Probabilistic Prognostics for Power Electronic Devices: } \address{ A Comparative Study of Monte Carlo and Latin Hypercube Sampling for Uncertainty-Aware RUL Estimation and Cost-Optimal Maintenance

Prognostics and Health Management (PHM) of power electronic devices is essential for ensuring reliability and enabling cost-effective maintenance in safety-critical applications such as electric vehicles (EVs) and energy conversion systems. In insulated-gate bipolar transistors (IGBTs), collector-emitter voltage (V_{C E}) degradation serves as a critical health indicator, as its progressive increase precedes catastrophic failure. This paper presents a comprehensive probabilistic prognostics framework that integrates statistical degradation modeling, uncertaintyaware Remaining Useful Life (RUL) estimation, probability-of-failure (PoF) assessment, hazard rate analysis, and cost-optimal maintenance decision-making. The failure threshold is defined as the maximum observed degradation voltage obtained from accelerated multi-device experimental datasets. Degradation rates are modeled using a normal distribution, and uncertainty propagation is performed using both Monte Carlo (MC) sampling and Latin Hypercube Sampling (LHS) techniques. A detailed comparative analysis evaluates convergence behavior, computational efficiency, and statistical consistency between MC ( 5000 samples) and LHS (500 samples). Results derived from experimental degradation data demonstrate a monotonic decrease in RUL as the voltage margin to failure reduces, with median RUL values and confidence intervals showing strong agreement between the two sampling strategies. Convergence studies reveal that LHS achieves statistical stability at significantly lower sample sizes, while computational timing indicates approximately 30−40 % faster execution compared to MC sampling. Probability-of-failure analysis indicates rapid risk escalation beyond 60 seconds at V_{C E}=3.5 V, and hazard rate estimation exhibits an increasing failure rate characteristic of wear-out mechanisms. Cost-optimal maintenance analysis further shows that preventive maintenance decisions are economically justified near critical degradation states and remain robust across varying failure cost ratios. The results demonstrate that Latin Hypercube Sampling provides superior sampling efficiency without compromising predictive accuracy, making it particularly suitable for real-time prognostics and risk-informed maintenance decision support in power electronic systems.

Keywords: Prognostics and Health Management, Remaining Useful Life, Monte Carlo Simulation, Latin Hypercube Sampling, Power Electronics Reliability, Probability of Failure, Hazard Rate, Maintenance Optimization, IGBT.