Journal of Korean Society of Industrial and Systems Engineering (산업경영시스템학회지)

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
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FIR CV-EWMA Control Chart

FIR CV-EWMA 관리도

  • Hong, Eui-Pyo (Dept. of Information and Industrial Engineering, Hanyang University) ;
  • Kang, Hae-Woon (Dept. of Information Engineering, Hanyang University) ;
  • Kang, Chang-Wook (Dept. of Information and Industrial Engineering, Hanyang University) ;
  • Baek, Jae-Won (Dept. of Information Engineering, Hanyang University)
  • 홍의표 (한양대학교 산업경영공학과) ;
  • 강해운 (한양대학교 산업공학과) ;
  • 강창욱 (한양대학교 산업경영공학과) ;
  • 백재원 (한양대학교 산업공학과)
  • Received : 2010.07.19
  • Accepted : 2010.09.13
  • Published : 2010.09.30
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Abstract

When the production run is short and process parameters change frequently, it is difficult to monitor the process using traditional control charts. In such a case, the coefficient of variation (CV) is very useful for monitoring the process variability. The CV control chart is an effective tool to control the mean and variability of process simultaneously. The CV control chart, however, is not sensitive at small shifts in the magnitude of CV. The CV-EWMA(exponentially weighted moving average) control chart which was developed recently is effective in detecting a small shifts of CV. Since the CV-EWMA control chart scheme can be viewed as a weighted average of all past and current CV values, it is very sensitive to small change of mean and variability of the process. In this paper, we propose an FIR(Fast initial response) CV-EWMA control chart to improve the sensitivity of a CV-EWMA scheme at process start-up or out-of-control process. Moreover, we suggest the values of design parameters and show the results of the performance study of FIR CV-EWMA control chart by the use of average run length(ARL). Also, we compared the performance of FIR CV-EWMA control chart with that of the CV-EWMA control chart and we found that the CV-EWMA control chart gives longer in-control ARL and much shorter out-of-control ARL.

Keywords

References

  1. 이만식, 강창욱, 심성보; "근사분포를 이용한 CV 관리도의 통계적 설계", 한국산업경영시스템학회지, 27(3) : 14-20, 2004.
  2. 홍의표, 강창욱, 백재원, 강해운; "EWMA 기법을 적용한 CV 관리도의 개발", 한국산업경영시스템학회지, 31(4) : 114-120, 2008.
  3. Bao, Y.; "Finite-Sample Moments of the Coefficient of Variation," Econometric Theory, 25(1) : 291-297, 2009. https://doi.org/10.1017/S0266466608090555
  4. Borror, C. M., Montgomery, D. C., and Runger, G. C.; "Robustness of the EWMA Control Chart to Nonnormality," Journal of Quality Technology, 31(3) : 309-316, 1991.
  5. Connett, J. E. and Lee, W. W.; "Estimation of the Coefficient of Variation from Laboratory Analysis of Split Specimens for Quality Control in Clinical Trials," Controlled Clinical trials, 11(1) : 24-36, 1990. https://doi.org/10.1016/0197-2456(90)90029-2
  6. Iglewicz, B. and Myers, R. H.; "Comparisons of Approximations to the Percentage Points of the Sample Coefficient of Variation," Technometrics, 12(1) : 166-169, 1970. https://doi.org/10.2307/1267363
  7. Kang, C. W., Lee, M. S., Seong, Y. J., and Hawkins, D. M.; "A Control Chart for the Coefficient of Variation," Journal of Quality Technology, 39(2) : 151-158, 2007.
  8. McKay, A. T.; "Distribution of the Coefficient of Variation and the Extended t Distribution," Journal of the Royal Statistical Society, 95(4) : 695-699, 1932. https://doi.org/10.2307/2342041
  9. Montgomery, D. C.; Introduction to Statistical Quality Control, 4th Edition, John Wiley and Sons, New York, 406-408, 2001.
  10. Nelson, L. S.; "Some Notes on Variation," Journal of Quality Technology, 31(4) : 459-462, 1999.
  11. Roberts, S. W.; "Control Chart Tests Based on Geometric Moving Average," Technometrics, 1(3) : 239-250, 1959. https://doi.org/10.2307/1266443
  12. Shi, L. et al.; "The Micro Array Quality Control Project Shows Inter and Intra Platform Reproducibility of Gene Expression Measurements," Nature Biotechnology, 24(9) : 1151-1161, 2006. https://doi.org/10.1038/nbt1239
  13. Steiner, S. H.; "EWMA Control Charts with Time Varying Control Limits and Fast Initial Response," Journal of Quality Technology, 31(1) : 75-86, 1999.
  14. Vangel, M. G.; "Confidence Intervals for a Normal Coefficient of Variation," The American Statistician, 15(1) : 21-25, 1996.
  15. Reh, W. and Scheffler, B.; "Significance Tests and Confidence Intervals for Coefficient of Variation," Computational Statistics and Data Analysis, 22(4) : 449-452, 1996. https://doi.org/10.1016/0167-9473(96)83707-8
  16. Wong, A. C. M. and Wu, J.; "Small Sample Asymptotic Inference for the Coefficient of Variation: Normal and Nonnormal Models," Journal of Statistical Planning and Inference, 104(1) : 73-82, 2002. https://doi.org/10.1016/S0378-3758(01)00241-5