In this study, the accuracy of the artificial neural network (ANN) was assessed considering the uncertainties associated with the randomness of the data and the lack of learning. The Monte-Carlo algorithm was applied to simulate the randomness of the input variables and evaluate the output distribution. It has been shown that under certain conditions, the GUM framework for uncertainty evaluation may completely fail. The ANN modeling technique can be used as an alternative method for estimating the expectation value and evaluating the associated uncertainty. Furthermore, unlike the GUM and Monte-Carlo frameworks, the ANN models do not require mathematical expressions between the input and output variables. On the other hand, owing to the uncertainty associated with the lack of learning, the ANN model may produce unrealistic results, even if a global minimum is approached. This behavior is explained by Bayesian theory which assumes that the output values generated by various runs are normally distributed at each target. This may lead to an unrealistic output when the overall distribution of the target values has a different distribution than that presumed by Bayesian theory. To minimize this drawback, the ANN model output should be calculated from sufficiently large repeated runs with new starting values of the weights and biases.