The problem of using time-varying trajectory data measured on many pro
cess variables over the finite duration of a batch process is consider
ed. Multiway principal-component analysis is used to compress the info
rmation contained in the data trajectories into low-dimensional spaces
that describe the operation of past batches. This approach facilitate
s the analysis of operational and quality-control problems in past bat
ches and allows for the development of multivariate statistical proces
s control charts for on-line monitoring of the progress of new batches
. Control limits for the proposed charts are developed using informati
on from the historical reference distribution of past successful batch
es. The method is applied to data collected from an industrial batch p
olymerization reactor.