The shipbuilding industry is characterized by high-risk business activities; therefore, caution should be taken in its operational processes. From upstream to downstream, the shipbuilding industry depends on other industries. In this study, a risk assessment was conducted on the construction of new vessels using the Bayesian network approach; accordingly, the risk assessment was carried out using a probabilistic value at risk (VaR). The study was carried out by PT PAL Indonesia in association with the construction of a new tanker ship (building production codes M271 and M272). An analysis was conducted on three main components of new vessel construction—design components, material and production components, and sub-components of the previous two components. From the study, we could conclude that the probability of delay for new vessel construction caused by design delay is 0.05; the probability of delay caused by material delay is 0.65; and the probability of delay caused by production delay is 0.3. For delays caused by design factors, a yard plan is the sub-component that contributes predominantly to delays (i.e., probability of 0.3). For delays caused by material factors, the sub-component with the greatest impact is hull and machinery outfitting, with a probability of 0.3. For delays caused by production factors, the sub-component with the biggest impact is hull construction, with a probability of 0.39. Thus, we could conclude that a project delay would occur if the material component and the hull construction sub-components were not handled properly.