Multivariate EWMA control charts using individual observations for process mean and variance monitoring and diagnosis

Abstract

Most multivariate control charts in the literature are designed to detect either mean or variation shifts rather than both. A simultaneous use of the Hotelling T ² and |S| control charts has been proposed but the Hotelling T ² reacts to mean shifts, dispersion changes, and changes of correlations among responses. The combination of two multivariate control charts into one chart sometimes loses the ability to provide detailed diagnostic information when a process is out-of-control. In this research a new multivariate control chart procedure based on exponentially weighted moving average (EWMA) statistics is proposed to monitor process mean and variance simultaneously to identify proper sources of variations. Two multivariate EWMA control charts using individual observations are proposed to achieve a quick detection of mean or variance shifts or both. Simulation studies show that the proposed charts are capable of identifying appropriate types of shifts in terms of correct detection percentages. A manufacturing example is used to demonstrate how the proposed charts can be properly set-up based on average run length values via simulations. In addition, correct detection rates of the proposed charts are explored.

Keywords:

• Hotelling T ²
• EWMA
• Multivariate control charts
• Statistical process control

Acknowledgments

The authors would like to thank the editor and two anonymous referees for their constructive feedbacks that lead to better presentation of this article. This research is based on Dr. Zhang's thesis while he was a graduate student at IMSE Department, Kansas State University. He was partially supported by Kansas Department of Transportation.