This project develops and validates a computational method for estimating time-dependent structural failure probabilities and their first- and second-order sensitivities to uncertain parameters. The method combines reliability analysis, optimization, and higher-order probability approximations. GPU-accelerated Monte Carlo simulations will provide reference results for structural, vibration, and degradation examples. Large sample sets, variance-reduction methods, and independent replications will be used to quantify statistical uncertainty and verify the accuracy of the proposed method. The project will deliver a reproducible framework for identifying parameters with the strongest linear and nonlinear influence on structural safety, supporting uncertainty quantification and reliability-based engineering design. During the six-month project, the work will deliver a reproducible framework for identifying parameters with the strongest linear and nonlinear influence on time-dependent structural safety.