An Empirical Monte Carlo Simulation Framework for Risk Assessment and Uncertainty Quantification in Complex Stochastic Systems

Abstract

Complex stochastic systems are shaped by uncertain input variables, nonlinear interactions, and low-probability failure events that cannot be adequately summarized by deterministic point estimates. This study develops and empirically evaluates a Monte Carlo simulation framework for risk assessment and uncertainty quantification in complex stochastic systems. The main empirical case uses the Artificial Intelligence for Industries (AI4I) 2020 Predictive Maintenance Dataset, which contains 10,000 operational observations and a binary machine-failure outcome. A calibrated random-forest risk model was trained on physical operating variables and then embedded within a Monte Carlo procedure using 100,000 stochastic scenarios generated by empirical resampling with controlled perturbation. The proposed framework estimates expected failure probability, uncertainty intervals, tail-risk indicators, risk-category shares, and sensitivity patterns. The main model achieved strong discrimination on the test set, with an area under the receiver operating characteristic curve (ROC-AUC) of 0.970, average precision of 0.744, and a Brier score of 0.015. The observed failure rate was 3.39%, while the simulated mean failure probability was 3.57%. Monte Carlo outputs showed that most scenarios were low risk, but 6.08% of scenarios exceeded a 10% failure-probability threshold, and the 95th-percentile risk index reached 19.21. A secondary credit-risk robustness case using 30,000 observations confirmed that the same simulation logic can be transferred to a financial default setting. The study contributes a transparent empirical framework that links stochastic inputs, calibrated risk prediction, tail-risk estimation, and decision-oriented interpretation of uncertainty.