Economic and Economic-Statistical Designs of Multivariate Coefficient of Variation Chart

Abstract

From the economic perspective, cost minimization is an important part of Statistical Process Control (SPC). The conventional approach in SPC focuses on monitoring the process mean and variance for possible shifts. In some processes, such as clinical and financial investments, the process mean and variance are not independent of one another. Thus, a separate monitoring of the mean and variance using two different control charts is not meaningful. Therefore, the coefficient of variation chart that measures the ratio of the process variance to the mean needs to be employed. In multivariate SPC, the quality characteristics that jointly control the process quality are correlated. Thus, the multivariate coefficient of variation (MCV) chart is used in process monitoring to monitor the process MCV. This work studies the economic and economic-statistical designs of the MCV chart. Optimal parameters that minimize the cost function of the MCV chart are computed. Furthermore, it is shown that adding statistical constraints to the economic design of the MCV chart improves the chart’s statistical performance with only a minimal increase in cost.