The damage condition of ships can be quantified by considering the damage penetration area; the larger the penetration area, the more severe the damage condition of the ship. Additionally, according to [21], the repair costs for the struck ships are related to the damage penetration area. It is reasonable to define the damage state of the collided ships based on damage penetration area associated with specific probabilistic damage condition. In this paper, the probability of a damaged ship being in a specific damage state is expressed as