The T2 chart with mixed samples to control bivariate autocorrelated processes

In this paper, we propose the use of the T-2 chart with the mixed sampling strategy (MS) to monitor the mean vector of bivariate processes with observations that fit to a first-order vector autoregressive model. With the MS, rational subgroups of size n are taken from the process and the selected units are regrouped to form the mixed samples. The units of the mixed samples are units selected from the last two rational subgroups. The aim of the proposed sampling strategy is to reduce the negative effect of the autocorrelation on the performance of the T-2 chart. When the two variables are autocorrelated, the MS always enhances the T-2 chart performance, however, the mixed samples are not recommended for bivariate processes with only one autocorrelated variable which is rarely affected by the assignable cause.