The effect of the autocorrelation on the performance of the T^sup 2^ chart

In this article, we consider the T2 control chart for bivariate samples of size n with observations that are not only cross-correlated but also autocorrelated. The cross covariance matrix of the sample mean vectors is derived with the assumption that the observations are described by a multivariate first order autoregressive model -- VAR (1). The combined effect of the correlation and autocorrelation on the performance of the T2 chart is also investigated. Earlier studies proved that changes in only one variable are detected faster when the variables are correlated. This result extends to the case that one or both variables are also autocorrelated.