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Wind turbines and their associated parts are subjected to cyclical loads, such as bending, torque, longitudinal stresses, and twisting moments. The novel spatiotemporal reliability technique described in this research is especially useful for high-dimensional structural systems that are either measured or numerically simulated during representative observational time span. As this study demonstrates, it is possible to predict risks of dynamic system failure or damage given the in situ environmental load pattern. As an engineering example for this reliability, the authors have chosen 10-MW floating wind turbines and their dynamic responses, under environmental loadings, caused by wind and waves. The aim of this study was to benchmark a state-of-the-art approach suitable for the reliable study of offshore wind turbines. Existing reliability methods do not easily cope with dynamic system high dimensionality. The advocated reliability technique enables accurate and efficient assessment of dynamic system failure probability, accounting for system nonlinearities and high dimensionality as well as cross-correlations between different system components.