The paper presents some background for an analysis of the risk of severe parametric roll motion for a ship operating in head seas. This background includes a consideration of basic probabilistic qualities of parametric roll in head seas: ergodic qualities and distributions, since these results are necessary to establish a method of prediction of extreme values. The ship motions that generate parametric excitation, heave and pitch, have also been studied in this analysis.The post-Panamax C11 class container carrier was chosen for analysis, since a vessel of this type is known to have suffered significant damage in an incident attributed to severe parametric roll. It was shown that despite large-amplitude of motion, pitch and heave retain their ergodic qualities and normal character of distribution, while the roll motions are clearly non-ergodic and do not have a normal distribution. The analysis is built upon the numerical simulation of ship motion in head seas using Large Amplitude Motion Program (LAMP).The paper also considers the effectiveness of anti-rolling devices in mitigating parametric roll by suppressing the parametric excitation. It was shown with numerical simulation that correctly tuned U-tube type of anti-rolling tank has to potential to reduce the occurrence of parametric roll and significantly increase the stability and safety of large modern container carriers.

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The paper reviews the status of a multi-year research effort for using the split-time method to calculate the probability of ship capsizing due to broaching-to in irregular waves. This required taking steps toward extending the existing theory of surf-riding and broaching-to, from regular waves to irregular waves and applying it to numerical simulation codes of ship motions. The extension of the theory for irregular waves leads to the formulation of a spatial-temporal framework for considering surf-riding where the celerity of irregular waves must be defined. An approximate metric for the likelihood of surf-riding in irregular waves has been proposed as the distance, in the phase plane, between the instantaneous position of a ship and the stable surfriding quasi-equilibrium at that instant. Further work includes studying the properties of the surfriding phase plane in irregular waves and statistics of surf-riding occurrences. This already complex setup becomes even more complex when, the ship motions are calculated with high accuracy, by using the more consistent, in ship hydrodynamics terms, formulation. Wave excitation can no longer be separated from stiffness while radiation and diffraction forces add a hydrodynamic memory effect. Furthermore, the irregularity of realistic ocean introduces new physical qualities to the phenomenon.The challenge to include surf-riding and broaching-to into a probabilistic assessment of stability based on advanced hydrodynamic codes has been taken up by the US Office of Naval Research (ONR) project "A Probabilistic Procedure for Evaluating the Dynamic Stability and

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