Multivariate binomial/multinomial control chart

Jian Li, Fugee Tsung and Changliang Zou

IISE Transactions, 2014, vol. 46, issue 5, 526-542

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.

Date: 2014
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DOI: 10.1080/0740817X.2013.849830

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