In this work, the influence of the initial heeling angle on the roll motion response of a ship in random beam wave is studied.

Specifically, the path integration method is applied to solve the Fokker-Planck equation, which governs the probability properties of the stochastic differential equation for the roll motion. The probability distributions of the roll motion response can then be obtained.

The results show that the initial heeling angle has limited influence on the roll motion response spectrum, but the probability density function of the roll motion response and distribution of extreme roll motion response can be significantly influenced by the heeling angle. As a result, the safety and stability of the ship will deteriorate dramatically.

The path integration method can be effective for studying the characteristics of ship roll motion under random waves.