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Because of the curse-of-dimensionality, high-dimensional processes presentchallenges to traditional multivariate statistical process monitoring (SPM)techniques. In addition, the unknown underlying distribution and complicateddependency among variables such as heteroscedasticity increase uncertainty ofestimated parameters, and decrease the effectiveness of control charts. Inaddition, the requirement of sufficient reference samples limits theapplication of traditional charts in high dimension low sample size scenarios(small n, large p). More difficulties appear in detecting and diagnosingabnormal behaviors that are caused by a small set of variables, i.e., sparsechanges. In this article, we propose a changepoint based control chart todetect sparse shifts in the mean vector of high-dimensional heteroscedasticprocesses. Our proposed method can start monitoring when the number ofobservations is a lot smaller than the dimensionality. The simulation resultsshow its robustness to nonnormality and heteroscedasticity. A real data exampleis used to illustrate the effectiveness of the proposed control chart inhigh-dimensional applications. Supplementary material and code are providedonline.

A Change-Point Based Control Chart for Detecting Sparse Changes in High-Dimensional Heteroscedastic Data