Simultaneous Univariate X_bar Charts to Control Bivariate Processes with Autocorrelated Data

In this article, we consider the simultaneous univariate X_bar charts (SU X_bar charts) for samples of n bivariate observation vectors that are not only cross‐correlated but also autocorrelated. The cross‐covariance matrix of the sample mean vectors was derived with the assumption that the observations are described by a first‐order vector autoregressive model. The combined effect of the cross‐correlation and autocorrelation on the performance of the SU X_bar charts is investigated. Depending on the autocorrelations and the nature of the disturbance, affecting only one or both variables, the SU _bar charts perform better with samples of size one than with samples of size two; in same cases even better than with samples of size four. When the two variables are affected by the assignable cause, the simultaneous charts tend to perform better than the T² chart as the autocorrelation and cross‐correlation increase.