Rail wear is the most common defect that affects sharply curved metro rails, thus impacting their renewal periods. This article presents a stochastic model, based on a Weibull distribution, for the estimation of the renewal periods of sharply curved metro rails based on the analysis of the characteristics of rail wear. The model considers several heterogeneous factors to determine their effects on the deterioration process and is shown to be able to estimate the life expectancy of these rails in any wear state, as well as their remaining lives and renewal periods, with respect to these heterogeneous factors. The model is validated by a case study of the Beijing Metro, based on 10 years of rail wear inspection data and heterogeneous factor data of 200 sharp curves.