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The use of artificial intelligence algorithms is rapidly gaining ground in engineering applications, including safety engineering. In this paper, we investigate the possibility of using neural networks to supplement fault trees in the safety analysis for the estimation of reliability and importance metrics. For this aim, we employ data from an existing fault tree that models cruise ships blackouts to train a neural network that uses base-event probabilities as input and outputs the estimated top-event probability/frequency. This is done to reduce computational time, as the fault tree model has an extensive number of basic events and is thus computationally demanding. The information that is used as input to the Fault Tree is randomly sampled from a Sobol sequence and is used to estimate the top event probability. The resulting data cloud that corresponds to the fault tree's input-output pairs, is used to train the neural network. The two models, i.e. the probabilistic and the neural network model, are compared to each in other in terms of accuracy and computational cost correlated with the number of sampling points that is used. The Fault Tree is developed in Matlab/Simulink and the neural network in Python. For case where the Neural Network is trained using 10,000 points, a 350 times decrease in computational cost is observed compared to the fault tree model, while the mean absolute percentage error (MAPE) remains at under 15%. Based on the results, recommendations for the application and future improvement of the artificial intelligent algorithms in the specific context are made.