Monte Carlo Methods for Uncertainty and Risk Assessment: A Methodological Review Across Engineering and Applied Statistics

This paper presents a methodological review of the Monte Carlo method as a toolkit for uncertainty analysis in engineering and applied statistical problems and systems. Monte Carlo simulation has become one of the most universal stochastic tools for analyzing systems subject to variability, incomplete information, and complex probabilistic dependencies. Drawing on 24 representative studies published between 1989 and 2025, this review examines the method’s fundamental principles, typical implementation workflows, and its broad spectrum of applications from structural reliability to financial evaluation. Particular attention is given to the advantages that explain its widespread adoption—flexibility, interpretability, and robustness under nonlinear and multidimensional settings—as well as to the limitations that constrain its reliability, including slow convergence, dependence on accurate input distributions, and computational costs. The review also highlights recent methodological advances that address these issues, such as hybrid frameworks combining Monte Carlo sampling with machine learning or intelligent variance reduction. Overall, the paper provides a consolidated view of how Monte Carlo methods contribute to engineering decision support and discusses future research directions toward more efficient and integrated stochastic analysis.