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Multivariate Quality Control Chart for Autocorrelated Processes

Author

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  • A. A. Kalgonda
  • S. R. Kulkarni

Abstract

Traditional multivariate statistical process control (SPC) techniques are based on the assumption that the successive observation vectors are independent. In recent years, due to automation of measurement and data collection systems, a process can be sampled at higher rates, which ultimately leads to autocorrelation. Consequently, when the autocorrelation is present in the data, it can have a serious impact on the performance of classical control charts. This paper considers the problem of monitoring the mean vector of a process in which observations can be modelled as a first-order vector autoregressive VAR (1) process. We propose a control chart called Z-chart which is based on the single step finite intersection test (Timm, 1996). An important feature of the proposed method is that it not only detects an out of control status but also helps in identifying variable(s) responsible for the out of control situation. The proposed method is illustrated with the help of suitable illustrations.

Suggested Citation

  • A. A. Kalgonda & S. R. Kulkarni, 2004. "Multivariate Quality Control Chart for Autocorrelated Processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(3), pages 317-327.
    • Handle: RePEc:taf:japsta:v:31:y:2004:i:3:p:317-327
    DOI: 10.1080/0266476042000184000
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    References listed on IDEAS

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    1. Alwan, Layth C & Roberts, Harry V, 1988. "Time-Series Modeling for Statistical Process Control," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 87-95, January.
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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. Jinho Kim & Myong K. Jeong & Elsayed A. Elsayed, 2017. "Monitoring multistage processes with autocorrelated observations," International Journal of Production Research, Taylor & Francis Journals, vol. 55(8), pages 2385-2396, April.
    3. Bock, David, 2007. "Consequences of using the probability of a false alarm as the false alarm measure," Research Reports 2007:3, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    4. Jeffrey Jarrett, 2014. "The quality movement in hospital care," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(6), pages 3153-3167, November.
    5. Roberto Campos Leoni & Marcela Aparecida Guerreiro Machado & Antonio Fernando Branco Costa, 2016. "The T -super-2 chart with mixed samples to control bivariate autocorrelated processes," International Journal of Production Research, Taylor & Francis Journals, vol. 54(11), pages 3294-3310, June.
    6. David Bock, 2008. "Aspects on the control of false alarms in statistical surveillance and the impact on the return of financial decision systems," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(2), pages 213-227.
    7. 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.
    8. Leoni, Roberto Campos & Costa, Antonio Fernando Branco & Machado, Marcela Aparecida Guerreiro, 2015. "The effect of the autocorrelation on the performance of the T2 chart," European Journal of Operational Research, Elsevier, vol. 247(1), pages 155-165.
    9. Jarrett, Jeffrey E. & Pan, Xia, 2007. "The quality control chart for monitoring multivariate autocorrelated processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3862-3870, May.

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