The concept of conditional stochastic processes provides a powerful tool for evaluation and estimation of wave loads on ships and offshore structures. This article first considers conditional waves with a focus on critical wave episodes. Then the inherent uncertainty in the results is illustrated with an application where measured wave responses are used to predict the future variation in the responses within the next 5–30 seconds. The main part of the article is devoted to the application of the First Order Reliability Method for derivation of critical wave episodes for different nonlinear wave-induced responses. A coupling with Monte Carlo simulations is shown to be able to give uniform accuracy for all exceedance levels with moderate computational time, even for rather complex nonlinear problems. The procedure is illustrated by examples dealing with overturning of jackup rigs, parametric rolling of ships, and slamming and whipping vibrations.

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