The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Notes on identifying source of out-of-control signals in phase II multivariate process monitoring

다변량 공정 모니터링에서 이상신호 발생시 원인 식별에 관한 연구

  • Lee, Sungim (Department of Applied Statistics, Dankook University)
  • Received : 2018.01.03
  • Accepted : 2018.01.17
  • Published : 2018.02.28
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Abstract

Multivariate process control has become important in various applied fields. For instance, there are many situations in which the simultaneous monitoring of multivariate quality characteristics is necessary for the manufacturing industry. Despite its importance, its practical usage is not as convenient because it is difficult to identify the source of the out-of-control signal in a multivariate control chart. In this paper, we will introduce how to detect the source of the out-of-control by using confidence intervals for new observations, and will discuss the identification and interpretation of the out-of-control variable through simulation studies.

최근 다변량 공정관리는 다양한 응용 분야에서 중요해지고 있는 추세이다. 예를 들어, 제조 산업 분야에서는 다변량 품질특성치를 동시에 모니터링할 필요가 있다. 그러나, 다변량 관리도는 이상신호가 발생한 경우 그 원인이 되는 개별적인 변수를 식별하기가 어렵기 때문에, 실제로는 기대만큼 유용하게 쓰이고 있지 않은 형편이다. 이에 본 논문에서는 새로운 관측치에 대한 개별적인 신뢰구간을 사용하여 이상신호의 원인을 탐지하는 세 가지 방법을 소개하고, 시뮬레이션 연구를 통해 이상신호의 원인이 되는 개별적인 변수를 식별하고 해석하는 데 있어 주의할 점이 무엇인지 살펴보기로 한다.

Keywords

References

  1. Alt, F. B. (1985). Multivariate quality control. In Kotz, S., Johnson, N. L., Read, C. R. (eds.) Encyclopedia of Statistical Sciences, (Vol. 6, pp. 111-122), John Wiley & Sons, New York.
  2. Doganaksoy, N., Faltin, F. W., and Tucker, W. T. (1991). Identification of out of control quality characteristics in a multivariate manufacturing environment, Communications in Statistics - Theory and Methods, 20, 2775-2790. https://doi.org/10.1080/03610929108830667
  3. Hayter, A. J. and Tsui, K. L. (1994). Identification and quantification in multivariate quality control problems, Journal of Quality Technology, 26, 197-208. https://doi.org/10.1080/00224065.1994.11979526
  4. Jackson, J. E. (1991). A User's Guide to Principal Components, John Wiley & Sons, New York.
  5. Kang, S. H. and Kim, S. B. (2016). Multivariate monitoring of the metal frame process in mobile device manufacturing, Journal of the Korean Institute of Industrial Engineers, 42, 1186-1195.
  6. Kenett, R. S. and Halevy, A. (1984). Some statistical aspects of quality conformance inspection in military specifications documents. In Proceedings of the 5th International Conference of the Israeli Society for Quality Assurance, Tel Aviv, 23-35.
  7. Lee, S. (2015). Effects of parameter estimation in phase I on phase II control limits for monitoring autocorrelated data, The Korean Journal of Applied Statistics, 28, 1025-1034. https://doi.org/10.5351/KJAS.2015.28.5.1025
  8. Mason, R. L., Tracy, N. D., and Young, J. C. (1995) Decomposition of $T^2$ for multivariate control chart interpretation, Journal of Quality Technology 27, 99-108. https://doi.org/10.1080/00224065.1995.11979573
  9. Mason, R. L., Tracy, N. D., and Young, J. C. (1997). A practical approach for interpreting Multivariate $T^2$ control chart, Journal of Quality Technology, 29, 396-406. https://doi.org/10.1080/00224065.1997.11979791
  10. Montgomery, D. C. (2005)., Introduction to Statistical Quality Control (5th ed), John Wiley & Sons, New York.
  11. Shewhart, W. A. (1926). Quality control charts, Bell System Technical Journal, 2, 593-603.
  12. Timm, N. H. (1996). Multivariate quality control using finite intersection tests, Journal of Quality Technology, 28, 233-243. https://doi.org/10.1080/00224065.1996.11979663