Optimal design of VSI (X)over-bar control charts for monitoring correlated samples

This paper develops an economic design of variable sampling interval (VSI) X control charts in which the next sample is taken sooner than usual if there is an indication that the process is off-target. When designing VSI X control charts, the underlying assumption is that the measurements within a sample are independent. However, there are many practical situations that violate this hypothesis. Accordingly, a cost model combining the multivariate normal distribution model given by Yang and Hancock with Bai and Lee's cost model is proposed to develop the design of VSI charts for correlated data. An evolutionary search method to find the optimal design parameters for this model is presented. Also, we compare VSI and traditional X charts with respect to expected cost per unit time, utilizing hypothetical cost and process parameters as well as various correlation coefficients. The results indicate that VSI control charts outperform the traditional control charts for larger mean shift when correlation is present. In addition, there is a difference between the design parameters of VSI charts when correlation is present or absent. Copyright (c) 2005 John Wiley & Sons, Ltd.