Multivariate Process Variability Monitoring

Abstract

Understanding multivariate variability is a difficult task because there is no single measure that can be properly used. This article presents a new measure that features good properties. If this measure is simultaneously used with generalized variance, it will give a better understanding of multivariate variability. It can also efficiently be used for large data sets with high dimensions. Furthermore, when it is used for constructing a Shewhart-type chart to monitor multivariate variability, the resulting chart has a much better out-of-control ARL than the generalized variance chart. An example illustrates its advantage.

Keywords:

• Control chart
• Generalized variance
• Multivariate variability measure
• Vector variance

Acknowledgments

The authors are very grateful to the Editor and referees for their constructive comment and suggestions that led to improvements in the presentation of the manuscript. They also thank ir. Sutarno at Indonesian Aerospace Ltd. for providing the data and giving permission to publish the results. A part of this research is a continuation of the first author's previous research supported by the Directorate General of Higher Education (DGHE), Republic of Indonesia, through the Tenth Competitive Grant Project (Hibah Bersaing X), contract number: 12/P2IPT/DPPM/PHBL/III/2003. The first author would like to thank the DGHE for the support.