The presented thesis contributes to the structural reliability problem by presenting a novel approach that enables for identification of stochastic oscillatory processes as a critical input for given mechanical models. The proposed method is based on a graphical representation of such processes utilizing state of the art image processing and pattern recognition techniques, leading to a set of finite rules that consistently identifies those realizations of stochastic processes that would lead to a critical response of a given mechanical model. To examine the validity of the suggested method, large sets of realizations of artificial non-stationary processes were generated from known models, several criteria for critical response were formulated and the results were statistically evaluated. Further, another important aspect relevant to the structural reliability problem, the life cycle civil engineering facing a growing number of deteriorating infrastructure and requesting an objective and rational performance quantification method, was elaborated. On a particular example, strategies for robustness-based performance assessment using non-linear modelling and series of artificially generated deterioration scenarios were discussed together with relevant reliability-based quantities and performance indicators in relation to structural damage. As a result, a methodology for analyzing the damage-based robustness margins of bridge systems under traffic loading was presented. As a whole, the thesis offers an evaluative perspective on an important aspects of quantified environmental hazards, the computational analysis of randomness and feasible solution strategies.