A methodology that determines the optimal shutdown time of a nuclear power plant is suggested. The shutdown time is decided considering the trade off between the cost of accident and the loss of profit due to the early shutdown. We adopt the bayesian approach in manipulating the model parameter that predicts the accidents. We build decision tree models and apply dynamic programming approach to decide whether to shutdown immediately or operate one more period. The branch parameters in decision trees are updated by bayesian approach. We apply real data to this model and provide the cost of accidents that guarantees the immediate shutdown.