The monitoring of multivariate systems that exhibit non-Gaussian behavior is addressed. Existing work advocates the use of independent component analysis (ICA) to extract the underlying non-Gaussian data structure. Since some of the source signals may be Gaussian, the use of principal component analysis (PCA) is proposed to capture the Gaussian and non-Gaussian source signals. A subsequent application of ICA then allows the extraction of non-Gaussian components from the retained principal components (PCs). A further contribution is the utilization of a support vector data description to determine a confidence limit for the non-Gaussian components. Finally, a statistical test is developed for determining how many non-Gaussian components are encapsulated within the retained PCs, and associated monitoring statistics are defined. The utility of the proposed scheme is demonstrated by a simulation example, and the analysis of recorded data from an industrial melter. (C) 2008 American Institute of Chemical Engineers.