MULTIVARIATE STATISTICAL PROCESS CONTROL FOR CORRELATION MATRICES

Measures of dispersion in the form of covariance control charts are the multivariate analog to the univariate R-chart, and are used in conjunction with multivariate location charts such as the Hotelling T2 chart, much as the R-chart is the companion to the univariate X-bar chart. Significantly more research has been directed towards location measures, but three multivariate statistics (|S|, Wi, and G) have been developed to measure dispersion. This research explores the correlation component of the covariance statistics and demonstrates that, in many cases, the contribution of correlation is less significant than originally believed, but also offers suggestions for how to implement a correlation control chart when this is the variable of primary interest.This research mathematically analyzes the potential use of the three covariance statistics (|S|, Wi, and G), modified for the special case of correlation. A simulation study is then performed to characterize the behavior of the two modified statistics that are found to be feasible. Parameters varied include the sample size (n), number of quality characteristics (p), the variance, and the number of correlation matrix entries that are perturbed. The performance and utility of the front-running correlation (modified Wi) statistic is then examined by comparison to similarly classed statistics and by trials with real and simulated data sets, respectively. Recommendations for the development of correlation control charts are presented, an outgrowth of which is the understanding that correlation often does not have a large effect on the dispersion measure in most cases