Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Parameter estimation in a readjustment procedure in the multivariate integrated process control

다변량 통합공정관리의 재수정 절차에서 모수추정

  • Cho, Gyo-Young (Department of Statistics, Kyungpook National University) ;
  • Park, Jong Suk (Department of Statistics, Kyungpook National University)
  • Received : 2013.08.29
  • Accepted : 2013.10.07
  • Published : 2013.11.30
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Abstract

This paper considers the multivariate integrated process control procedure for detecting special causes in a multivariate IMA(1, 1) process. When the multivariate control chart signals, the special cause will be detected and eliminated from the process. However, when the elimination of the special cause costs high or is not practically possible, an alternative action is to readjust the process with approximately modified adjustment scheme. In this paper, we estimate parameters in the readjustment procedure after having a true signal in the multivariate integrated process control.

다변량 통합공정관리의 기본절차는 잡음이 내재하는 공정에 수정조치를 취하여 공정편차벡터를 백색잡음벡터로 전환하도록 하여 공정제곱편차벡터를 최소화하게 되는 것이며, 이러한 다변량 통합공정관리의 수정활동을 하는 경우 공정에 이상원인이 발생하면 관리도를 통해 이를 탐지하고 제거하게 된다. 수정된 공정은 이상원인 발생 전에는 백색잡음이지만, 이상원인 발생 후 다양한 형태의 시계열 모형으로 변환하게 된다. 만약 수정된 공정을 탐지하여 이상원인의 신호가 발생한 경우 교정활동을 통하여 이를 제거해야 하지만, 구조적으로 교정이 불가능 하거나 교정활동의 비용이 많이 발생하는 경우에는 이상원인의 효과를 감안하여 수정활동을 재조정해야할 것이다. 이 논문에서는 공정모형으로 다변량 IMA(1,1)모형을 가정하고 다변량 통합공정관리 절차를 수행하는 경우 이상신호가 발생한 후 재수정 절차에서 필요한 모수추정을 하고자 한다.

Keywords

References

  1. Box, G. E. P. and Kramer, T. (1992). Statistical process control and feedback adjustment adjustment - A discussion. Technometrics, 34, 251-285. https://doi.org/10.2307/1270028
  2. Cho, G. and Park, J. (2011). A readjustment procedure in the multivariate integrated process control. Journal of the Korean Data & Information Science Society, 22, 1123-1135.
  3. Del Castillo, E. (2002). Statistical process adjustment for quality control, John Wiley and Sons, New York.
  4. Jiang, W. (2004). A joint monitoring scheme for automatically controlled processes. IIE transactions, 36, 1201-1210. https://doi.org/10.1080/07408170490507828
  5. Lee, J. and Lee, H. (2007). Change point estimators in monitoring the parameters of an AR(1) plus an additional random error model. Journal of Korean Data & Information Science Society, 18, 963-972.
  6. Montgomery, D. C. (1999). A perspective on models and the quality sciences: Some challenges and future directions. ASQ Statistics Division Newsletter, 18, 8-13.
  7. Nembhard, H. B. and Chen, S. (2007). Cuscore control charts for generalized feedback-control system. Quality and Reliability Engineering International, 23, 483-502. https://doi.org/10.1002/qre.831
  8. 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
  9. 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
  10. 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
  11. Park, C. and Lee, J. (2009). A readjustment procedure after signaling in the integrated process control. Communications for Statistical Applications and Methods, 16, 429-436. https://doi.org/10.5351/CKSS.2009.16.3.429
  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. Vander Wiel, S. A. (1996). Monitoring processes that wander using integrated moving average models. Technometrics, 38, 139-151.

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