A Review of Dispersion Control Charts for Multivariate Individual Observations

TL;DR

This paper reviews the development of multivariate control charts for monitoring process covariance matrices using individual observations, highlighting research gaps and suggesting future directions.

Contribution

It categorizes existing methods, analyzes their advantages and limitations, and identifies areas needing further research, especially in CUSUM, high-dimensional, and non-parametric charts.

Findings

30 relevant articles from 1987-2019 analyzed

Less research on CUSUM, high-dimensional, non-parametric charts

Provides future research suggestions

Abstract

A multivariate control chart is designed to monitor process parameters of multiple correlated quality characteristics. Often data on multivariate processes are collected as individual observations, i.e. as vectors one at the time. Various control charts have been proposed in the literature to monitor the covariance matrix of a process when individual observations are collected. In this study, we review this literature; we find 30 relevant articles from the period 1987-2019. We group the articles into five categories. We observe that less research has been done on CUSUM, high-dimensional and non-parametric type control charts for monitoring the process covariance matrix. We describe each proposed method, state their advantages, and limitations. Finally, we give suggestions for future research.