Applying Hotelling's T2 Statistic to Batch Processes

Abstract

In this paper we show the usefulness of Hotelling's T2 statistic for monitoring batch processes in both Phase I and Phase II operations. Discussions of necessary adaptations, such as in the formulas for computing the statistic and its distribution, are included. In a Phase I operation, where the focus is on detecting and removing outliers, consideration is given to batch processes where the batch observations are taken from either a common multivariate normal distribution or a series of multivariate normal distributions with different mean vectors. In a Phase II operation, where the monitoring of future observations is of primary concern, emphasis is placed on the application of the T2 statistic using a known or estimated in-control mean vector. A variety of data sets taken from different types of industrial batch processes are used to illustrate these techniques.