This paper presents the application of a Bayesian nonparametric time-series model to process monitoring and fault classification for industrial robotic tasks. By means of an alignment task performed with a real robot, we show how the proposed approach allows to learn a set of sensor signature models encoding the spatial and temporal correlations among wrench measurements recorded during a number of successful task executions. Using these models, it is possible to detect continuously and on-line deviations from the expected sensor readings. Separate models are learned for a set of possible error scenarios involving a human modifying the workspace configuration. These non-nominal task executions are correctly detected and classified with an on-line algorithm, which opens the possibility for the development of error-specific recovery strategies. Our work is complementary to previous approaches in robotics, where process monitors based on probabilistic models, but limited to contact events, were developed for control purposes. Instead, in this paper we focus on capturing dynamic models of sensor signatures throughout the whole task, therefore allowing continuous monitoring and extending the system ability to interpret and react to errors.