The skipping strategy to reduce the effect of the autocorrelation on the T (2) chart's performance

Abstract

In this article, we consider the T (2) 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 were derived with the assumption that the observations are described by a first-order vector autoregressive model-VAR (1). To counteract the undesired effect of autocorrelation, we build up the samples taking one item from the production line and skipping one, two, or more before selecting the next one. The skipping strategy always improves the chart's performance, except when only one variable is affected by the assignable cause, and the observations of this variable are not autocorrelated. If only one item is skipped, the average run length (ARL) reduces in more than 30 %, on average. If two items are skipped, this number increases to 40 %.