Multivariate Generalizations of Cumulative Sum Quality-Control Schemes

This article presents the design procedures and average run lengths for two mulativariater cumulative sum (CUSUM) quality-control procedures. The first CUSUM procedure reduces each multivariate observation to a scalar and then forms a CUSUM of the scalars. The second CUSUM procedure forms a CUSUM vector directly from the observations. These two procedures are compared with each other and with the multivariate Shewhart chart. Other multivariate quality-control procedures are mentioned. Robustness, the fast initial response feature for CUSUM schemes, and combined Shewhart-CUSUM schemes are discussed.