Industrial experiences with multivariate statistical analysis of batch process data

The data collected from a batch process over time from multiple sensors can be arranged in a matrix of J-variables × K-time points. Data collected on multiple batches can be arranged in a cube of I-batches × J-variables × K-time points. The analysis of a cube of data can be performed by unfolding in two different ways, batch unfolding giving an I × JK data matrix or observation unfolding resulting in an IK × J data matrix, followed by PCA. The data can also be analyzed directly using three-way methods such as PARAFAC or Tucker3. In the literature there is no clear agreement as to the most effective approach for the analysis of batch data.This paper makes detailed comparisons between the two unfolding approaches and the Tucker3 method. Batch data from a fermentation process at The Dow Chemical Company San Diego facility is used for this study. The three methods were found to be complementary to each other and a well-trained chemometrician/practitioner will find all three methods to be useful for batch data analysis. The batch unfolding MPCA is more sensitive to the overall batch variation while the observation unfolding MPLS is more sensitive to the localized batch variation. The Tucker3 method is in good balance in terms of detecting both variations.