Comparisons of multivariate quality control charts by the use of various correlation structures

Several quality control schemes have been extensively compared using multivariate normal data sets simulated with various correlation structures. They include multiple univariate CUSUM charts, multivariate EWMA charts, multivariate CUSUM charts and Shewhart T² chart. This paper considers a new approach of the multivariate EWMA chart, in which the smoothing matrix has full elements instead of only diagonal elements. Performance of the schemes is measured by average run length (ARL), coefficient of variation of run length and rank in order of signaling of off-target shifts in the process mean vector. The schemes are also compared by noncentrality parameter. The multivariate CUSUM charts are generally affected by the correlation structure. The multivariate EWMA charts provide better ARL performance. Especially, the new EWMA chart shows remarkable results in small shifts.