ON THE ECONOMIC DESIGN OF MULTIVARIATE CONTROL CHARTS

ABSTRACT

It is an increasingly common practice to monitor several related quality characteristics of a product or process using a multivariate control chart procedure. Several types of multivariate control charts, including Hotelling's χ ² and T ² control charts, have been developed in attempts to improve monitoring by using the correlation structure that exists between quality characteristics. The purpose of this paper is to summarize the assumptions made regarding the out-of-control process shift in the economic design of multivariate control charts and to address their consequences. We study the average run length (ARL) properties of the χ ² control chart using a numerical example and show that this chart can perform ineffectively under the assumed out-of-control conditions when designed using the economic approach. Following Healy,[1] we offer an alternative procedure that has improved ARL properties and overall performance. These results can be important to researchers and practitioners who are interested in using the economic design of multivariate control procedures.

Keywords:

• Statistical process control
• Hotelling's χ² control chart
• Cumulative sum (CUSUM) chart
• Average run length

Acknowledgments