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Flexible modelling of a bivariate degradation process with a shared frailty and an application to fatigue crack data

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  • Barui, Sandip
  • Mitra, Debanjan
  • Balakrishnan, Narayanaswamy

Abstract

Examples of units with two performance characteristics that degrade over time are ubiquitous in reliability engineering. In this article, we develop a flexible model for bivariate degradation data pertaining to units in which the degradation processes corresponding to the performance characteristics are likely dependent on each other. The proposed model has two features: the degradation processes are marginally modelled by gamma processes, and the dependence between them is modelled by a shared frailty term that is assumed to follow the generalized gamma distribution. We show that this model is far more flexible and efficient than many of the commonly used models for capturing dependence between the performance characteristics. A computational technique for the maximum likelihood estimation, based on Monte Carlo simulation, is developed for the proposed model. Then, the method of estimation is evaluated through an elaborate Monte Carlo simulation study. The joint reliability function of the unit with two performance characteristics and its estimation are also discussed in this general setting. The proposed model is extended to the case of multiple performance characteristics. Finally, a case study is presented in which a real degradation data pertaining to fatigue cracks is analysed through the proposed model to demonstrate its usefulness.

Suggested Citation

  • Barui, Sandip & Mitra, Debanjan & Balakrishnan, Narayanaswamy, 2024. "Flexible modelling of a bivariate degradation process with a shared frailty and an application to fatigue crack data," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    • Handle: RePEc:eee:reensy:v:242:y:2024:i:c:s0951832023006361
    DOI: 10.1016/j.ress.2023.109722
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    References listed on IDEAS

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    1. G. Asha & A. Vincent Raja & Nalini Ravishanker, 2018. "Reliability modelling incorporating load share and frailty," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(2), pages 206-223, March.
    2. Dai, Xinliang & Qu, Sheng & Sui, Hao & Wu, Pingbo, 2022. "Reliability modelling of wheel wear deterioration using conditional bivariate gamma processes and Bayesian hierarchical models," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    3. Sun, Fuqiang & Fu, Fangyou & Liao, Haitao & Xu, Dan, 2020. "Analysis of multivariate dependent accelerated degradation data using a random-effect general Wiener process and D-vine Copula," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    4. Pan, Yongjun & Sun, Yu & Li, Zhixiong & Gardoni, Paolo, 2023. "Machine learning approaches to estimate suspension parameters for performance degradation assessment using accurate dynamic simulations," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    5. Sun, Fuqiang & Li, Hao & Cheng, Yuanyuan & Liao, Haitao, 2021. "Reliability analysis for a system experiencing dependent degradation processes and random shocks based on a nonlinear Wiener process model," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    6. Song, Kai & Cui, Lirong, 2022. "A common random effect induced bivariate gamma degradation process with application to remaining useful life prediction," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    7. Almeida, Marco Pollo & Paixão, Rafael S. & Ramos, Pedro L. & Tomazella, Vera & Louzada, Francisco & Ehlers, Ricardo S., 2020. "Bayesian non-parametric frailty model for dependent competing risks in a repairable systems framework," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    8. Barker, C.T. & Newby, M.J., 2009. "Optimal non-periodic inspection for a multivariate degradation model," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 33-43.
    9. Li, Zhanhang & Zhou, Jian & Nassif, Hani & Coit, David & Bae, Jinwoo, 2023. "Fusing physics-inferred information from stochastic model with machine learning approaches for degradation prediction," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    10. Palayangoda, Lochana K. & Ng, Hon Keung Tony, 2021. "Semiparametric and nonparametric evaluation of first-passage distribution of bivariate degradation processes," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    11. Pan, Zhengqiang & Balakrishnan, Narayanaswamy, 2011. "Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes," Reliability Engineering and System Safety, Elsevier, vol. 96(8), pages 949-957.
    12. Cha, Ji Hwan & Finkelstein, Maxim, 2014. "Some notes on unobserved parameters (frailties) in reliability modeling," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 99-103.
    13. Fang, Guanqi & Pan, Rong & Hong, Yili, 2020. "Copula-based reliability analysis of degrading systems with dependent failures," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
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