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EWMA 기법을 적용한 CV 관리도의 개발

Development of CV Control Chart Using EWMA Technique

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주제분류산업공학

초록

The control chart is widely used statistical process control(SPC) tool that searches for assignable cause of variation and detects any change of process. Generally, control chart and are most frequently used. When the production run is short and process parameter changes 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 shift in the magnitude of CV. In this paper, we propose an CV-EWMA (exponentially weighted moving average) control chart which is effective in detecting a small shift 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. We suggest the values of design parameters and show the results of the performance study of CV-EWMA control chart by the use of average run length (). When we compared the performance of CV-EWMA control chart with that of the CV control chart, we found that the CV-EWMA control chart gives longer in-control ARL and much shorter out-of-control ARL.

Abstract

The control chart is widely used statistical process control(SPC) tool that searches for assignable cause of variation and detects any change of process. Generally, control chart and are most frequently used. When the production run is short and process parameter changes 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 shift in the magnitude of CV. In this paper, we propose an CV-EWMA (exponentially weighted moving average) control chart which is effective in detecting a small shift 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. We suggest the values of design parameters and show the results of the performance study of CV-EWMA control chart by the use of average run length (). When we compared the performance of CV-EWMA control chart with that of the CV control chart, we found that the CV-EWMA control chart gives longer in-control ARL and much shorter out-of-control ARL.

참고문헌 (13)

  1. 이만식, "근사분포를 이용한 CV관리도의 통계적 설계", 산업경영시스템학회지, 27(3), pp.14~20 (2004), 한국산업경영시스템학회
  2. Borror, C. M., "Robustness of the EWMA Control Chart to Nonnormality", Journal of Quality Technology, 31(3), pp.309~316 (1991)
  3. Connett, J. E., "Estimation of the Coefficient of Variation from Laboratory Analysis of Split Specimens for Quality Control in Clinical Trials", Controlled Clinical trials, 11(1), pp.24~36 (1990)
  4. Iglewicz, B., "Comparisons of Approximations to the Percentage Points of the Sample Coefficient of Variation", Technometrics, 12(1), pp.166~169 (1970)
  5. Kang, C. W., "A Control Chart for the Coefficient of Variation", Journal of Quality Technology, 39(2), pp.151~158 (2007)
  6. McKay, A. T., "Distribution of the Coefficient of Variation and the Extended t Distribution", Journal of the Royal Statistical Society, 95(4), pp.695~699 (1932)
  7. Montgomery, D. C., "Introduction to Statistical Quality Control, 4th Edition", pp.406~408 (2001), John Wiley & Sons
  8. Nelson, L. S., "Some Notes on Variation", Journal of Quality Technology, 31(4), pp.459~462 (1999)
  9. Roberts, S. W., "Control Chart Tests Based on Geometric Moving Average", Technometrics, 1(3), pp.239~250 (1959)
  10. Shi, L. et al., "The Micro Array Quality Control Project Shows Inter and Intra Platform Reproducibility of Gene Expression Measurements", Nature Biotechnology, 24(9), pp.1151~1161 (2006)
  11. Vangel, M. G., "Confidence Intervals for a Normal Coefficient of Variation", The American Statistician, 15(1), pp.21~25 (1996)
  12. Reh, W., "Significance Tests and Confidence Intervals for Coefficient of Variation", Computational Statistics and Data Analysis, 22(4), pp.449~452 (1996)
  13. Wong, A. C. M., "Small Sample Asymptotic Inference for the Coefficient of Variation : Normal and Nonnormal Models", Journal of Statistical Planning and Inference, 104(1), pp.73~82 (2002)

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