This paper reviews advances over the last decade in the field of computational structural reliability modelling. The discussion is focused on problems of time-variant/time-invariant reliability at the component level. Three broad classes of problems are considered: (a) time-invariant reliability problems involving static problems, (b) problems of time-variant reliability analysis for deterministically parametered dynamical systems driven by random excitations, and (c) time-variant reliability analysis of randomly parametered dynamical systems subjected to random excitations. Four classes of approaches are discussed: (a) analytical methods based on first/second order reliability analyses (for time-invariant reliability analysis) and level crossing based approaches for time-variant reliability problems, (b) methods based on importance sampling strategies (including the Girsanov transformation based method for dynamical systems), (c) particle and trajectory splitting based methods, and (d) methods that employ machine learning based tools (primarily involving development of surrogate models and active learning strategies) in tackling reliability problems. The focus of the discussions is on methodological advances, and questions related to specific applications are not addressed. The review presents critical discussions on the relative merits of alternative approaches (in terms of computational efficiency, accuracy, scalability, treatment of rare events, ability to handle geometric complexities linked to failure surface, and suitability for high-dimensional problems) and identifies several directions for future research.

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