To better utilize historical process data from faulty operations, supervised learning methods, such as Fisher discriminant analysis (FDA), have been adopted in process monitoring. However, such methods can only separate known faults from normal operations, and they have no means to deal with unknown faults. In addition, most of these methods are not designed for handling non-Gaussian distributed data; however, non-Gaussianity is frequently observed in industrial processes. In this paper, a hybrid multivariate approach named mixture discriminant monitoring (MDM) was proposed, in which supervised learning and statistical process control (SPC) charting techniques are integrated. MDM is capable of solving both of the above problems simultaneously during online process monitoring. Then, for known faults, a root-cause diagnosis can be automatically achieved, while for unknown faults, abnormal variables can be isolated through missing variable analysis. MDM was used on the benchmark Tennessee Eastman (TE) process, and the results showed the capability of the proposed approach.