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Multivariate binomial/multinomial control chart

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  • Jian Li
  • Fugee Tsung
  • Changliang Zou

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.

Suggested Citation

  • Jian Li & Fugee Tsung & Changliang Zou, 2014. "Multivariate binomial/multinomial control chart," IISE Transactions, Taylor & Francis Journals, vol. 46(5), pages 526-542.
    • Handle: RePEc:taf:uiiexx:v:46:y:2014:i:5:p:526-542
    DOI: 10.1080/0740817X.2013.849830
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    Cited by:

    1. Ricardo Saldanha Morais & Roberto da Costa Quinino & Emilio Suyama & Linda Lee Ho, 2019. "Estimators of parameters of a mixture of three multinomial distributions based on simple majority results," Statistical Papers, Springer, vol. 60(4), pages 1283-1316, August.
    2. Sotirios Bersimis & Athanasios Sachlas & Philippe Castagliola, 2017. "Controlling Bivariate Categorical Processes using Scan Rules," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1135-1149, December.
    3. Shengjin Gan & Su-Fen Yang & Li-Pang Chen, 2023. "A New EWMA Control Chart for Monitoring Multinomial Proportions," Sustainability, MDPI, vol. 15(15), pages 1-19, July.
    4. Chia-Ding Hou & Rung-Hung Su, 2024. "An Outlier Detection Approach to Recognize the Sources of a Process Failure within a Multivariate Poisson Process," Mathematics, MDPI, vol. 12(18), pages 1-10, September.

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