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

TL;DR

This paper introduces a change-point based control chart designed to detect sparse mean shifts in high-dimensional heteroscedastic data, effective even with small sample sizes and robust to nonnormality.

Contribution

It proposes a novel control chart that can monitor high-dimensional heteroscedastic processes with limited data, addressing challenges of traditional methods in such settings.

Findings

Robust detection of sparse shifts in high-dimensional data

Effective with small sample sizes and heteroscedasticity

Validated through simulations and real data examples

Abstract

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.