, 2010). It can furthermore be expected that the collision damage may lead to progressive hull failure, which is not accounted for

in the model. The spilled oil volume depends on the damage opening and position above or below the waterline (Tavakoli et al., 2010), and may be expected to depend on vessel motion in waves, dynamic pressure differences due to wave action and the shape of the opening. Not all these variables are included in the BN, leading to uncertainty regarding the damage extent. The assumption that all oil in all breached tanks is spilled, is conservative, see Section 4.3.1. Metformin cell line One aspect of predictive validity concerns a behavior sensitivity test. In particular, the parameter Saracatinib supplier sensitivity of the model output in terms of oil outflow is determined for each node of the presented BN, using the sensitivity function as proposed

by Chan and Darwiche (2002): equation(25) f(z)=(c1z+c2)(c3z+c4)Here, f(z) is the output probability of interest given parameter variables z, which have the following form: equation(26) z=p(Y=yi|π)z=p(Y=yi|π)where yi is one state of a network variable Y, and π a combination of states for Y’s parent nodes. The constants ci, i = 1…4 are computed based on the model. The sensitivity value is determined based on the first derivative of the sensitivity function. Table 8 shows the maximum absolute sensitivity values of the ten most sensitive BN nodes, with variable “Oil Outflow” as output. This indicates that the oil outflow is very sensitive to the impact location, the speed of the striking ship, the struck ship mass and the impact angle. Interestingly, the presented BN model shows only very limited sensitivity to the tank arrangement. A qualitative features analysis can be made based on the accident scenarios of Table 7 and Fig. 9. Considering e.g.

scenario 1, it is seen that an impact outside the cargo area (l: [0–0.2]) almost certainly leads to no oil outflow under an oblique impact angle. If a perpendicular impact is considered, the model leads to more probable bigger spills if the impact happens near the aft cargo bulkhead. If the impact occurs in the midship area (l: [0.4–0.6]), there is a non-zero Selleck DAPT probability of no spill under oblique impact angles, but when impact angles are close to perpendicular there always is a spill. Such behavior can qualitatively be expected as under oblique angles, it is possible that the double hull is not breached whereas for the same available deformation energy under perpendicular impacts, the double hull will be breached. Similar behaviors can be derived from the considered cases of scenario 2, where it is also seen that the probabilities for larger spill volumes are larger than for scenario 1. This can also be expected as scenario 2 considers a larger product tanker than scenario 2.