A new multivariate EWMA control chart via multiple testing. (February 2015) - Park, Jangho; Jun, Chi-Hyuck
Highlights: A new type of multivariate EWMA control chart is considered for detecting the process mean shift. A multiple hypothesis testing is performed using a series of T -square statistics. Benjamini–Hochberg procedure has been applied to develop a new control scheme. A density estimation is adopted to approximate the distribution of the T -square statistics. Abstract: This paper proposes a new type of multivariate EWMA control chart for detecting the process mean shift on the basis of a series of most recent T -squared statistics. We established a multiple hypothesis testing which uses the false discovery rate as the error to be controlled. Particularly, Benjamini–Hochberg procedure is applied to develop a new control scheme. A nonparametric density estimation based on the Parzen windows is adopted to approximate the distribution of the T -square statistics, from which the p -values are calculated. The performance of the proposed control charts is evaluated in terms of the out-of-control average run length and the in-control average run length according to various non-centrality parameters associated with the mean shifts. The result shows that the proposed control chart performs better than the existing multivariate EWMA chart for all mean shifts. The proposed method seems to be rigorous in the sense that error rates for the multiple hypotheses are considered in an integrated way via FDR rather than considering type I and II errors separately.