The aim of this paper is to detect the incipient anomalies in a ultraprecision machining (UPM) process by integrating multiple in situ sensor signals. To realize this aim we forward a Bayesian non-parametric Dirichlet Process (DP) decision-making approach for real-time monitoring of UPM process using the data gathered from multiple, heterogeneous sensors. The sensor signals are acquired under different experimental conditions from a UPM setup instrumented with a heterogeneous sensing array consisting of miniature tri-axis force, tri-axis vibration, and acoustic emission (AE) sensors mounted in close proximity to the cutting tool. We track the prominent nonlinear and non-Gaussian signal patterns evident in the experimentally acquired sensor data using an adaptive non-parametric DP modeling technique. A cohesive decision concerning the UPM process condition is made by developing a new supervised learning method, which integrates the DP-model state estimates with an evidence theoretic sensor data fusion method. Using this combined DP-evidence theoretic approach, UPM process drifts and anomalies, such as sudden changes in the depth of cut, feed rate, and spindle speed that deleteriously affect surface finish, and hence cause high yield losses, are detected and classified with over 90% accuracy (with % standard deviation). We compared these results with popular classification techniques, e.g., naive Bayes, self-organizing map, and support vector machine; these conventional techniques had classification accuracy in the range of 83%-88%. Consequently, this research makes the following practically relevant contributions: 1) real-time identification of the incipient UPM process anomalies from multiple sensors and 2) prescribing the optimal subset of sensors signals contingent to particular process anomalies.