Multivariate Control Charts for Monitoring Autocorrelated Processes

Hotelling's T2 chart is one of the most popular control charts for monitoring identically and independently distributed random vectors. Recently, Alwan and Alwan (1994) and Apley and Tsung (2002) studied the use of the T2 chart for detecting mean shifts of a univariate autocorrelated process by transforming the univariate variables into multivariate vectors. This paper examines the global properties of the T2 test when shift information is unavailable. When shift directions are known a priori, the efficiency of the T2 test can be improved by a generalized likelihood ratio test (GLRT) taking into consideration the special shift patterns. The proposed control chart has an intrinsic relationship with the residuals-based GLRT procedure studied in Vander Wiel (1996) and Apley and Shi (1999). Retaining the T2 chart's advantages of a wide range sensitivity for mean shift detection, the proposed control chart is shown to outperform the T2 chart and the residual-based GLRT procedure when monitoring the mean of a univariate autocorrelated process. Performance enhancement and deterioration in the face of gradual shifts are also discussed.