Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Multioutput LS-SVR based residual MCUSUM control chart for autocorrelated process

  • Hwang, Changha (Department of Applied Statistics, Dankook University)
  • Received : 2016.01.15
  • Accepted : 2016.02.16
  • Published : 2016.03.31
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Abstract

Most classical control charts assume that processes are serially independent, and autocorrelation among variables makes them unreliable. To address this issue, a variety of statistical approaches has been employed to estimate the serial structure of the process. In this paper, we propose a multioutput least squares support vector regression and apply it to construct a residual multivariate cumulative sum control chart for detecting changes in the process mean vector. Numerical studies demonstrate that the proposed multioutput least squares support vector regression based control chart provides more satisfying results in detecting small shifts in the process mean vector.

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References

  1. Callao, M. P. and Rius, A. (2003). Time series: a complementary technique to control charts for monitoring analytical systems. Chemometrics and Intelligent Laboratory Systems, 66, 79-87. https://doi.org/10.1016/S0169-7439(03)00009-1
  2. Chan, L. K. and Li, G. Y. (1994). A multivariate control chart for detecting linear trends. Communications in Statistics: Simulation and Computation, 23, 997-1012. https://doi.org/10.1080/03610919408813213
  3. Dooley, J. and Guo, K. (1992). Identification of change structure in statistical process control. International Journal of Production Research, 30, 1655-1669. https://doi.org/10.1080/00207549208948112
  4. Harris, T. J. and Ross, W. H. (1991). Statistical process control procedures for correlated observations. Canadian Journal of Chemical Engineering, 69, 48-57. https://doi.org/10.1002/cjce.5450690106
  5. Healy, J. D. (1987). A note on multivariate CUSUM procedures. Technometrics, 29, 409-412. https://doi.org/10.1080/00401706.1987.10488268
  6. Hunter, J. S. (1998). The Box-Jenkins manual adjustment chart. Quality Progress, 31, 129-137.
  7. Hwang, H. (2014). Support vector quantile regression for autoregressive data. Journal of the Korean Data & Information Science Society, 25, 1539-1547. https://doi.org/10.7465/jkdi.2014.25.6.1539
  8. Hwang, H. (2015). Partially linear support vector orthogonal quantile regression with measurement errors. Journal of the Korean Data & Information Science Society, 26, 209-216. https://doi.org/10.7465/jkdi.2015.26.1.209
  9. Issam, B. K. and Mohamed, L. (2008). Support vector regression based residual MCUSUM control chart for autocorrelated process. Applied Mathematics and Computation, 201, 565-574. https://doi.org/10.1016/j.amc.2007.12.059
  10. Jamal, A., Seyed, T. Akhavan, N. and Babak, A. (2007). Artificial neural networks in applying MCUSUM residuals charts for AR(1) processes. Applied Mathematics and Computation, 189, 1889-1901. https://doi.org/10.1016/j.amc.2006.12.081
  11. Khediri, I. B. and Limam, M. (2008). Support vector regression based residual MCUSUM control chart for autocorrelated process. Applied Mathematics and Computation, 201, 565-574. https://doi.org/10.1016/j.amc.2007.12.059
  12. Khediri, I. B., Weihs, C. and Limam, M. (2010). Support vector regression control charts for multivariate nonlinear autocorrelated processes. Chemometrics and Intelligent Laboratory Systems, 103, 76-81. https://doi.org/10.1016/j.chemolab.2010.05.021
  13. Lawrence, J. (1994). Introduction to Neural Networks, California Scientific Software Press, California.
  14. Lucas, J. M. and Crosier, R. B. (1982). Fast initial response for cumulative sum quality control schemes. Technometrics, 24, 199-205. https://doi.org/10.1080/00401706.1982.10487759
  15. Mercer, J. (1909). Functions of Positive and Negative Type and Their Connection with Theory of Integral Equations. Philosophical transactions of the royal society of London. Series A, containing papers of a mathematical or physical character, 415-446.
  16. Noorossana, R. and Vaghefi, S. J. M. (2006). Effect of autocorrelation on performance of the MCUSUM control chart. Quality and Reliability Engineering International, 22, 191-197. https://doi.org/10.1002/qre.695
  17. Orlando, O., Atienza, L. C. and Tang, B. W. (2002). A CUSUM scheme for autocorrelated observations. Journal of Quality Technology, 34, 187-199. https://doi.org/10.1080/00224065.2002.11980145
  18. Seok, K. (2015). Semisupervised support vector quantile regression. Journal of the Korean Data & Information Science Society, 26, 517-524. https://doi.org/10.7465/jkdi.2015.26.2.517
  19. Shim, J. and Hwang, C. (2014).. Support vector quantile regression ensemble with bagging. Journal of the Korean Data & Information Science Society, 25, 677-684. https://doi.org/10.7465/jkdi.2014.25.3.677
  20. Shim, J. and Seok, K. (2014). A transductive least squares support vector machine with the difference convex algorithm. Journal of the Korean Data & Information Science Society, 25, 455-464. https://doi.org/10.7465/jkdi.2014.25.2.455
  21. Smola, A. and Scholkopf, B. (1998). On a kernel-based method for pattern recognition, regression, approximation and operator inversion. Algorithmica, 22, 211-231. https://doi.org/10.1007/PL00013831
  22. Snoussi, A., Ghourabi, M. E. and Limam, M. (2005). On SPC for short run autocorrelated data. Communication in Statistics, Simulation and Computation, 34, 219-234. https://doi.org/10.1081/SAC-200047110
  23. Suykens, J. A. K. and Vanderwalle, J. (1999). Least square support vector machine classifier. Neural Processing Letters, 9, 293-300. https://doi.org/10.1023/A:1018628609742
  24. Suykens, J. A. K., Vanderwalle, J. and De Moor, B. (2001). Optimal control by least squares support vector machines. Neural Networks, 14, 23-35. https://doi.org/10.1016/S0893-6080(00)00077-0
  25. Wahba, G. (1990). Spline models for observational data, SIAM, Philadelphia.
  26. Xu, S., An, X., Qiao, X., Zhu, L. and Li, L. (2013). Multi-output least-squares support vector regression machines, Pattern Recognition Letters, 34, 1078-1084. https://doi.org/10.1016/j.patrec.2013.01.015

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