The robustness of sufficient reduction methods for detecting shifts of various types in multivariate processes

Applications of shift detection are of interest in several disciplines. Sufficient reduction (SR) methods have been developed for detecting a shift in a multivariate process under different conditions in several studies. However, all methods were proposed to detect only a constant, but persistent, mean shift. In practice, there might be other types of (mean) shift to be considered. Our purpose here is to investigate the robustness of SR methods for detecting different types of shift in a multivariate process. Four shift types are considered. The performances of the SR methods are compared against other statistical techniques used in multivariate process control. The evaluation was conducted via simulation by estimating four measures. The results show that in a process of independent observations the Wessman method performs well for detecting all sizes of single spike shift and small constant, linear, and exponential shifts. In an autocorrelated process the Parallel, Frisén, and Wessman methods produce a high number of false alarms. The Siripanthana and Stillman method gives shorter delays for detecting small shifts of all types, while the vector autoregressive chart gives a shorter delay for a large constant shift. The applications of SR methods to real health surveillance data are illustrated, with examples from food poisoning and pneumonia monitoring in Thailand.