In this paper, we address the problem of detecting anomalies in the reaction wheel assemblies (RWAs) of a satellite. These anomalies can alert of an impending failure in a RWA, and effective detection would allow to take preventive action. To this end, we propose a novel algorithm that detects and categorizes anomalies in the friction profile of an RWA, where the profile relates spin rate to measured friction torque. The algorithm, developed in a probabilistic framework, runs in real-time and has a tunable false positive rate as a parameter. The performance of the proposed method is thoroughly tested in a number of numerical experiments, with different anomalies of varying severity.