Multivariate statistical procedures for monitoring the progress of batch processes are developed. Multi-way partial least squares (MPLS) is used to extract the information from the process measurement variable trajectories that is more relevant to the final quality variables of the product. The only information needed is a historical database of past successful batches. New batches can be monitored through simple monitoring charts which are consistent with the philosophy of statistical process control. These charts monitor the batch operation and provide on-line predictions of the final product qualities. Approximate confidence intervals for the predictions from PLS models are developed. The approach is illustrated using a simulation study of a styrene-butadiene batch reactor.