Due to the increasing size of offshore wind turbines, the jack-up vessels and cranes installing them need to increase in size. The increase in length of the crane boom results in an increase of the dynamic response of the crane. This increase in response results in higher loads in the crane. The magnitude of the higher loads are unknown and not yet accounted for in crane design. To get a better insight in the dynamic response of the crane and higher loads, a probabilistic model is developed to quantify the annual probability of the crane. To define the different crane operations, a measurement data set of crane operations is made available. From this data set, the different lifts types, exposure times and occurrences are identified. Multiple jack-up configurations are chosen with different water depth and wave heading. Next to the crane and jack-up configuration, long-term wave statistics are used for the environmental conditions, as input for the probabilistic model. Time-domain simulations are performed in a rigid multi-body analysis software, to simulate the dynamic response of the crane, due to wave induced excitations. Due to the random nature of waves, convergence of the results is researched. For this, numerous time-domain simulations with different sea-states have to be performed, this is unwanted. A methodology is developed, using the frequency domain, to limit the number of required time-domain simulations. Using the devised methodology, configurations with similar statistical description can be identified and grouped. The annual probability of failure can be calculated using the devised methodology and probabilistic model. The resulting annual probability of failure is small, much smaller than required. A sensitivity analysis is performed, it is found that the annual probability of failure depends greatly on the input of the probabilistic model. From the results and sensitivity analysis, multiple recommendations are given to decrease the sensitivity of the result. It can be said that from the devised methodology, a basis has been laid to quantify the annual probability of failure of the crane in normal operations.