Multivariate Exponentially Weighted Moving Covariance Matrix

Abstract

Multivariate exponentially weighted moving average (MEWMA) charts are among the best control charts for detecting small changes in any direction. The well-known MEWMA is directed at changes in the mean vector. But changes can occur in either the location or the variability of the correlated multivariate quality characteristics, calling for parallel methodologies for detecting changes in the covariance matrix. This article discusses an exponentially weighted moving covariance matrix for monitoring the stability of the covariance matrix of a process. Used together with the location MEWMA, this chart provides a way to satisfy Shewhart's dictum that proper process control monitor both mean and variability. We show that the chart is competitive, generally outperforming current control charts for the covariance matrix.

KEY WORDS: :

• Average run length
• Average run length bias
• Regression adjustment