The Synthetic Control Chart Based on Two Sample Variances for Monitoring the Covariance Matrix

Abstract

In this article, we propose a new statistic to control the covariance matrix of bivariate processes. This new statistic is based on the sample variances of the two quality characteristics, in short VMAX statistic. The points plotted on the chart correspond to the maximum of the values of these two variances. The reasons to consider the VMAX statistic instead of the generalized variance vertical bar S vertical bar are its faster detection of process changes and its better diagnostic feature, that is, with the VMAX statistic it is easier to identify the out-of-control variable. We study the synthetic chart based on the VMAX statistic. The proposed chart is always more efficient than the chart based on the generalized variance vertical bar S vertical bar. An example is presented to illustrate the application of the proposed chart. Copyright (C) 2008 John Wiley & Sons, Ltd.