The theory of batch MSPC control charts is extended and improved control charts an developed. Unfold-PCA, PARAFAC and Tucker3 models are discussed and used as a basis for these charts. The results of the different models are compared and the performance of the control charts based on these models is investigated. It is found that this performance depends on the type of fault occuring in the batch process. A strategy is provided to partition reference data describing the normal operating conditions, in order to be able to monitor a new incomplete batch on-line.