The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Optimal Design of a EWMA Chart to Monitor the Normal Process Mean

  • Lee, Jae-Heon (Department of Applied Statistics, Chung-Ang University)
  • Received : 2012.03.02
  • Accepted : 2012.06.05
  • Published : 2012.06.30
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Abstract

EWMA(exponentially weighted moving average) charts and CUSUM(cumulative sum) charts are very effective to detect small shifts in the process mean. These charts have some control-chart parameters that allow the charts and be tuned and be more sensitive to certain shifts. The EWMA chart requires users to specify the value of a smoothing parameter, which can also be designed for the size of the mean shift. However, the size of the mean shift that occurs in applications is usually unknown and EWMA charts can perform poorly when the actual size of the mean shift is significantly different from the assumed size. In this paper, we propose the design procedure to find the optimal smoothing parameter of the EWMA chart when the size of the mean shift is unknown.

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References

  1. Capizzi, G. and Masarotto, G. (2003). An adaptive exponentially weighted moving average control chart, Technometrics, 45, 199-207. https://doi.org/10.1198/004017003000000023
  2. Crowder, S. V. (1987a). A simple method for studying run length distributions of exponentially weighted moving average charts, Technometrics, 29, 401-407.
  3. Crowder, S. V. (1987b). Average run lengths of exponentially weighted moving average control charts, Journal of Quality Technology, 19, 161-164. https://doi.org/10.1080/00224065.1987.11979055
  4. Jiang, W., Shu, L. and Apley, D. W. (2008). Adaptive CUSUM procedures with EWMA-based shift estimators, IIE Transactions, 40, 992-1003. https://doi.org/10.1080/07408170801961412
  5. Lucas, J. M. (1982). Combined Shewhart-CUSUM quality control schemes, Journal of Quality Technology, 14, 52-59.
  6. Page, E. (1954). Continuous inspection schemes, Biometrika, 41, 100-115. https://doi.org/10.1093/biomet/41.1-2.100
  7. Reynolds, JR., M. R. and Lou, J. (2010). An evaluation of a GLR control chart for monitoring the process mean, Journal of Quality Technology, 42, 287-310. https://doi.org/10.1080/00224065.2010.11917825
  8. Reynolds, JR., M. R. and Stoumbos, Z. G. (2004a). Control charts and the efficient allocation of sampling resources, Technometrics, 46, 200-214. https://doi.org/10.1198/004017004000000257
  9. Reynolds, JR., M. R. and Stoumbos, Z. G. (2004b). Should observations be grouped for effective process monitoring?, Journal of Quality Technology, 36, 343-366. https://doi.org/10.1080/00224065.2004.11980283
  10. Reynolds, JR., M. R. and Stoumbos, Z. G. (2006). Comparisons of some exponentially weighted moving average control charts for monitoring the process mean and variance, Technometrics, 48, 550-567. https://doi.org/10.1198/004017006000000255
  11. Roberts, S. W. (1959). Control chart tests based on geometric moving averages, Technometrics, 1, 239-250. https://doi.org/10.1080/00401706.1959.10489860
  12. Ryu, J.-H., Wan, H. and Kim, S. (2010). Optimal design of a CUSUM chart for a mean shift of unknown size, Journal of Quality Technology, 42, 311-326. https://doi.org/10.1080/00224065.2010.11917826
  13. Shu, L. and Jiang, W. (2006). A Markov chain model for the adaptive CUSUM control chart, Journal of Quality Technology, 38, 135-147. https://doi.org/10.1080/00224065.2006.11918601
  14. Sparks, R. S. (2000). CUSUM charts for signaling varying location shifts, Journal of Quality Technology, 32, 157-171. https://doi.org/10.1080/00224065.2000.11979987
  15. Zhao, Y., Tsung, F. and Wang, Z. (2005). Dual CUSUM control schemes for detecting a range of mean shifts, IIE Transactions, 37, 1047-1057. https://doi.org/10.1080/07408170500232321