Multiway principal component analysis (MPCA) and multiway partial-least squares (MPLS) are well-established methods for the analysis of historical data from batch processes, and for monitoring the progress of new batches. Direct measurements made on prior batches can also be incorporated into the analysis by monitoring with multiblock methods. An extension of the multiblock MPCA/MPLS approach is introduced to explicitly incorporate batch-to-batch trajectory information summarized by the scores of previous batches, while keeping all the advantages and monitoring statistics of the traditional
IntroductionBatch and semibatch processes are the main production devices in pharmaceuticals, paint-coating, adhesive, and in most of the specialty-chemical industries. However, such processes suffer from variations in initial charge, operating conditions, and impurity concentrations in raw materials. To allow for more consistent operation and final product quality, control and monitoring schemes have been implemented around such processes. The use of multivariate statistical process control methods based on multiway principal component analysis (MPCA), and multiway partial-least squares (MPLS), and their associated monitoring statistics have been shown to be successful with industrial data for both the analysis of completed batches, and for the on-line monitoring of new batches (MacGregor and Nomikos, 1992; MacGregor, 1994, 1995a,b;MacGregor and Kourti, 1995;. The success of such methods is largely because of the fact that the type of normal operating data necessary for building the required model is always readily available, and that the statistical control charts used for analysis and monitoring are easily developed from these data. One of the main characteristics of such methods is that the evolving within-batch measurement trajectories are projected into low dimensional latent variable spaces that summarize all the relevant information, and allow monitoring charts to be built in the reduced spaces where visually inspection and interpretation are easier.Multiway PCA and PLS for the analysis, monitoring, and prediction of final product quality in batch processes were first introduced by Nomikos and MacGregor (1992, 1995a. They illustrated the detection of abnormal batches with several criteria, such as the Q statistic (also known as square prediction error (SPE) or distance to the model in the X space (DMODX)), the instantaneous SPE (for on-line monitoring) and the PCA or PLS score plots or equivalently Hotelling's T 2 statistic. modes of operation, and prior processing conditions into the analysis and monitoring of batch processes. These multiblock methods allow one to incorporate any measured variable from prior batches into the analysis and monitoring schemes. In this article, we propose a variation of these multiblock methods to incorporate the PCA or PLS scores from prior batches.Recently, Dorsey and Lee (2001) proposed a monitoring framework based on state-space models that purported to consider batch-to-batch vari...