Statistical process control charts for batch operations based on independent component analysis

A significant step forward in recent years, in regard to multivariate statistical process control (MSPC) for operational condition monitoring and fault diagnosis, has been the introduction of principal component analysis (PCA) for the compression of process data. An alternative technique that has been studied more recently for data compression is independent component analysis (ICA). Published work has shown that, in some applications of statistical process monitoring, ICA-based methods have exhibited advantages over those based on other data compression techniques. However, it is inappropriate to use ICA in the same way as PCA to derive Hotelling's T-2 and SPE (squared prediction error) charts, because the independent components are separated by maximizing their non-Gaussianity, whereas the satisfying Gaussian distribution is the basis of T-2 and SPE monitoring charts, as well as univariate statistical process control (SPC) charts. In this paper, we propose a new method for deriving SPC charts based on ICA, which can overcome the aforementioned limitation of non-Gaussianity of the independent components (ICs). The method generates a smaller number of variables, i.e., ICs to monitor, each with time-varying upper and lower control SPC limits, and, therefore, can be used to monitor the evolution of a batch run from one time point to another. The method is illustrated in detail by reference to a simulated semibatch polymerization reactor. To test its capability for generalization, it is also applied to a data set that has been collected from industry and proved to be able to detect all seven faults in a straightforward way. A third case study that was studied in the literature for batch statistical monitoring is used in this work, to compare the performance of the current approach with that of other methods. It proves that the new approach can detect the faults earlier than a similar PCA-based method, the PCA-based T-2 approach, and the SPE approach. Comparison with a recently proposed multi-way ICA method in the literature was also made.