Loyola University Maryland

Mathematical Sciences Seminar

January 31, 2011
3PM, KH 004

A Multivariate CUSUM Chart Accommodating Prior Information About Potential Shifts

Wei Liu
University of Minnesota - Twin Cities


We consider statistical process control (SPC) for Phase II monitoring of the process mean when the process measurement is multivariate. In cases when the direction of a potential mean shift is known, Healy (1987) generalized the univariate cumulative sum (CUSUM) chart to multivariate cases, using the likelihood ratio inferences, and the generalized CUSUM chart was shown to be efficient. Other existing multivariate control charts usually do not use any prior information about the potential mean shift, making them less efficient in cases when such prior information is available. In this paper, we suggest a multivariate CUSUM chart for applications in which the mean shift direction is not completely known but it follows a prior distribution. This chart can be regarded as a compromise of Healy's CUSUM chart and other existing multivariate control charts, in terms of proper accommodation of prior information about the potential shift. Numerical studies show that it performs well in cases when such prior information is available.