가변추출간격을 이용한 c 관리도의 최적설계

Optimal Design of c Control Chart using Variable Sampling Interval

  • 박주영 (울산과학대학 산업경영과)
  • 발행 : 2007.04.30

초록

Even though the ad hoc Shewhart methods remain controversial due to various mathematical flaws, there is little disagreement among researchers and practitioners when a set of process data has a skewness distribution. In the context and language of process control, the error related to the process data shows that time to signal increases when a control parameter shifts to a skewness direction. In real-world industrial settings, however, quality practitioners often need to consider a skewness distribution. To address this situation, we developed an enhanced design method to utilize advantages of the traditional attribute control chart and to overcome its associated shortcomings. The proposed design method minimizes bias, i.e., an average time to signal for the shift of process from the target value (ATS) curve, as well as it applies a variable sampling interval (VSI) method to an attribute control chart for detecting a process shift efficiently. The results of the factorial experiment obtained by various parameter circumstances show that the VSI c control chart using nearly unbiased ATS design provides the smallest decreasing rate in ATS among other charts for all experimental cases.

키워드

참고문헌

  1. S. B. Soffer., "Transformed Chart for Variable Sample Size." Journal of Quality Technology, Vol. 13, No. 3, pp. 189-191, 1981 https://doi.org/10.1080/00224065.1981.11978751
  2. Rocke, D. M., "The adjusted chart and chart for varying sample sizes", Journal of Quality Technology, Vol. 22, No. 3, pp. 206-209, 1990 https://doi.org/10.1080/00224065.1990.11979240
  3. Ryan, T. P. and Schwertman, N. C., "Optimal limits for attributes control charts", Journal of Quality Technology, Vol. 29, No. 1, pp. 86-98, 1997 https://doi.org/10.1080/00224065.1997.11979728
  4. Pignatiello, J. J. Acosta, C. A. Rao, B. V., "Performance of Control Charts for Monitoring Process Dispersion", INDUSTRIAL ENGINEERING RESEARCH CONFERENCE PROCEEDINGS, Vol. 4 No. 1, pp. 256-355, 1995
  5. Acosta-Mejia, C. A., "Improved charts to monitor process quality", IIE Transactions, Vol. 31, pp. 509-516, 1999
  6. Champ, C. W. and Woodall, W. H., "Exact results for Shewhart control charts with supplementary runs rules", Technometrics, Vol. 29, No. 4, pp. 393-399, 1987 https://doi.org/10.2307/1269449
  7. Zhang, L., Bebbington, M. S., Lai, C. D., and Govindaraju, K., On statistical design of the $S^2$ control chart, Submitted for publication, 2003
  8. Arnold, J. C, "A Markovian Sampling Policy Applied to Quality Monitoring of Streams," Biometrics, 26, pp. 739-747, 1970 https://doi.org/10.2307/2528720
  9. Costa, A. F. B, " $\bar{X}$Charts with Variable Sample Size," Journal of Quality Technology. Vol 26, No. 3, pp. 401-407, 1994
  10. Reynolds, M. R. and Amin, R. W. et al, " $\bar{X}$ Charts with Variable Sampling Interval," Technometrics. Vol. 30, No. 2, pp. 181-191, 1988 https://doi.org/10.2307/1270164
  11. Cui R. and Reynolds. M. R. Jr, " $\bar{X}$ Chart With Runs Rules and Variable Sampling Intervals," Technical Report 88-1, Virginia Polytechnic Institute and State University, Dept. of Statistics, 1988
  12. Costa, A. F. B, " $\bar{X}$ Chart with Variable Smaple Size and Sampling Intervals," Journal of Quality Technology. Vol. 29 No. 7, pp. 401-407, 1997
  13. Reynold, M. R. and Amin, R. W. et al, " CUSUM Charts with Variable Sampling Intervals," Technometrics, Vol. 32, No. 4, pp. 371-384, 1990 https://doi.org/10.2307/1270114
  14. Prabhu, S. S. and Montgomery, D. C, " A Combined Adaptive Sample Size and Sampling Interval $\bar{X}$ Control Scheme," Journal of Quality Technology. Vol. 26, pp. 164-176, 1994 https://doi.org/10.1080/00224065.1994.11979524