Statistica Sinica 11(2001), 747-766

MULTIVARIATE CUMULATIVE SUM CONTROL CHARTS

BASED ON PROJECTION PURSUIT

Hung-Man Ngai and Jian Zhang$^\dagger$

University of British Columbia, $^\dagger$Academia Sinica, Beijing

and $^\dagger$Universite Catholique de Louvain

Abstract: A natural multivariate extension of the two-sided cumulative sum chart is proposed via projection pursuit. A modification is given for improving its performance for the special situation in which the process mean is already shifted at the time the charting begins. Simulation studies show that the new charts have slightly better performance than the competing charts (MC1, MEWMA1 and MEWMA2) in terms of the average delayed run length and standard deviation of the delayed run length, while performing a little worse in terms of the average run length. A distinctive advantage of the proposed charts is that they are more effective than the MC1, MEWMA1, MEWMA2, the combined $\chi^2$-MEWMA1 and the combined $\chi^2$-MEWMA2 charts against the inertia in reacting to mean shifts.

Key words and phrases: Average run length, CUSUM control chart, multivariate control chart, projection pursuit.