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Applying State Space to SPC: Monitoring Multivariate Time Series

Author

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  • Xia Pan
  • Jeffrey Jarrett

Abstract

Monitoring cross-sectional and serially interdependent processes has become a new issue in statistical process control (SPC). In up-to-date SPC literature, Kalman filtering was reported to monitor univariate autocorrelated processes. This paper applies a Kalman filter or state-space method for SPC to monitoring multivariate time series. We use Aoki's approach to estimate the parameter matrices of a state-space model. Multivariate Hotelling T2 control charts are employed to monitor the residuals of the state-space. Examples of this approach are illustrated.

Suggested Citation

  • Xia Pan & Jeffrey Jarrett, 2004. "Applying State Space to SPC: Monitoring Multivariate Time Series," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(4), pages 397-418.
    • Handle: RePEc:taf:japsta:v:31:y:2004:i:4:p:397-418
    DOI: 10.1080/02664760410001681701
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    Citations

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    Cited by:

    1. Jeffrey E. Jarrett & Xia Pan, 2007. "Monitoring Variability and Analyzing Multivariate Autocorrelated Processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(4), pages 459-469.
    2. Pan, Xia & Jarrett, Jeffrey, 2007. "Using vector autoregressive residuals to monitor multivariate processes in the presence of serial correlation," International Journal of Production Economics, Elsevier, vol. 106(1), pages 204-216, March.
    3. Jeffrey Jarrett, 2014. "The quality movement in hospital care," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(6), pages 3153-3167, November.
    4. Sangahn Kim & Mehmet Turkoz, 2022. "Bayesian sequential update for monitoring and control of high-dimensional processes," Annals of Operations Research, Springer, vol. 317(2), pages 693-715, October.
    5. Xia Pan & Jeffrey Jarrett, 2012. "Why and how to use vector autoregressive models for quality control: the guideline and procedures," Quality & Quantity: International Journal of Methodology, Springer, vol. 46(3), pages 935-948, April.
    6. Ord, J. Keith & Koehler, Anne B. & Snyder, Ralph D. & Hyndman, Rob J., 2009. "Monitoring processes with changing variances," International Journal of Forecasting, Elsevier, vol. 25(3), pages 518-525, July.
    7. A. Snoussi, 2011. "SPC for short-run multivariate autocorrelated processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2303-2312.
    8. E. Andersson & D. Bock & M. Frisen, 2006. "Some statistical aspects of methods for detection of turning points in business cycles," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(3), pages 257-278.

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