Journal of the Korean Data and Information Science Society

한국데이터정보과학회 (The Korean Data and Information Science Society)
권호 표지

자기회귀이동평균(1,1) 잡음모형에서 이상원인 탐지 및 재수정 절차

Procedure for monitoring special causes and readjustment in ARMA(1,1) noise model

  • 이재헌 (중앙대학교 수학통계학부) ;
  • 김미정 (중앙대학교 수학통계학부)
  • Lee, Jae-Heon (Department of Statistics, Chung-Ang University) ;
  • Kim, Mi-Jung (Department of Statistics, Chung-Ang University)
  • 투고 : 2010.06.08
  • 심사 : 2010.08.02
  • 발행 : 2010.09.30
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⟨ 이전 논문 다음 논문 ⟩

초록

통합공정관리는 공정의 변동을 줄이기 위하여 공학적 공정관리와 통계적 공정관리를 병행하는 절차이다. 통합공정관리의 기본적인 절차는 잡음과 이상원인이 공존하는 공정에 대하여 매시점마다 수정절차를 통하여 공정편차를 백색잡음으로 전환하며, 수정된 공정을 관리도를 이용하여 이상원인의 발생 여부를 탐지하게 된다. 이때 공정은 이상원인 발생 전에는 백색잡음이 되지만, 이상원인 발생 후에는 이상원인과 수정절차의 효과가 혼합되어 다양한 형태의 시계열 모형으로 변환하게 된다. 이 논문에서는 잡음모형으로 자기회귀이동평균(1,1) 모형을 가정하고 통합공정관리 절차를 수행하는 경우, 지수가중이동평균 관리도를 사용하여 이상원인을 탐지하는 절차에 대한 효율을 살펴보았다. 또한 이상원인의 신호 후 이를 제거하기 힘든 경우 사용할 수 있는 재수정 절차를 제안하였다.

An integrated process control (IPC) procedure is a scheme which simultaneously applies the engineering control procedure (EPC) and statistical control procedure (SPC) techniques to reduce the variation of a process. In the IPC procedure, the observed deviations are monitored during the process where adjustments are repeatedly done by its controller. Because the effects of the noise, the special cause, and the adjustment are mixed, the use and properties of the SPC procedure for the out-of-control process are complicated. This paper considers efficiency of EWMA charts for detecting special causes in an ARMA(1,1) noise model with a minimum mean squared error adjustment policy. And we propose the readjustment procedure after having a true signal. This procedure can be considered when the elimination of the special cause is not practically possible.

키워드

참고문헌

  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., Jenkins, G. M. and Reinsel, G. C. (1994). Time series analysis, forecasting and control, 3rd Ed., Prentice Hall, Englewood Cliffs, New Jersey.
  3. Hu, S. J. and Roan, C. (1996). Change patterns of time series-based control charts. Journal of Quality Technology, 28, 302-312. https://doi.org/10.1080/00224065.1996.11979680
  4. Jiang, W. and Tsui, K. L. (2002). SPC monitoring of MMSE- and PI-controlled processes. Journal of Quality Technology, 34, 384–398. https://doi.org/10.1080/00224065.2002.11980171
  5. Jiang, W. (2004). A joint monitoring scheme for automatically controlled processes. IIE Transactions, 36, 1201–1210. https://doi.org/10.1080/07408170490507828
  6. Lee, H. Y. and Lee, J. (2009). Change point estimators in monitoring the parameters of an IMA(1,1) model. Journal of the Korean Data & Information Science Society, 20, 435–443.
  7. Lee, J. and Lee, H. Y. (2007). Change point estimators in monitoring the parameters of an AR(1) plus an additional random error model. Journal of the Korean Data & Information Science Society, 18, 963–972.
  8. Nembhard, H. B. and Chen, S. (2007). Cuscore control charts for generalized feedback-control systems. Quality and Reliability Engineering International, 23, 483–502. https://doi.org/10.1002/qre.831
  9. Pan, R. and Del Castillo, E. (2003). Integration of sequential process adjustment and process monitoring techniques. Quality and Reliability Engineering International, 19, 371–386. https://doi.org/10.1002/qre.590
  10. Park, C. (2007). An algorithm for the properties of the integrated process control with bounded adjustments and EWMA monitoring. International Journal of Production Research, 45, 5571–5587. https://doi.org/10.1080/00207540701325397
  11. Park, C. and Lee, J. (2008). An integrated process control scheme based on the future loss. The Korean Journal of Applied Statistics, 21, 247–264. https://doi.org/10.5351/KJAS.2008.21.2.247
  12. Park, C. and Reynolds, M., Jr. (2008). Economic design of an integrated process control procedure with repeated adjustments and EWMA monitoring. Journal of the Korean Statistical Society, 37, 155–174. https://doi.org/10.1016/j.jkss.2007.10.005
  13. Runger, G., Testik, M. C. and Tsung, F. (2006). Relationships among control charts used with feedback control. Quality and Reliability Engineering International, 22, 877–887. https://doi.org/10.1002/qre.774
  14. Tsung, F. and Tsui, K. L. (2003). A mean-shift pattern study on integration of SPC and APC for process monitoring. IIE Transactions, 35, 231–242. https://doi.org/10.1080/07408170304365
  15. Vander Wiel, S. A. (1996). Monitoring processes that wander using integrated moving average models. Technometrics, 38, 139-151. https://doi.org/10.2307/1270407