Performance monitoring of a multi-product semi-batch process

Traditionally principal components analysis (PCA) has been viewed as a single-population method. In particular in multivariate sta- tistical process control, PCA has been used to monitor single product production. An extension to principal components analysis is presented which enables the simultaneous monitoring of a number of product grades or recipes. The method is based upon the existence of a common eigenvector subspace for the sample variance±covariancematrices of the individual products. The pooled sample variance± covariance matrix of the individual products is then used to estimate the principal component loadings of the multi-group model. The methodology is applied to a semi-discrete industrial batch process manufacturing a number of recipes. The industrial application illus- trates that the detection and diagnostic capabilities of the multi-groupmodel are comparable to those achieved by developing a separate statistical representation for the individual products.