Probabilistic Reliability Modeling of Turbofan Degradation: Survival Analysis and Simulation

Abstract

Reliability analysis is essential for evaluating the safety, durability, and maintenance readiness of engineering systems that operate under uncertain degradation conditions. This study develops and empirically evaluates a probabilistic reliability framework that combines lifetime distribution fitting, survival estimation, failure-rate modeling, remaining-useful-life prediction, and Monte Carlo uncertainty simulation. The empirical case uses a public turbofan engine degradation benchmark containing run-to-failure training trajectories, incomplete test trajectories, operating-condition settings, sensor measurements, and true remaining-useful-life labels. The proposed framework first converts degradation trajectories into lifetime and remaining-useful-life indicators, then estimates reliability and cumulative failure probability using Weibull and empirical survival functions. A regularized prediction model links operating cycles and sensor behavior to remaining useful life, while bootstrap-based Monte Carlo simulation propagates uncertainty in the fitted lifetime distribution. The main single-condition, single-fault subset contains 100 complete training engines and 100 test engines. Its empirical mean lifetime was 206.31 cycles, and the Weibull model produced a shape parameter of 4.409 and a scale parameter of 225.026 cycles, indicating wear-out-dominated degradation. Estimated reliability declined from 0.846 at 150 cycles to 0.552 at 200 cycles. The prediction model achieved a root mean square error (RMSE) of 22.545 cycles in the main subset, with similar performance in the secondary robustness subsets. The findings show that probabilistic reliability modeling gives decision-makers more informative maintenance evidence than deterministic point estimates because it links degradation, failure probability, uncertainty intervals, and operational risk thresholds in one interpretable structure.