A multivariate EWMA control chart for monitoring process variability with individual observations

Abstract

A control chart is proposed to effectively monitor changes in the population variance-covariance matrix of a multivariate normal process when individual observations are collected. The proposed control chart is constructed based on first taking the exponentially weighted moving average of the product of each observation and its transpose. Appropriate statistics which are based on square distances between estimators and true parameters are then developed to detect changes in the variances and covariances of the variance-covariance matrix. The simulation studies show that the proposed control chart outperforms existing procedures in cases where either the variances or correlations increase or both increase. The improvement in performance of the proposed control chart is particularly notable when variables are strongly positively correlated. The proposed control chart is applied to a real-life example taken from the semiconductor industry.