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

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
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Power Enhanced Design of Robust Control Charts for Autocorrelated Processes : Application on Sensor Data in Semiconductor Manufacturing

검출력 향상된 자기상관 공정용 관리도의 강건 설계 : 반도체 공정설비 센서데이터 응용

  • Lee, Hyun-Cheol (Department of Business Administration, Korea Aerospace University)
  • 이현철 (한국항공대학교 경영학과)
  • Received : 2011.09.19
  • Accepted : 2011.11.23
  • Published : 2011.12.31
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Abstract

Monitoring auto correlated processes is prevalent in recent manufacturing environments. As a proactive control for manufacturing processes is emphasized especially in the semiconductor industry, it is natural to monitor real-time status of equipment through sensor rather than resultant output status of the processes. Equipment's sensor data show various forms of correlation features. Among them, considerable amount of sensor data, statistically autocorrelated, is well represented by Box-Jenkins autoregressive moving average (ARMA) model. In this paper, we present a design method of statistical process control (SPC) used for monitoring processes represented by the ARMA model. The proposed method shows benefits in the power of detecting process changes, and considers robustness to ARMA modeling errors simultaneously. We prove benefits through Monte carlo simulation-based investigations.

Keywords

References

  1. 김윤배, 박대수; "분계점 붓스트랩 방법을 이용한 자기상관을 갖는 공정의 $\bar{X}$ 관리도", 품질경영학회지, 28(2) : 39-56, 2000.
  2. 이재준, 이종선; "자기상관 공정에 대한 누적합관리도에서 설계모수 값의 결정", 품질경영학회지, 36(4) : 87-92, 2008.
  3. 이정형, 전태윤, 조신섭; "자기상관을 갖는 공정의 로버스트 누적합관리도", 품질경영학회지, 27(4) : 123-142, 1999.
  4. Alwan, L. C. and Roberts, H. V.; "Time-Series Modeling for Statistical Process Control," Journal of Business and Economic Statistics, 6(1) : 87-95, 1988.
  5. Apley, D. W.; "Time Series Control Charts in the Presence of Model Uncertainty," Journal of Manufacturing Science and Engineering, 124(4) : 891-898, 2002. https://doi.org/10.1115/1.1510520
  6. Apley, D. W. and Lee, H. C.; "Design of Exponentially Weighted Moving Average Control Charts for Autocorrelated Processes With Model Uncertainty," Technometrics, 45(3) : 187-198, 2003. https://doi.org/10.1198/004017003000000014
  7. Apley, D. W. and Lee, H. C.; "Robustness Comparison of Exponentially Weighted Moving-Average Charts on Autocorrelated Data and on Residuals," Journal of Quality Technology, 40(4) : 428-447, 2008.
  8. Apley, D. W. and Lee, H. C.; "The Effects of Model Parameter Deviations on the Variance of a Linearly Filtered Time Series," Naval Research Logistics, 57(5) : 460-471, 2010.
  9. Box, G., Jenkins, G., and Reinsel, G.; Time Series Analysis, Forecasting and Control, 4th Edition, John Wiley and Sons, Inc., New Jersey, 2008.
  10. English, J. R., Lee, S., Martin, T. W., and Tilmon, C.; "Detecting changes in autoregressive processes with $\bar{X}$ and EWMA charts," IIE Transactions, 32(12) : 1103-1113, 2000.
  11. Johnson, R. A. and Bagshaw, M.; "The Effect of Serial Correlation on the Performance of CUSUM tests," Technometrics, 16(1) : 103-112, 1974. https://doi.org/10.1080/00401706.1974.10489155
  12. Lee, H. C.; "Robust Design of Control Charts for Autocorrelated Processes with Model Uncertainty," Ph.D. Dissertation, Texas A&M University, College Station, Texas, U.S.A., 2004.
  13. Lee, H. C. and Apley, D. W.; "Improved Design of Robust Exponentially Weighted Moving Average Control Charts for Autocorrelated Processes," Quality and Reliability Engineering International, 27(3) : 337-352, 2011. https://doi.org/10.1002/qre.1126
  14. Lin, W. S. and Adams, B. M.; "Combined Control Charts for Forecast-Based Monitoring Schemes," Journal of Quality Technology, 28(3) : 289-301, 1996.
  15. Lu, C. W. and Reynolds, M. R., Jr.; "EWMA Control Charts for Monitoring the Mean of Autocorrelated Processes," Journal of Quality Technology, 31(2) : 166-188, 1999.
  16. Lucas, J. M. and Saccucci, M. S.; "Exponentially Weighted Moving Average Control Schemes : Properties and Enhancements," Technometrics, 32(1) : 1-12, 1990. https://doi.org/10.1080/00401706.1990.10484583
  17. Montgomery, D. C. and Mastrangelo, C. M.; "Some Statistical Process Control Methods for Autocorrelated Data," Journal of Quality Technology, 23(3) : 179-193, 1991.
  18. Runger G. C., Willemain, T. R., and Prabhu, S.; "Average Run Lengths for Cusum Control Charts Applied to Residuals," Communications in Statistics : Theory and Methods, 24(1) : 273-282, 1995. https://doi.org/10.1080/03610929508831487
  19. Schmid, W.; "On EWMA Charts for Time Series," Frontiers of Statistical Quality Control, 5 : 115-137, 1997.
  20. Superville, C. R. and Adams, B. M.; "An Evaluation of Forecast-Based Quality Control Schemes," Communications in Statistics : Simulation and Computation, 23(3) : 645-661, 1994. https://doi.org/10.1080/03610919408813191
  21. Testik, M. C.; "Model Inadequacy and Residuals Control Charts for Autocorrelated Processes," Quality and Reliability Engineering International, 21(2) : 115-130, 2005. https://doi.org/10.1002/qre.611
  22. Vander Weil, S. A.; "Monitoring Processes That Wander Using Integrated Moving Average Models," Technometrics, 38(2) : 139-151, 1996.
  23. Vasilopoulos, A. V. and Stamboulis, A. P.; "Modification of Control Chart Limits in the Presence of Data Correlation," Journal of Quality Technology, 10(1) : 20-30, 1978.
  24. Wardell, D. G., Moskowitz, H., and Plante, R. D.; "Run-Length Distributions of Special-Cause Control Charts for Correlated Processes," Technometrics, 36(1) : 3-17, 1994. https://doi.org/10.1080/00401706.1994.10485393
  25. Zhang, N. F.; "A Statistical Control Chart for Stationary Process Data," Technometrics, 40(1) : 24-38, 1998. https://doi.org/10.1080/00401706.1998.10485479