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