Statistical process control methods for monitoring processes with multivariate measurements in both the product quality variable space and the process variable space are considered. Traditional multivariate control charts based onχ2andT2statistics are shown to be very effective for detecting events when the multivariate space is not too large or ill-conditioned. Methods for detecting the variable(s) contributing to the out-of-control signal of the multivariate chart are suggested. Newer approaches based on principal component analysis and partial least squares are able to handle large ill-conditioned measurement spaces; they also provide diagnostics which can point to possible assignable causes for the event. The methods are illustrated on a simulated process of a high pressure low density polyethylene reactor, and examples of their application to a variety of industrial processes are referenced.