A Bivariate Control Chart for Paired Measurements

Abstract

A signal from a multivariate control chart may be difficult to explain. One of the techniques used to facilitate this action is to chart the principal components, but if the components are not easily interpreted the problem remains. This paper expands upon previous work and provides an interesting bivariate setting in which the principal components have meaningful interpretations. When monitoring a process with paired measurements on a single sample, the principal components of the corresponding correlation matrix actually represent the characteristics of interest for process control. Further, the correlation coefficient between the original variables is the only additional information needed to describe the condition of the process.

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