It is well known from linear analyses in stochastic seaway that the mean out-crossing rate of a level r is given through the reliability index, defined as r divided by the standard deviation. Hence, the reliability index becomes inversely proportional to the significant wave height. For non-linear processes the mean out-crossing rate depends non-linearly on the response level r and a good estimate can be found using the First Order Reliability Method (FORM), see e.g. Jensen and Capul (2006). The FORM analysis also shows that the reliability index is strictly inversely proportional to the significant wave height irrespectively of the non-linearity in the system. However, the FORM analysis only gives an approximation to the mean out-crossing rate. A more exact result can be obtained by Monte Carlo simulations, but the necessary length of the time domain simulations for very low out-crossing rates might be prohibitive long. In such cases the property mentioned above for the FORM reliability index can be assumed valid in the Monte Carlo simulations making it possible to increase the out-crossing rates and thus reduced the necessary length of the time domain simulations by applying a larger significant wave height than relevant from a design point-of-view. The mean out-crossing rate thus obtained can then afterwards be scaled down to the actual significant wave height. Some previous results using this property have been presented by Tonguc and So¨ding (1986), albeit in a more empirical way. In the present paper the usefulness of this property to estimate extreme wave loads will be evaluated considering the overturning of a jack-up rig.
