Robotic machining is a relatively new and promising technology that aims to substitute the conventional approach of Computer Numeric Control machine tools. Due to the low positional accuracy and variable stiffness of the industrial robots, the machining operations performed by robotic systems are subject to variations in the quality of the finished product. The main focus of this work is to provide a means of improving the performance of a robotic machining process by the use of in-process monitoring of key process variables that directly influence the quality of the machined part. To this end, an intelligent monitoring system is designed, which uses sensor signals collected during machining to predict the amount of errors that the robotic system introduces into the manufacturing process in terms of imperfections of the finished product. A multi-step learning procedure that allows training of process models to take place during normal operation of the process is proposed. Moreover, applying an iterative probabilistic approach, these models are able to estimate, given the current training dataset, whether the prediction is likely to be correct and further training data is requested if necessary. The proposed monitoring system was tested in a robotic countersinking experiment for the in-process prediction of the countersink depth-of-cut and the results showed good ability of the models to provide accurate and reliable predictions.