Should Observations be Grouped for Effective Monitoring of Multivariate Process Variability?

TL;DR

This paper compares methods for monitoring multivariate process variability, finding that individual observation-based charts detect shifts faster than grouped observation charts, especially with overlapping subgroups.

Contribution

It evaluates and compares the performance of different multivariate variability monitoring charts, highlighting the effectiveness of overlapping subgroup methods.

Findings

Individual observation charts detect shifts faster.

Overlapping subgroup charts outperform nonoverlapping ones.

Monitoring with individual observations is most effective for sustained shifts.

Abstract

A multivariate dispersion control chart monitors changes in the process variability of multiple correlated quality characteristics. In this article, we investigate and compare the performance of charts designed to monitor variability based on individual and grouped multivariate observations. We compare one of the most well-known methods for monitoring individual observations -- a multivariate EWMA chart proposed by Huwang et al -- to various charts based on grouped observations. In addition, we compare charts based on monitoring with overlapping and nonoverlapping subgroups. We recommend using charts based on overlapping subgroups when monitoring with subgroup data. The effect of subgroup size is also investigated. Steady-state average time to signal is used as performance measure. We show that monitoring methods based on individual observations are the quickest in detecting sustained shifts in the process variability. We use a simulation study to obtain our results and illustrated these with a case study.