Failure rate is an important parameter in the reliability study of power systems. Failure rate of distribution feeders is usually considered as a constant parameter in power distribution systems study however in fact, it is a variable parameter which is dependent on various internal and external factors. The historical and statistic data is used to predict the variable failure rate. In this paper, the vegetation-related variable failure rate of overhead distribution feeders is considered for analysis and prediction. Whereas the collected statistic data usually contains practical errors and noises, here the Factor Analysis is used for data mining and removing the outliers. Then, a multi-layer artificial neural network is used to predict the failure rate. Moreover, the neural network is used to analyze the input data. Case studies of a typical 32-feeder distribution network show that the factor analysis and neural network methods emphasize their results. The proposed method can be implemented to reduce complexity, remove the outliers and increase reliability of the prediction.