Testing variability in multivariate quality control: A conditional entropy measure approach

In this paper the concept of entropy is used to construct multivariate quality-control charts to monitor multivariate variability in a process. It is assumed that the data parent population is multivariate normal with covariance structure Σ and estimator S. The asymptotic distribution of the sample entropy is obtained. It is shown that the use of |S| as an overall measure of variability is not satisfactory and it is proposed a conditional entropy approach when the correlation matrix P0 is known or fixed. Under these assumptions, two new overall variability measures are defined based on the sample variances and ranges on the variables under consideration. Control charts are developed using these concepts and are applied to a multivariate quality-control example.