Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Modifications of single and double EWMA feedback controllers for balancing the mean squared deviation and the adjustment variance

편차제곱평균과 수정량분산의 균형을 위한 단일 및 이중 지수가중이동평균 피드백 수정기의 수정

  • 박창순 (중앙대학교 수학통계학부) ;
  • 권성구 (중앙대학교 일반대학원 통계학과)
  • Published : 2009.01.31
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Abstract

The process controller in the adjustment procedure is often used effectively to control the process level close to target when noise is present and unremovable. Examples of the robust controller are single EWMA controller and double EWMA controller. Double EWMA controller is designed to reduce the offset of the process deviation, which single EWMA can not eliminate. In this paper, the two controllers are modified by taking EWMA of the original controller to reduce the adjustment variance, which may become excessively large when the two given controllers are implemented. It is shown that the EWMA modification of the given controllers is successful in reducing the adjustment variance, while the mean squared deviation increases slightly.

수정절차에서 공정수정기는 잡음이 존재하지만 제거할 수 없을 때 공정수준을 목표치에 가깝게 수정하는데 종종 유용하게 사용된다. 강건 수정기의 예로는 단일 및 이중 지수가중이동평균 수정기가 있다. 이중 지수가중이동평균 수정기는 단일 지수가중이동평균 수정기가 제거할 수 없는 공정편차의 치우침을 줄일 수 있도록 고안되었다. 이 논문에서는 이 두 가지 수정기가 적용될 때 과도하게 커질 수 있는 수정량분산을 줄일 수 있도록 원래의 수정기에 지수가중이동평균을 적용함으로써 수정되었다. 주어지 수정기에 대한 지수가중이동평균 수정은 편차제곱평균은 조금 증가시키지만, 수정량분산을 줄이는데 성공적임을 보이고 있다.

Keywords

References

  1. Box, G. E. P. and Kramer, T. (1992). Statistical process control and feedback adjustment-a discussion. Technometrics, 34, 251-285. https://doi.org/10.2307/1270028
  2. Box, G. E. P. and Luce.no, A. (1997). Statistical control by monitoring and feedback adjustment, New York, NY: John Wiley and Sons.
  3. Butler, S. W. and Stefani, J. A. (1994). Supervisory run-to-run control of a polysilicon gate etch using in situ ellipsometry. IEEE Transactions on Semiconductor Manufacturing, 7, 193-201. https://doi.org/10.1109/66.286855
  4. Del Castillo, E. (1999). Long-run and transient analysis of a double EWMA feedback controller. IIE Transactions, 31, 1157-1169.
  5. Del Castillo, E. (2001). Some properties of EWMA feedback quality adjustment schemes for drifting disturbances. Journal of Quality Technology, 33, 153-166. https://doi.org/10.1080/00224065.2001.11980064
  6. Del Castillo, E. (2002). Statistical process adjustment for quality control, Wiley.
  7. Del Castillo, E., and Hurwitz, A. (1997). Run to run process control: a review and some extensions. Journal of Quality Technology, 29, 184-196. https://doi.org/10.1080/00224065.1997.11979749
  8. Edgar, T. F., Butler, S. W., Campbell, W. J., Pfeiffer, C., Bode, C., Hwang, S. B., Balakrishnan, K. S. and Hahn, J. (2000). Automatic control in microelectronics manufacturing: practices, challenges and possibilities. Automatica, 36, 1567-1603. https://doi.org/10.1016/S0005-1098(00)00084-4
  9. Garcia, C. E. and Morari, M. (1985). Internal model control. 2. design procedure for multivariable systems. Industrial and Engineering Chemistry, Process Design and Development, 24, 472-484. https://doi.org/10.1021/i200029a043
  10. Morari, M. and Zafiriou, E. (1989). Robust process control, Upper Saddle River, N.J. : Prentice Hall.
  11. Moyne, J., del Castillo, E. and Hurwitz, A., eds (2000). Run to run control in semiconductor manufacturing, Boca Raton, Fla.: CRC Press.
  12. Sachs, E., Hu, A. and Ingolfsson, A. (1995). Run by run process control: combining SPC and feedback control. IEEE Transactions on Semiconductor Manufacturing, 8, 26-43. https://doi.org/10.1109/66.350755