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Directional change‐point detection for process control with multivariate categorical data

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  • Jian Li
  • Fugee Tsung
  • Changliang Zou

Abstract

Most modern processes involve multiple quality characteristics that are all measured on attribute levels, and their overall quality is determined by these characteristics simultaneously. The characteristic factors usually correlate with each other, making multivariate categorical control techniques a must. We study Phase I analysis of multivariate categorical processes (MCPs) to identify the presence of change‐points in the reference dataset. A directional change‐point detection method based on log‐linear models is proposed. The method exploits directional shift information and integrates MCPs into the unified framework of multivariate binomial and multivariate multinomial distributions. A diagnostic scheme for identifying the change‐point location and the shift direction is also suggested. Numerical simulations are conducted to demonstrate the detection effectiveness and the diagnostic accuracy.© 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013

Suggested Citation

  • Jian Li & Fugee Tsung & Changliang Zou, 2013. "Directional change‐point detection for process control with multivariate categorical data," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(2), pages 160-173, March.
    • Handle: RePEc:wly:navres:v:60:y:2013:i:2:p:160-173
    DOI: 10.1002/nav.21525
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    References listed on IDEAS

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    1. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
    2. Bersimis, Sotiris & Psarakis, Stelios & Panaretos, John, 2006. "Multivariate Statistical Process Control Charts: An Overview," MPRA Paper 6399, University Library of Munich, Germany.
    3. David Siegmund, 2004. "Model selection in irregular problems: Applications to mapping quantitative trait loci," Biometrika, Biometrika Trust, vol. 91(4), pages 785-800, December.
    4. Nancy R. Zhang & David O. Siegmund, 2007. "A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data," Biometrics, The International Biometric Society, vol. 63(1), pages 22-32, March.
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    1. Guanfu Liu & Xiaolong Pu & Lei Wang & Dongdong Xiang, 2015. "CUSUM chart for detecting range shifts when monotonicity of likelihood ratio is invalid," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(8), pages 1635-1644, August.

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