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Control Charts in the Presence of Data Correlation

Author

Listed:
  • Don G. Wardell

    (College of Business and Economics, University of Idaho, Moscow, Idaho 83843)

  • Herbert Moskowitz

    (Krannert Graduate School of Management, Purdue University, West Lafayette, Indiana 47907)

  • Robert D. Plante

    (Krannert Graduate School of Management, Purdue University, West Lafayette, Indiana 47907)

Abstract

Traditional statistical process control charts assume that observations are independent and normally distributed about some mean. We investigate the robustness of traditional charts to data correlation when the correlation can be described by an ARMA(1,1) model. We compare the performance of the Shewhart chart and the Exponentially Weighted Moving Average (EWMA) chart to the performance of the Special-Cause Control (SCC) chart and the Common-Cause Control (CCC) chart proposed by Alwan and Roberts (1988), which are designed to account for data correlation. We also explore the possibility of putting limits on the CCC chart, in order to predict quality abnormalities. The measure of performance used is the average run length (ARL). The results show that the ability of the EWMA chart to detect shifts in the process mean is quite robust to data correlation, while the corresponding individuals Shewhart chart rarely detects such shifts more quickly than the other charts. The SCC and CCC charts are shown to be preferred in most cases when a shift in the process mean exceeds 2 standard deviations. The experimental results can aid practitioners in deciding which chart would be most effective at detecting specified shifts in the process mean given the nature of their particular correlated environments. Two methodologies are utilized to explain the relative performance of the SPC charts compared: the dynamic step response function, and response surface methodology. Such methods not only facilitate a discussion of our results, but also make it possible to predict the relative performance of the charts when the process can be described by a model which is more complex than the ARMA(1,1) model.

Suggested Citation

  • Don G. Wardell & Herbert Moskowitz & Robert D. Plante, 1992. "Control Charts in the Presence of Data Correlation," Management Science, INFORMS, vol. 38(8), pages 1084-1105, August.
    • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:8:p:1084-1105
    DOI: 10.1287/mnsc.38.8.1084
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    Citations

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    Cited by:

    1. Du, Shichang & Lv, Jun, 2013. "Minimal Euclidean distance chart based on support vector regression for monitoring mean shifts of auto-correlated processes," International Journal of Production Economics, Elsevier, vol. 141(1), pages 377-387.
    2. Nan Chen & Yuan Yuan & Shiyu Zhou, 2011. "Performance analysis of queue length monitoring of M/G/1 systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(8), pages 782-794, December.
    3. Gulser Koksal & Burcu Kantar & Taylan Ali Ula & Murat Caner Testik, 2008. "The effect of Phase I sample size on the run length performance of control charts for autocorrelated data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(1), pages 67-87.
    4. 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.
    5. Marta Benková & Dagmar Bednárová & Gabriela Bogdanovská & Marcela Pavlíčková, 2023. "Use of Statistical Process Control for Coking Time Monitoring," Mathematics, MDPI, vol. 11(16), pages 1-30, August.
    6. Schmid Wolfgang & Okhrin Yarema, 2003. "Tail behaviour of a general family of control charts," Statistics & Risk Modeling, De Gruyter, vol. 21(1/2003), pages 79-92, January.
    7. Haimonti Dutta, 2022. "A Consensus Algorithm for Linear Support Vector Machines," Management Science, INFORMS, vol. 68(5), pages 3703-3725, May.
    8. Cook, Deborah F. & Zobel, Christopher W. & Wolfe, Mary Leigh, 2006. "Environmental statistical process control using an augmented neural network classification approach," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1631-1642, November.
    9. Ridley, D. & Duke, D., 2007. "Moving -window spectral model based statistical process control," International Journal of Production Economics, Elsevier, vol. 105(2), pages 492-509, February.
    10. 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.
    11. Ramjee, Radhika & Crato, Nuno & Ray, Bonnie K., 2002. "A note on moving average forecasts of long memory processes with an application to quality control," International Journal of Forecasting, Elsevier, vol. 18(2), pages 291-297.

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