Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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Statistical Design of CV-CUSUM Control Chart Using Fast Initial Response

FIR을 이용한 CV-CUSUM 관리도의 통계적 설계

  • Received : 2010.02.14
  • Accepted : 2010.08.24
  • Published : 2010.09.30
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Abstract

The coefficient of variation represents the ratio of the standard deviation to the mean, and it is a useful statistic for comparing the degree of variation from one data series to another, even if the means are drastically different from each other. Recently, the CV control chart is developed for monitoring processes in such situations. However, the CV control chart has low performance in detecting small shift. Due to the development of equipment and technique, currently, small shift of process occurs more frequently than large shift. In this paper, we proposes the CV-CUSUM control chart using CUSUM scheme which is cumulative sum of the deviations between each data point and a target value to detect a small shift in the process. We also found that the FIR(fast initial response) CUSUM control chart is especially valuable at start-up or after a CV-CUSUM control chart has signaled out-of-control.

Keywords

References

  1. 이만식, 강창욱, 심성보(2004), "근사분포를 이용한 CV 관리도의 통계적 설계", 한국산업경영시스템학회지, 27권, 3호, pp. 14-20.
  2. 홍의표, 강창욱, 백재원, 강해운(2008), "EWMA 기법을 적용한 CV 관리도의 개발", 한국산업경영시스템학회지, 31권, 4호, pp. 114-120.
  3. Connett, J. E. and Lee, W. W.(1990), "Estimation of the Coefficient of Variation from Laboratory Analysis of Split Specimens for Quality Control in Clinical Trials", Controlled Clinical Trials, Vol. 11, pp. 24-36. https://doi.org/10.1016/0197-2456(90)90029-2
  4. Chang, J. T. and Fricker JR. R. D.(1999), "Detecting When a Monotonically Increasing Mean has Crossed a Threshold", Journal of Quality Technology, Vol. 31, No 2, pp. 217-233.. https://doi.org/10.1080/00224065.1999.11979916
  5. Hawkins, D. M. and Olwell, H. D.(1997), Cumulative Sum Charts and Charting for Quality Improvement, Springer, New York.
  6. Iglewicz, B. and Myers, R. H.(1970), "Comparisons of Approximations to the Percentage Points of the Sample Coefficient of Variation", Technometrics, Vol. 12, No 1, pp. 166-169. https://doi.org/10.2307/1267363
  7. Kang, C. W., Lee, M. S., Seong, Y. J., and Hawkins, D. M.(2007), "A Control Chart for the Coefficient of Variation", Journal of Quality Technology, Vol. 39, pp. 151-158. https://doi.org/10.1080/00224065.2007.11917682
  8. Lucas, J. M. and Crosier, R. B.(1982), "Fast Initial Response for CUSUM Quality Control Schemes", Technometrics, Vol. 24, No 3, pp. 199-205. https://doi.org/10.2307/1268679
  9. McKay, A. T.(1932), "Distribution of the Coefficient of Variation and the Extended "t" Distribution", Journal of the Royal Statistical Society, Vol. 95, No. 4, pp. 695-698. https://doi.org/10.2307/2342041
  10. Nelson, L. S.(1999), "Some Notes on Variation", Journal of Quality Technology, Vol. 31, No. 4, pp. 459-462. https://doi.org/10.1080/00224065.1999.11979952
  11. Reh, W. and Scheffler, B.(1996), "Significance and Tests Confidence Intervals for Tests and Coefficient of Variation", Computational Statistics & Data Analysis, Vol. 22, pp. 449-452. https://doi.org/10.1016/0167-9473(96)83707-8
  12. Shi, L. et al.(2006), "The Micro Array Quality Control Project Shows Inter and Intra Platform Reproducibility of Gene Expression Measurements", Nature Biotechnology, Vol. 24, No. 9, pp. 1151-1161. https://doi.org/10.1038/nbt1239
  13. Vangel, M. G.(1996), "Confidence Intervals for a Normal Coefficient of Variation", The American Statistician, Vol. 15, No. 1, pp. 21-25.