Cumulative sum control charts for the covariance matrix

Cumulative sum (CUSUM) charts for controlling the covariance matrix are proposed via the projection pursuit method. Unlike traditional charts for covariance, the proposed charts can be used in a low-volume or short-run environment. It is shown that the proposed procedures are more effective than various existing ones. Their applications to monitoring a process with paired measurements are demonstrated. The CUSUM chart based on the likelihood ratio is also investigated. The performances of the two now kinds of CUSUM charts axe similar. However, the likelihood ratio-based CUSUM chart requires that the size of each subgroup is larger than the dimension of the quality characteristics.