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The effect of Phase I sample size on the run length performance of control charts for autocorrelated data

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  • Gulser Koksal
  • Burcu Kantar
  • Taylan Ali Ula
  • Murat Caner Testik

Abstract

Traditional control charts assume independence of observations obtained from the monitored process. However, if the observations are autocorrelated, these charts often do not perform as intended by the design requirements. Recently, several control charts have been proposed to deal with autocorrelated observations. The residual chart, modified Shewhart chart, EWMAST chart, and ARMA chart are such charts widely used for monitoring the occurrence of assignable causes in a process when the process exhibits inherent autocorrelation. Besides autocorrelation, one other issue is the unknown values of true process parameters to be used in the control chart design, which are often estimated from a reference sample of in-control observations. Performances of the above-mentioned control charts for autocorrelated processes are significantly affected by the sample size used in a Phase I study to estimate the control chart parameters. In this study, we investigate the effect of Phase I sample size on the run length performance of these four charts for monitoring the changes in the mean of an autocorrelated process, namely an AR(1) process. A discussion of the practical implications of the results and suggestions on the sample size requirements for effective process monitoring are provided.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:1:p:67-87
    DOI: 10.1080/02664760701683619
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    References listed on IDEAS

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    1. 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.
    2. 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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