In this paper we present a statistical approach to the estimation of the time in which an operating gear will achieve the critical stage. The approach relies on measured vibration signals. From these signals features are extracted first and then their evolution over time is predicted. This is accomplished using a dynamic model that relates hidden degradation phenomena with measured outputs. The Expectation-Maximization algorithm is used to estimate the parameters of the underlying state-space model on-line. Time to reach safety alarm threshold is determined by making the prediction using the estimated linear model. The results obtained on a pilot test bed are presented.