Multivariate statistical control of batch processes with variable duration

Batch processes are widely used in several industrial sectors. In those processes performance is described by variables which are monitored as the batch progresses, typically using control charts based on multiway principal components analysis (CCPs). Here we investigate the special case of batches with variable duration, which cannot be directly monitored using CCPs. We propose a new quality control strategy for monitoring such batches which are not aligned or time warped with respect to their trajectories, but are rather completed using an alternative scheme such that all information on the variability in batch profiles along the time axis is preserved. The completed data set is reduced using the Statis method and monitoring of batch performance is accomplished directly on principal plane graphs, from which non-parametric control charts are derived.