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Extreme value predictions of the roll motion of ships are considered within the framework of the First Order Reliability Method focusing on the applicability of the Poisson assumption for the peak value statistics. The examples considered are a ship rolling in dead sea condition under the combined action of waves and wind and a ship experiences parametric rolling.

The international Maritime Organization (IMO) Weather Criterion has proven to be the governing stability criteria regarding minimum metacentric height for e.g., small ferries and large passenger ships. The formulation of the Weather Criterion is based on some empirical relations derived many years ago for vessels not necessarily representative for current new buildings with large superstructures. Thus, it seems reasonable to investigate the possibility of capsizing in beam sea under the joint action of waves and wind using direct time domain simulations. This has already been done in several studies. Here, it is combined with the first order reliability method (FORM) to define possible combined critical wave and wind scenarios leading to capsize and corresponding probability of capsize. The FORM results for a fictitious vessel are compared with Monte Carlo simulations, and good agreement is found at a much lesser computational effort. Finally, the results for an existing small ferry will be discussed in the light of the current weather criterion. 1. Introduction Recently, the International Maritime Organization (IMO) has initiated a thorough revision of the intact stability rules in the framework of goal-based design, e.g., Peters et al. (2013). Several draft guidelines have been issued, e.g., SDC 1/INF.8 (IMO 2013) discussing in details the requirements for the hydrodynamic software to be applied including qualitative and quantitative assessment procedures. The focus so far has been mostly on failure modes related to the change of righting lever in waves, notably parametric rolling and pure loss of stability, whereas the dead ship behavior in beam sea still is based on the existing Weather Criterion issued by IMO (1985) as Resolution A.562. This criterion is based to a large extent on model tests of older hull forms and does not provide any probability of capsize for a given vessel, just a pass/no pass result. Furthermore, the wave environment is not explicitly specified in the criterion thus leading to the same requirement whether the ship is sailing in restricted areas or not. A very detailed and precise description of the drawbacks in the IMO Weather Criterion, as applied to modern ships, is given in Bulian and Francescutto (2004). In a recent study by Tompuri et al. (2015), a detailed investigation on application of the second generation intact stability criteria has been done. However, the criterion for dead ship condition is excluded from this thorough study because the criterion is thought to be still in the early phase of development.

Previous research has shown that the First Order Reliability Method (FORM) can be an efficient method for estimation of outcrossing rates and extreme value statistics for stationary stochastic processes. This is so also for bifurcation type of processes like parametric roll of ships. The present paper discusses this solution procedure with a focus on the computational efficiency of FORM as compared with Monte Carlo Simulation (MCS).

The IMO Weather Criterion has proven to be the governing stability criteria regarding minimum GM for e.g. small ferries and large passenger ships. The formulation of the Weather Criterion is based on some empirical relations derived many years ago for vessels not necessary representative for current new buildings with large superstructures. Thus it seems rea-sonable to investigate the possibility of capsizing in beam sea under the joint action of waves and wind using direct time domain simulations. This has already been done in several studies. Here it is combined with the First Order Reliability Method to define possible combined critical wave and wind scenarios leading to capsize and corresponding probability of capsize. The results for a fictitious vessel are compared with Monte Carlo simulation and good agreement is found at a much lesser computational effort. Finally, the results for a large container vessel and a small ferry will be discussed in the light of the current weather criterion.