To make a better decision about when to shutdown a nuclear power plant, we build a decision model using influence diagrams. We proceed the analysis adopting a bayesian approach. Firstly, an accident arrival rate is assumed to be known and this assumption is relaxed later. We perform our analysis on the cases of exponential time to accidents, and gamma distribution for the arrival rate. An optimal shutdown time is obtained considering the trade-off between the costs incurred by an accident due to late shutdown and the possible loss of revenues due to the early shutdown. We also derive the upper bound of the failure rate where we may operate the plant.