Journal of the Korean Data and Information Science Society

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

DOI QR Code

Robust determination of control parameters in K chart with respect to data structures

데이터 구조에 강건한 K 관리도의 관리 모수 결정

  • Park, Ingkeun (Department of Applied Statistics, Dankook University) ;
  • Lee, Sungim (Department of Applied Statistics, Dankook University)
  • Received : 2015.09.05
  • Accepted : 2015.10.12
  • Published : 2015.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

These days Shewhart control chart for evaluating stability of the process is widely used in various field. But it must follow strict assumption of distribution. In real-life problems, this assumption is often violated when many quality characteristics follow non-normal distribution. Moreover, it is more serious in multivariate quality characteristics. To overcome this problem, many researchers have studied the non-parametric control charts. Recently, SVDD (Support Vector Data Description) control chart based on RBF (Radial Basis Function) Kernel, which is called K-chart, determines description of data region on in-control process and is used in various field. But it is important to select kernel parameter or etc. in order to apply the K-chart and they must be predetermined. For this, many researchers use grid search for optimizing parameters. But it has some problems such as selecting search range, calculating cost and time, etc. In this paper, we research the efficiency of selecting parameter regions as data structure vary via simulation study and propose a new method for determining parameters so that it can be easily used and discuss a robust choice of parameters for various data structures. In addition, we apply it on the real example and evaluate its performance.

공정의 안정성을 평가하기 위해 사용되는 Shewhart 관리도 기법은 최근 다양한 분야에서 널리 응용되고 있지만, 품질 특성치에 대한 엄격한 확률분포를 가정한다. 하지만 현업에서 수집되고 있는 데이터의 확률분포는 알려진 경우가 많지 않으며, 다변량 데이터로 확장될수록 확률분포를 결정하는데 더 큰 어려움이 따른다. 이러한 문제점을 해결하기 위해 다양한 비모수 관리도 기법이 연구되었는데, 최근 연구되고 있는 비모수 관리도 기법 중 하나인 RBF (Radial Basis Function) 커널 기반의 SVDD (Support Vector Data Description) 관리도는 관리상태 하의 데이터 영역에 대한 경계를 결정함으로써 공정의 이상상태를 탐지하는 기법으로 K 관리도로 불리우며, 다양한 분야에서 적용되고 있다. 그런데 K 관리도를 적용하기 위해서는 관리도의 성능을 결정짓는 커널모수 등의 선택이 중요하며, 관리도를 작성하기 전에 미리 결정되어야 한다. 이를 위해 기존의 연구들은 격자 탐색법 등을 활용하여 모수를 결정하고 있지만, 선택 가능한 범위에 대한 반복적인 계산으로 최적값을 선택하고 있어 계산 비용이 커지고 또 시간 등의 문제로 실제 문제에 적용하기 어려운 점이 있다. 따라서 본 연구에서는 데이터의 구조에 따라 모의실험을 통해 선택 가능한 영역에서의 효율성을 비교 검토하고, 이를 바탕으로 쉽게 적용할 수 있는 새로운 모수 선택 방법을 제안하고자 한다. 이를 통해 데이터 구조에 대해 강건함을 보이는 모수의 선택과 K 관리도의 구성을 논의하고 실제 자료에 적용해 보았다.

Keywords

References

  1. Bakir, S. (2006). Distribution-free quality control charts based on signed-rank-like statistics. Communications in Statistics: Theory and Methods, 35, 743-757. https://doi.org/10.1080/03610920500498907
  2. Brereton, R. G. (2011). One-class classifiers. Journal of Chemometrics, 25, 225-246. https://doi.org/10.1002/cem.1397
  3. Camci, F., Chinnam, R. B. and Ellis, R. D. (2008). Robust kernel distance multivariate control chart using support vector principles. International Journal of Production Research, 46, 5075-5095. https://doi.org/10.1080/00207540500543265
  4. Chakraborti, S., Van der Laan, P. and Bakir, S. T. (2001). Nonparametric control charts: An overview and some results. Journal of Quality Technology, 3, 304-315.
  5. Cho, G. and Park, J. (2013). Parameter estimation in a readjustment procedure in the multivariate integrated process control. Journal of the Korean Data & Information Science Society, 24, 1275-1283. https://doi.org/10.7465/jkdi.2013.24.6.1275
  6. Cook, D. F. and Chiu, C. C. (1998). Using radial basis function neural networks to recognize shifts in correlated manufacturing process parameters. IIE Transactions, 30, 227-234.
  7. Cristianini, N. and Shawe-Taylor, J. (2000). An introduction to Support Vector Machines: and other kernel-based learning methods, Cambridge University Press, New York.
  8. Gani, W, and Limam, M. (2013). On the use of the K-chart for phase II monitoring of simple linear profiles. Journal of Quality and Reliability Engineering, 2013, 8.
  9. Gani, W., Taleb, H. and Limam, M. (2010). Support vector regression based residual control charts. Journal of Applied Statistics, 37, 309-324. https://doi.org/10.1080/02664760903002667
  10. Ge, Z., Gao, F. and Song, Z. (2011). Batch process monitoring based on support vector data description method. Journal of Process Control, 21, 949-959. https://doi.org/10.1016/j.jprocont.2011.02.004
  11. Huang, J. and Ling, C. X. (2005). Using auc and accuracy in evaluating learning algorithms. IEEE Transactions on Knowledge and Data Engineering, 17, 299-310. https://doi.org/10.1109/TKDE.2005.50
  12. Jung, K. Y. and Lee, J. (2015). Multivariate process control procedure using a decision tree learning technique. Journal of the Korean Data & Information Science Society, 26, 639-652. https://doi.org/10.7465/jkdi.2015.26.3.639
  13. Kim, S. B., Jitpitaklert, W. and Sukchotrat, T. (2010). One-class classification-based control charts for monitoring autocorrelated multivariate processes. Communications in Statistics: Simulation and Computation, 39, 461-474. https://doi.org/10.1080/03610910903480826
  14. Kim, S. B., Sukchotrat, T. and Park, S. -K. (2011). A nonparametric fault isolation approach through one-class classification algorithms. IIE Transactions, 43, 505-517. https://doi.org/10.1080/0740817X.2010.523769
  15. Kim, S. H., Alexopoulos, C., Tsui, K. L. and Wilson, J. R. (2007). A distribution-free tabular CUSUM chart for autocorrelated data. IIE Transactions, 39, 317-330. https://doi.org/10.1080/07408170600743946
  16. Kittiwachana, S., Ferreira, D. L. S., Lloyd, G. R., Fido, L. A., Thompson, D. R., Escott, R. E. A. and Brereton, R. G. (2010). One class classifiers for process monitoring illustrated by the application to online HPLC of a continuous process. Journal of Chemometrics, 24, 96-110. https://doi.org/10.1002/cem.1281
  17. Kubat, M. and Matwin, S. (1997). Addressing the curse of imbalanced data sets: One-sided sampling. Proceedings of the Fourteenth International Conference on Machine Learning, 179-186.
  18. Kumar, S., Choudhary, A. K., Kumar, M., Shankar, R. and Tiwari, M. K. (2006). Kernel distance-based robust support vector methods and its application in developing a robust K-chart. International Journal of Production Research, 44, 77-96. https://doi.org/10.1080/00207540500216037
  19. Liu, X., Lee, K., McAfee, M. and Irwin, G. W. (2011). Improved nonlinear PCA for process monitoring using support vector data description. Journal of Process Control, 21, 1306-1317. https://doi.org/10.1016/j.jprocont.2011.07.003
  20. Montgomery, D. C. (2009). Introduction to Statistical Quality Control, 6th ed, Wiley, USA.
  21. Moon, J. and Lee, S. (2013). Detection of the change in blogger sentiment using multivariate control charts. The Korean Journal of Applied Statistics, 26, 903-913. https://doi.org/10.5351/KJAS.2013.26.6.903
  22. Polansky, A. M. (2001). A smooth nonparametric approach to multivariate process capability. Technometrics, 43, 199-211. https://doi.org/10.1198/004017001750386314
  23. Schilling, E. G. and Nelson, P. R. (1976). The effect of non-normality on the control limits of X charts. Journal of Quality Technology, 8, 183-188. https://doi.org/10.1080/00224065.1976.11980743
  24. Schlkopf, B. (2000). Statistical learning and kernel methods. Proceedings of the Interdisciplinary College 2000, Gunne, Germany, March.
  25. Sukchotrat, T., Kim, S. B. and Tsung, F. (2010). One-class classification-based control charts for multivariate process monitoring. IIE Transactions, 42, 107-120.
  26. Sun, R. and Tsung, F. (2003). A kernel-distance-based multivariate control chart using support vector methods. International Journal of Production Research, 41, 2975-2989. https://doi.org/10.1080/1352816031000075224
  27. Tax, D. M. J. (2001). One Class Classification, Delft Technical University, Delft.
  28. Tax, D. M. J., Ypma, A. and Duin, R. P. W. (1999a). Pump failure detection using support vectordata description. Proceedings of the Third International Symposium on Advances in Intelligent Data Analysis, Amsterdam, Netherlands, 415-425.
  29. Tax, D. M. J., Ypma, A. and Duin, R. P. W. (1999b). Support vector data description applied to machine vibration analysis. Proceedings of the Fifth Annual Conference of the Advanced School for Computing and Imaging, Heijen, Netherlands, 398-405.
  30. Tax, D. M. J. and Duin, R. P. W. (1999c). Data domain description using support vectors. Proceedings of the European Symposium on Artificial Neural Networks, Bruges, Belgium, 251-256.
  31. Tax, D. M. J. and Duin, R. P. W. (2004). Support vector data description. Machine Learning, 54, 45-66. https://doi.org/10.1023/B:MACH.0000008084.60811.49
  32. Theissler, A. and Dear, I. (2013). Autonomously determining the parameters for SVDD with RBF kernel from a one-class training set. International Journal of Computer, Information, Systems and Control Engineering, 7, 390-398.
  33. Vapnik, V. (1998). Statistical Learning Theory, Wiley, New York, 1998.
  34. Wang, C. K., Ting, Y., Liu, Y. H. and Hariyanto, G. (2009). A novel approach to generate artificial outliers for support vector data description. IEEE International Symposium on Industrial Electronics, Seoul Olympic Parktel, Seoul, Korea, July 5-8.