On monitoring shift in the mean processes with vector autoregressive residual control charts of individual observation

In this paper, we purpose a monitoring scheme of individual observation that can be modeled as a first-order vector autoregressive process and develop it to mean square successive difference matrix based on residuals. Due to the effect of shift in mean process on VAR residual charts, we investigate the T²-type charts performance of T²_VAR(1) residual and T²_D control charts as an individual observation. Then we compare both T²-type charts using upper control limit approximation with α=0.005 (fix) based simulation. From the results of comparison, it shows that the T²_D chart for a small to moderate level of shift in the process mean vector gives a better performance than the T²_VAR(1) charts. Conversely, the T²_D charts indicate a fault detection in large level of shift and the T²_VAR(1) chart is more reliable on outliers detection. Thus, the result may not only provide a good option for quick response on monitoring scheme for residual, but also provide the way to avoid fault detection in a multivariate process.