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Nonlinear general path models for degradation data with dynamic covariates

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  • Zhibing Xu
  • Yili Hong
  • Ran Jin

Abstract

Degradation data have been widely used to estimate product reliability. Because of technology advancement, time‐varying usage and environmental variables, which are called dynamic covariates, can be easily recorded nowadays, in addition to the traditional degradation measurements. The use of dynamic covariates is appealing because they have the potential to explain more variability in degradation paths. We propose a class of general path models to incorporate dynamic covariates for modeling of degradation paths. Physically motivated nonlinear functions are used to describe the degradation paths, and random effects are used to describe unit‐to‐unit variability. The covariate effects are modeled by shape‐restricted splines. The estimation of unknown model parameters is challenging because of the involvement of nonlinear relationships, random effects, and shaped‐restricted splines. We develop an efficient procedure for parameter estimations. The performance of the proposed method is evaluated by simulations. An outdoor coating weathering dataset is used to illustrate the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

Suggested Citation

  • Zhibing Xu & Yili Hong & Ran Jin, 2016. "Nonlinear general path models for degradation data with dynamic covariates," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(2), pages 153-167, March.
    • Handle: RePEc:wly:apsmbi:v:32:y:2016:i:2:p:153-167
    DOI: 10.1002/asmb.2129
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    Cited by:

    1. Xu, Huyang & Fard, Nasser & Fang, Yuanchen, 2020. "Time series chain graph for modeling reliability covariates in degradation process," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    2. Minhee Kim & Todd Allen & Kaibo Liu, 2023. "Covariate Dependent Sparse Functional Data Analysis," INFORMS Joural on Data Science, INFORMS, vol. 2(1), pages 81-98, April.
    3. Marwa Belhaj Salem & Mitra Fouladirad & Estelle Deloux, 2021. "Prognostic and Classification of Dynamic Degradation in a Mechanical System Using Variance Gamma Process," Mathematics, MDPI, vol. 9(3), pages 1-25, January.
    4. Sun, Xuxue & Cai, Wenjun & Li, Mingyang, 2021. "A hierarchical modeling approach for degradation data with mixed-type covariates and latent heterogeneity," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    5. Jahani, Salman & Zhou, Shiyu & Veeramani, Dharmaraj, 2021. "Stochastic prognostics under multiple time-varying environmental factors," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    6. Chi, Zhexiang & Chen, Ruoran & Huang, Simin & Li, Yan-Fu & Zhou, Bin & Zhang, Wenjuan, 2020. "Multi-State System Modeling and Reliability Assessment for Groups of High-speed Train Wheels," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    7. Chatenet, Q. & Remy, E. & Gagnon, M. & Fouladirad, M. & Tahan, A.S., 2021. "Modeling cavitation erosion using non-homogeneous gamma process," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    8. Ensiyeh Nezakati & Mostafa Razmkhah & Firoozeh Haghighi, 2019. "Reliability analysis of a k-out-of-n:F system under a linear degradation model with calibrations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 537-552, June.
    9. Saberzadeh, Zahra & Razmkhah, Mostafa, 2022. "Reliability of degrading complex systems with two dependent components per element," Reliability Engineering and System Safety, Elsevier, vol. 222(C).

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