Machine Learning for Covariate-Driven Changes in Weibull Scale Parameter
Received: 28 September 2025 | Revised: 19 November 2025 | Accepted: 25 November 2025 | Online: 9 February 2026
Corresponding author: Surya Michrandi Nasution
Abstract
This research addresses the limitations of conventional, static survival models for Remaining Useful Life (RUL) estimation in Prognostics and Health Management (PHM) by proposing and implementing a data-driven framework. The study posits that a system's characteristic life, represented by the Weibull scale parameter (λ), is not static but a dynamic variable influenced by time-varying operational and environmental factors, or covariates. Unlike traditional methods, such as the Accelerated Failure Time (AFT) model, which rely on restrictive linear assumptions to link covariates to the lifetime model, this methodology employs supervised Machine Learning (ML) models to quantify this complex and potentially non-linear relationship. The methodology is validated using the National Aeronautics and Space Administration (NASA) Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) aircraft engine degradation dataset. The results demonstrate that ensemble-based methods like Light Gradient Boosting Machine (LightGBM) and Extreme Gradient Boosting (XGBoost) significantly outperform classical statistical models across a suite of standard regression metrics and custom-developed Weibull-centric error metrics. The consistent performance rankings across all metrics validate the effectiveness of the proposed approach and confirm its capability to capture the intricate degradation dynamics of real-world systems.
Keywords:
Prognostics and Health Management (PHM), weibull distribution, Remaining Useful Life (RUL), Accelerated Failure Time (AFT), machine learning, supervised learningDownloads
References
P. Dersin, Modeling Remaining Useful Life Dynamics in Reliability Engineering, 1st ed. Boca Raton: CRC Press, 2023. DOI: https://doi.org/10.1201/9781003250685-1
N. L. Clement and R. C. Lasky, "Weibull Distribution and Analysis: 2019," in 2020 Pan Pacific Microelectronics Symposium (Pan Pacific), HI, USA, Feb. 2020, pp. 1–5. DOI: https://doi.org/10.23919/PanPacific48324.2020.9059313
R. Saikia and M. P. Barman, "A Review on Accelerated Failure Time Models," International Journal of Statistics and Systems, vol. 12, no. 2, pp. 311–322, 2017.
I. De Pater and M. Mitici, "Novel Metrics to Evaluate Probabilistic Remaining Useful Life Prognostics with Applications to Turbofan Engines," PHM Society European Conference, vol. 7, no. 1, pp. 96–109, June 2022. DOI: https://doi.org/10.36001/phme.2022.v7i1.3320
M. Mitici, I. De Pater, A. Barros, and Z. Zeng, "Dynamic predictive maintenance for multiple components using data-driven probabilistic RUL prognostics: The case of turbofan engines," Reliability Engineering & System Safety, vol. 234, June 2023, Art. no. 109199. DOI: https://doi.org/10.1016/j.ress.2023.109199
M. Salinas-Camus and N. Eleftheroglou, "Uncertainty in Aircraft Turbofan Engine Prognostics on the C-MAPSS Dataset," PHM Society European Conference, vol. 8, no. 1, June 2024, Art. no. 10. DOI: https://doi.org/10.36001/phme.2024.v8i1.4007
M. Dhada, L. Bull, M. Girolami, and A. Parlikad, "Collaborative prognosis using a Weibull statistical hierarchical model," Reliability Engineering & System Safety, vol. 262, Oct. 2025, Art. no. 111110. DOI: https://doi.org/10.1016/j.ress.2025.111110
A. Saxena, K. Goebel, D. Simon, and N. Eklund, "Damage propagation modeling for aircraft engine run-to-failure simulation," in 2008 International Conference on Prognostics and Health Management, Denver, CO, USA, Oct. 2008, pp. 1–9. DOI: https://doi.org/10.1109/PHM.2008.4711414
D. Maulud and A. M. Abdulazeez, "A Review on Linear Regression Comprehensive in Machine Learning," Journal of Applied Science and Technology Trends, vol. 1, no. 2, pp. 140–147, Dec. 2020. DOI: https://doi.org/10.38094/jastt1457
Z. Jun, "The Development and Application of Support Vector Machine," Journal of Physics: Conference Series, vol. 1748, no. 5, Jan. 2021, Art. no. 052006. DOI: https://doi.org/10.1088/1742-6596/1748/5/052006
A. F. Jadama and M. K Toray, "Ensemble Learning: Methods, Techniques, Application," Preprint, 2024.
Z. Zhu, "Systematic Optimization of Overfitting Problem in Machine Learning," Highlights in Science, Engineering and Technology, vol. 111, pp. 353–359, Aug. 2024. DOI: https://doi.org/10.54097/3tkzrj84
H. A. Salman, A. Kalakech, and A. Steiti, "Random Forest Algorithm Overview," Babylonian Journal of Machine Learning, vol. 2024, pp. 69–79, June 2024. DOI: https://doi.org/10.58496/BJML/2024/007
T. Chen and C. Guestrin, "XGBoost: A Scalable Tree Boosting System," in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco California USA, Aug. 2016, pp. 785–794. DOI: https://doi.org/10.1145/2939672.2939785
V. S. F. Gonçalves and V. R. De Carvalho, "A Review of Interpretability Methods for Gradient Boosting Decision Trees," Journal of the Brazilian Computer Society, vol. 31, no. 1, pp. 640–654, Aug. 2025. DOI: https://doi.org/10.5753/jbcs.2025.5324
L. B. V. De Amorim, G. D. C. Cavalcanti, and R. M. O. Cruz, "The choice of scaling technique matters for classification performance," Applied Soft Computing, vol. 133, Jan. 2023, Art. no. 109924. DOI: https://doi.org/10.1016/j.asoc.2022.109924
T. O. Hodson, "Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not," Geoscientific Model Development, vol. 15, no. 14, pp. 5481–5487, July 2022. DOI: https://doi.org/10.5194/gmd-15-5481-2022
N. A. M. Ikbal, S. A. Halim, and N. Ali, "Estimating Weibull Parameters Using Maximum Likelihood Estimation and Ordinary Least Squares: Simulation Study and Application on Meteorological Data," Mathematics and Statistics, vol. 10, no. 2, pp. 269–292, Mar. 2022. DOI: https://doi.org/10.13189/ms.2022.100201
M. Mwita, J. Mbelwa, J. Agbinya, and A. Elikana Sam, "The Effect of Hyperparameter Optimization on the Estimation of Performance Metrics in Network Traffic Prediction using the Gradient Boosting Machine Model," Engineering, Technology & Applied Science Research, vol. 13, no. 3, pp. 10714–10720, June 2023. DOI: https://doi.org/10.48084/etasr.5548
T. Yu and H. Zhu, "Hyper-Parameter Optimization: A Review of Algorithms and Applications." arXiv, Mar. 2020.
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Copyright (c) 2025 Muhammad Fitran Ramadhan, Nabil De Nozyra, Fahrial Al Akbar Warsito Putra, Surya Michrandi Nasution, Reza Rendian Septiawan
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