Multivariate binomial/multinomial control chart

Abstract

This article considers statistical process control for multivariate categorical processes. In particular, there is a focus on multivariate binomial and multivariate multinomial processes. More and more real applications involve categorical quality characteristics, which cannot be measured on a continuous scale. These characteristic factors usually correlate with each other, indicating a need for multivariate charting techniques. However, there is a scarcity of research on monitoring multivariate categorical data, and most existing methods lack robustness for some deficiencies. This article reports the use of log-linear models for characterizing the relationship among categorical factors that are adapted into a framework of multivariate binomial and multivariate multinomial distributions. A Phase II control chart is proposed that is robust in efficiently detecting various shifts, especially those in interaction effects representing the dependence among factors. Numerical simulations and a real data example demonstrate the effectiveness of the chart.