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The main aim of this paper is to propose a probabilistic short-circuit approach to generate the probability distributions of the System Average RMS Variation Index (SARFI) index. The proposed methodology is based on the combination of the admittance summation method in phase coordinates with the Monte Carlo method. This new approach has been tested in a feeder belonging to an electricity distribution company in the Northeast of Brazil to generate the probability distributions of the SARFI index. The tests results demonstrated that the proposed model is a powerful tool to stochastic prediction of voltage sags.