Reliable prediction of industrial components Remaining Useful Life using Cox and Weibull models: A Comparative Study
DOI:
https://doi.org/10.56294/dm20251102Keywords:
Remaining Useful Life (RUL), Predictive Maintenance, Reliability, Cox Proportional Hazards Model, Weibull Model, Survival AnalysisAbstract
Predicting the Remaining Useful Life (RUL) of industrial equipment is a cornerstone of predictive maintenance strategies aimed at minimizing downtime and optimizing maintenance costs. This study presents a comparative evaluation of two prominent survival analysis techniques Cox Proportional Hazards (Cox PH) and the Weibull model for RUL prediction using the AI4I 2020 Predictive Maintenance Dataset. We implement a robust analytical framework incorporating Kaplan-Meier survival curves, log-rank tests, and multivariate survival modeling. Our methodology includes detailed data preprocessing, model validation using the C-index and Akaike Information Criterion (AIC), and the identification of significant predictors of failure. The results reveal that the Cox PH model outperforms the Weibull model in terms of flexibility, predictive accuracy, and capacity to handle multiple covariates. This work highlights the strengths and limitations of both models and emphasizes the superior applicability of the Cox PH model for complex industrial datasets. These findings offer actionable insights for developing more reliable, data-driven maintenance strategies in Industry 4.0 environments.
References
1. Predictive Maintenance: A Novel Framework for a Data-Driven, Semi-Supervised, and Partially Online Prognostic Health Management Application in Industries [Internet]. [cité 18 juin 2025]. Disponible sur: https://www.mdpi.com/2076-3417/11/8/3380
2. Zhu T, Ran Y, Zhou X, Wen Y. A Survey of Predictive Maintenance: Systems, Purposes and Approaches [Internet]. arXiv; 2024 [cité 18 juin 2025]. Disponible sur: http://arxiv.org/abs/1912.07383
3. Si G, Xia T, Zhu Y, Du S, Xi L. Triple-level opportunistic maintenance policy for leasehold service network of multi-location production lines. Reliability Engineering & System Safety. 1 oct 2019;190:106519.
4. Zheng H, Kong X, Xu H, Yang J. Reliability analysis of products based on proportional hazard model with degradation trend and environmental factor. Reliability Engineering & System Safety. 1 déc 2021;216:107964.
5. Meeker WQ, Escobar LA, Pascual FG. Statistical Methods for Reliability Data. John Wiley & Sons; 2021. 708 p.
6. Liu J, Wang ,Bing Xing, Wang ,Shasha, and Zhou H. The prediction of RULs for Weibull or gamma k-out-of-n system with nonidentical components based on component data. Quality Technology & Quantitative Management. 0(0):1‑26.
7. Zhang H, Gao Z, Du C, Bi S, Fang Y, Yun F, et al. Parameter estimation of three-parameter Weibull probability model based on outlier detection. RSC Advances. 2022;12(53):34154‑64.
8. Feng J, Zhang H, Li F. Investigating the relevance of major signaling pathways in cancer survival using a biologically meaningful deep learning model. BMC bioinformatics. déc 2021;22(1):47.
9. Mathpati YC, More KS, Tripura T, Nayek R, Chakraborty S. MAntRA: A framework for model agnostic reliability analysis. Reliability Engineering & System Safety. 1 juill 2023;235:109233.
10. Zhou D, Sun CP, Du YM, Guan X. Degradation and reliability of multi-function systems using the hazard rate matrix and Markovian approximation. Reliability Engineering & System Safety. 1 févr 2022;218:108166.
11. Xu A, Wang R, Weng X, Wu Q, Zhuang L. Strategic integration of adaptive sampling and ensemble techniques in federated learning for aircraft engine remaining useful life prediction. Applied Soft Computing. 1 mai 2025;175:113067.
12. Zhang S, Zhai Q, Li Y. Degradation modeling and RUL prediction with Wiener process considering measurable and unobservable external impacts. Reliability Engineering & System Safety. 1 mars 2023;231:109021.
13. A Novel Remaining Useful Life Prediction Approach Combined eXtreme Gradient Boosting and Multi-Quantile Recurrent Neural Network | IEEE Journals & Magazine | IEEE Xplore [Internet]. [cité 15 févr 2025]. Disponible sur: https://ieeexplore.ieee.org/abstract/document/10478510
14. Smith AM, Hinchcliffe GR. RCM--Gateway to World Class Maintenance. Elsevier; 2003. 362 p.
15. Moncada-Torres A, van Maaren MC, Hendriks MP, Siesling S, Geleijnse G. Explainable machine learning can outperform Cox regression predictions and provide insights in breast cancer survival. Sci Rep. 26 mars 2021;11(1):6968.
16. Collett D. Modelling Survival Data in Medical Research. 4e éd. New York: Chapman and Hall/CRC; 2023. 556 p.
17. Hasegawa T. Sample size determination for the weighted log-rank test with the Fleming-Harrington class of weights in cancer vaccine studies. Pharm Stat. 2014;13(2):128‑35.
18. Bender R, Augustin T, Blettner M. Generating survival times to simulate Cox proportional hazards models. Statistics in Medicine. 15 juin 2005;24(11):1713‑23.
19. Chen C, Liu Y, Wang S, Sun X, Di Cairano-Gilfedder C, Titmus S, et al. Predictive maintenance using cox proportional hazard deep learning. Advanced Engineering Informatics. 1 avr 2020;44:101054.
20. Yang Z, Kanniainen J, Krogerus T, Emmert-Streib F. Prognostic modeling of predictive maintenance with survival analysis for mobile work equipment. Sci Rep. 20 mai 2022;12(1):8529.
21. Parii D, Janssen E, Tang G, Kouzinopoulos C, Pietrasik M. Predicting the Lifespan of Industrial Printheads with Survival Analysis [Internet]. arXiv; 2025 [cité 18 juin 2025]. Disponible sur: http://arxiv.org/abs/2504.07638
22. Khuntia SR, Zghal F, Bhuyan R, Schenkel E, Duvivier P, Blancke O, et al. Use of survival analysis and simulation to improve maintenance planning of high voltage instrument transformers in the Dutch transmission system [Internet]. arXiv; 2023 [cité 15 juill 2025]. Disponible sur: http://arxiv.org/abs/2301.01239
23. Lillelund CM, Pannullo F, Jakobsen MO, Pedersen CF. Predicting Survival Time of Ball Bearings in the Presence of Censoring [Internet]. arXiv; 2023 [cité 15 juill 2025]. Disponible sur: http://arxiv.org/abs/2309.07188
24. Cavalcante T, Ospina R, Leiva V, Cabezas X, Martin-Barreiro C. Weibull Regression and Machine Learning Survival Models: Methodology, Comparison, and Application to Biomedical Data Related to Cardiac Surgery. Biology. mars 2023;12(3):442.
25. Petsinis P, Naskos A, Gounaris A. Analysis of key flavors of event-driven predictive maintenance using logs of phenomena described by Weibull distributions [Internet]. arXiv; 2021 [cité 15 juill 2025]. Disponible sur: http://arxiv.org/abs/2101.07033
26. Karmakar B, Pradhan B. Residual lifetime prediction for heterogeneous degradation data by Bayesian semi-parametric method [Internet]. arXiv; 2025 [cité 18 juin 2025]. Disponible sur: http://arxiv.org/abs/2504.15794.
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Copyright (c) 2025 Hamdi Alaoui Abdelhafid, Anwar Meddaoui , Ahmed En-nhaili (Author)

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