In chemical kinetics and batch processes K variables are measured on the batches at regular time intervals. This gives a J x K matrix for each batch (J time points times K variables). Consequently, a set of N normal batches gives a three-way matrix of dimension (N x J x K). The case when batches have different length is also discussed. In a typical industrial application of batch modelling, the purpose is to diagnose an evolving batch as normal or not, and to obtain indications of variables that together behave abnormally in batch process upsets. Other applications giving the same form of data include pharmaco-kinetics, clinical and pharmacological trials where patients (or mice) are followed over time, material stability testing and other kinetic investigations. A new approach to the multivariate modelling of three-way kinetic and batch process data is presented. This approach is based on an initial PLS analysis of the ((N x J) x K) unfolded matrix ((batch x time) x variables) with 'local time' used as a single y-variable. This is followed by a simple statistical analysis of the resulting scores and results in multivariate control charts suitable for monitoring the kinetics of new experiments or batches. 'Upsets' are effectively diagnosed in these charts, and variables contributing to the upsets are indicated in contribution plots. In addition, the degree of 'maturity' of the batch can be as predicted vs. observed local time. The analysis of batch data with respect to various questions is discussed with respect to typical objectives, overview and summary, classification, and quantitative modelling. This is illustrated by an industrial example of yeast production. (C) 1998 Elsevier Science B.V. All rights reserved.

Multivariate statistical process control (MSPC) is applied to an electrolysis process. The process produces extremely pure copper, and to monitor its quality the levels of eight metal impurities were recorded twice a day. These quality data are analysed adopting an (1) 'intuitive' univariate approach, and (2) with multivariate techniques. It is demonstrated that the univariate analysis gives confusing results with regards to outlier detection, while the multivariate approach identifies two types of outliers. Moreover, it is shown how the results from the multivariate principal component analysis (PCA) method can be displayed graphically in multivariate control charts, Multivariate Shewhart, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are used and compared. Also, an informationally powerful control chart, the simultaneous scores monitoring and residual tracking (SMART) chart, is introduced and used. (C) 1998 Elsevier Science B.V. All rights reserved.

A multivariate technique (projection to latent structures, PLS) was used for modelling the production of an amino acid, lysine. Lysine fermentations were divided into three growth phases. Separate PLS-models were constructed for each of these phases. We demonstrate that sequential PLS-models can be used for fed-batch fermentation modelling.

Multivariate time series analysis is applied to understand and model the dynamics of an electrolytic process manufacturing copper. Here, eight metal impurities were measured, twice daily, over a period of one year, to characterize the quality of the copper. In the data analysis, these eight variables were summarized by means of principal component analysis (PCA). Two principal component (PC) scores were sufficient to well summarize the eight measured variables (R2=0.67). Subsequently, the dynamics of these PC-scores (latent variables) were investigated using multivariate time series analysis, i.e., partial least squares (PLS) modelling of the lagged latent variables. Stochastic models of the auto-regressive moving average (ARMA) family were appropriate for both PC-scores. Hence, the dynamics of both scores make the exponentially weighted moving average (EWMA) control chart suitable for process monitoring.

Multivariate batch modelling of baker's yeast production : CAC96 - International Conference Chemometrivs in Analytical Chemistry, Tarragona