Multivariate SPC for batch processes

The batch process is an efficient production procedure but poses a challenge for online monitoring due to multivariate and time series characteristics. Multivariate principal component analysis (MPCA) has been applied to historical data from industrial batch processes as a precursor to process monitoring. Online monitoring is accomplished by computing and plotting the squared prediction error (SPE) derived from MPCA models. Online monitoring of batch processes by MPCA, however, is not straightforward. Using MPCA requires preliminary work such as transforming the structure of sample batch data, determination of unknown parameters and prediction of unobserved data values. The most problematic part of these preliminary tasks is determining the time period of intervention, k*, for collecting online batch information. This determination of k* is a critical weakness of MPCA because any actual signal information after k* is not contained in the collected online batch data.; To develop appropriate guidelines for using MPCA with batch processes, twelve different schemes are used for generating sample batch data. Each scheme provides batch data with unique multivariate and time series characteristics. In particular, different combinations of models are used for generating a mean profile and various strengths of cross correlation and serial correlation used in the model error component. To evaluate the performance of the SPE charts, two different sizes of mean shifts are considered for three different time periods. The T2 control chart is constructed as an alternative method. The performance of the T2 control chart is compared to SPE control chart performance.; The results show the performance of the SPE chart is critically affected by the time period of the mean shift and k* while the T2 chart is primarily affected by the size of the mean shift and the autocorrelation structure of the error terms in the underlying model. Based on comparisons for the designed cases, the T2 chart performance is superior to that of the SPE chart for the sample batch data characteristics considered in this study. The guidelines developed for monitoring batch processes recommend using the T2 chart for online monitoring.