  Because of the curse-of-dimensionality, high-dimensional processes present
challenges to traditional multivariate statistical process monitoring (SPM)
techniques. In addition, the unknown underlying distribution and complicated
dependency among variables such as heteroscedasticity increase uncertainty of
estimated parameters, and decrease the effectiveness of control charts. In
addition, the requirement of sufficient reference samples limits the
application of traditional charts in high dimension low sample size scenarios
(small n, large p). More difficulties appear in detecting and diagnosing
abnormal behaviors that are caused by a small set of variables, i.e., sparse
changes. In this article, we propose a changepoint based control chart to
detect sparse shifts in the mean vector of high-dimensional heteroscedastic
processes. Our proposed method can start monitoring when the number of
observations is a lot smaller than the dimensionality. The simulation results
show its robustness to nonnormality and heteroscedasticity. A real data example
is used to illustrate the effectiveness of the proposed control chart in
high-dimensional applications. Supplementary material and code are provided
online.
