Informative score-loading-contribution plots for multi-response process monitoring

The projection based multivariate data methods of principal component regression (PCR) and partial least squares regression (PLSR) are well established in the field of process monitoring. Use of score and loading plots for visualization is, however, complicated when many components are required for good predictions, and the information is therefore often compressed into less informative T2 and contribution plots. The score information may, however, be further compressed by projection onto subspaces spanned by the vectors of prediction coefficients for the response variables. This is especially attractive in the case of two response variables, i.e. when the model reduction results in a single score-loading biplot. Contribution vectors for the process variables, as well as a confidence ellipse, may also be included in such a plot. As illustrated in an industrial data example, such a score-loading-contribution plot provides means of both failure detection and fault diagnosis.