A multivariate synthetic double sampling T2 control chart

In this article, we propose a multivariate synthetic double sampling T2 chart to monitor the mean vector of a multivariate process. The proposed chart combines the double sampling (DS) T2 chart and the conforming run length (CRL) chart. On the whole, the proposed chart performs better than its standard counterparts, namely, the Hotelling’s T2, DS T2, and synthetic T2 charts, in terms of the average run length (ARL) and average number of observations to sample (ANOS). The proposed chart also outperforms the multivariate exponentially weighted moving average (MEWMA) chart for moderate and large shifts but the latter is more sensitive than the former towards small shifts. For a variable sample size chart, like the synthetic DS T2 chart, ANOS is a more meaningful performance measure than ARL. ANOS relates to the actual number of observations sampled but ARL merely deals with the number of sampling stages taken. Interpretation based on ARL is more complicated as either n1 or n1 + n2 observations are taken in each sampling stage.

► We propose the synthetic DS T2 chart by integrating the DS T2 chart and the CRL chart.
► We compare the ARL1 and ANOS1 performances of the synthetic DS T2, synthetic T2, DS T2, Hotelling’s T2 and MEWMA charts.
► The synthetic DS T2 chart outperforms other charts for moderate and large shifts.
► The MEWMA chart surpasses other charts for small shifts.