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.

• Multivariate Quality Control
• Outliers
• Phase I
• Phase II

Additional information

Notes on contributors

Robert L. Mason

Dr. Mason is a Staff Analyst in the Statistical Analysis Section. He is a Fellow of ASQ.

Youn-Min Chou

Dr. Chou is a Professor in the Division of Mathematics and Statistics. She is a Fellow of ASQ.

John C. Young

Dr. Young is a Professor in the Department of Mathematics, Computer Science, and Statistics.