Simultaneous Univariate X-bar Charts to Control Bivariate Processes with Autocorrelated Data

Abstract

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.