North Carolina State University)

Abstract

Systems commonly experience competing risks of internal degradation and random shocks. Random shocks may cause damage to the system, and the degrees of the damage affect system degradation differently. In this paper, we consider a system, namely, a damage-resistant system, designed to withstand shocks up to a specified threshold. To consider the system damage resistance, we first propose a new shock classification based on the shock magnitude and define the damage resistance level of the system accordingly. Furthermore, because the system will be more vulnerable to shocks over time, we divide the system degradation process into two stages and propose nonlinear Wiener process degradation models with two stages by incorporating the system damage resilience level with the new shock classification. The closed-form system reliability functions for these two stages are further derived. Lastly, we conduct numerical examples with real-world data to demonstrate the practical application of our proposed model.

Suggested Citation

  • Yuhan Hu & Mengmeng Zhu & Huizhong Lin, 2025. "A nonlinear wiener process degradation model with damage resistance for reliability analysis," Annals of Operations Research, Springer, vol. 352(1), pages 169-192, September.
    • Handle: RePEc:spr:annopr:v:352:y:2025:i:1:d:10.1007_s10479-025-06695-5
    DOI: 10.1007/s10479-025-06695-5
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    References listed on IDEAS

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    1. Lei Jiang & Qianmei Feng & David W. Coit, 2015. "Modeling zoned shock effects on stochastic degradation in dependent failure processes," IISE Transactions, Taylor & Francis Journals, vol. 47(5), pages 460-470, May.
    2. Caiyun Niu & Xiaolin Liang & Bingfeng Ge & Xue Tian & Yingwu Chen, 2016. "Optimal replacement policy for a repairable system with deterioration based on a renewal-geometric process," Annals of Operations Research, Springer, vol. 244(1), pages 49-66, September.
    3. Zhang, Zhengxin & Si, Xiaosheng & Hu, Changhua & Lei, Yaguo, 2018. "Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods," European Journal of Operational Research, Elsevier, vol. 271(3), pages 775-796.
    4. Mengmeng Zhu, 2022. "A new framework of complex system reliability with imperfect maintenance policy," Annals of Operations Research, Springer, vol. 312(1), pages 553-579, May.
    5. Phalguni Nanda & Prajamitra Bhuyan & Anup Dewanji, 2022. "Optimal replacement policy under cumulative damage model and strength degradation with applications," Annals of Operations Research, Springer, vol. 315(2), pages 1345-1371, August.
    6. Yuhan Hu & Mengmeng Zhu, 2023. "System Reliability Models with Random Shocks and Uncertainty: A State-of-the-Art Review," Springer Series in Reliability Engineering, in: Vijay Kumar & Hoang Pham (ed.), Predictive Analytics in System Reliability, pages 19-38, Springer.
    7. Mengmeng Zhu & Hoang Pham, 2019. "A Novel System Reliability Modeling of Hardware, Software, and Interactions of Hardware and Software," Mathematics, MDPI, vol. 7(11), pages 1-14, November.
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