The second-generation intact stability criteria of International Maritime Organization (IMO) has entered the trial period. This paper focuses on the surf-riding/ broaching stability failure mode in irregular waves. It reproduce the process of the surf-riding/broaching phenomenon through massive repeated numerical simulations with different speeds, wave directions, wave spectrum truncation ranges and metacentric heights ( GM) by adopting a six degrees of freedom (6-DoF) numerical modeling. Hilbert transform is used to calculate the instantaneous wave velocity to identify the ‘speed increase’ state, and the probability of ‘speed increase’, broaching, excessive yawing and rolling are quantitatively studied. It is found that the occurrence of ‘speed increase’ is closely related to the surf-riding, and its probability estimates increase with the increase of the ship speed. Most ships capsize after experiencing a relatively long and continuous duration of ‘speed increase’, and the wave spectrum frequency truncation has a great impact on the probability estimates of ‘speed increase’. However, the probability estimates of broaching after ‘speed increase’ increase sharply with the increase of the wave angle for the ships at the same speed. The total duration of broaching can account for 30% to 50% of the total duration of ‘speed increase’ at high speed when the wave angle reaches 30 degrees. With the increase of the ship speed, the proportion of the duration of broaching in the total time of excessive yawing gradually increases to 60% to 80%, indicating that the yawing at high speed is mainly caused by broaching. The same as the variation of the probability of broaching after ‘speed increase’, the probability estimates of excessive rolling also increases with the increase of wave angle. The quantitative probability estimates of the ‘speed increase’, broaching and excessive yawing and rolling can provide technical support for the application of the second generation intact stability criteria of IMO.