Control Charts for Joint Monitoring of Mean and Variance: An Overview

In the control chart literature, a number of one-and two-chart schemes has been developed to simultaneously monitor the mean and variance parameters of normally distributed processes. These "joint" monitoring schemes are useful for situations in which special causes can result in a change in both the mean and the variance, and they allow practitioners to avoid the inflated false alarm rate which results from simply using two independent control charts (one each for mean and variance) without adjusting for multiple testing. We present an overview of this literature covering some of the one-and two-chart schemes, including those that are appropriate in parameters known (standards known) and unknown (standards unknown) situations. We also discuss some of the joint monitoring schemes for multivariate processes, autocorrelated data, and individual observations. In addition, noting that normality is often an elusive assumption, we discuss some available nonparametric schemes for jointly monitoring location and scale. We end with a conclusion and some recommendations for areas of further research.