Abstract
In statistical quality control, one of the most widely used tools are the control charts. The main problem of the multivariate control charts lies in that they only indicate that a change in the process has happened, but they do not show which variable or variables are the source of this change. In the specialized literature there
are many approaches to tackle this problem, although the most usual consists on the decomposition of the T2 statistic. In this research, we propose an alternative method through the application of classification trees. The results show that this method constitutes a good tool to help to interpret the multivariate control charts.
References
Alt, F.B. (1985) ”Multivariate quality control” , en: N.L. Johnson & S. Kotz (Eds.) Encyclopedia of Statistical Sciences vol. 6, John Wiley & Sons, New York.
Aparisi, F.; Avendaño, G.; Sanz, J. (2006) “Techniques to interpret T 2 control chart signals”, IIE Transactions 38: 647–657.
Breiman, L.; Friedman, J.H.; Olshen, R.; Stone, C.J. (1984) Classification and Regression Trees. Wadsworth International Group, Belmont.
Chang S.I.; Aw C.A. (1996) “A neural fuzzy control chart for detecting and classifying process mean shifts”, International Journal of Production Research 34(8): 2265–2278.
Cheng, C.S. (1995) “A multi-layer neural network model for detecting changes in the process mean”, Computers and Industrial Engineering 28(1): 51–61.
Cheng, C.S. (1997) “A neural network approach for the analysis of control chart patterns”, International Journal of Production Research 35(3): 667–697.
Doganaksoy, N.; Faltin, F.W.; Tucker W.T. (1991) “Identification of out of control quality characteristics in a multivariate manufacturing enviroment”, Communications in Statistics - Theory and Methods 20: 2775–2790.
Guh, R.S. (2003) “Integrating artificial intelligence into on-line statistical process control” , Quality and Reliability Engineering International 19: 1–20.
Guh, R.S. (2007) “On-line identification and quantification of mean shifts in bivariate processes using a neural network-based approach”, Quality and Reliability Engineering International 23: 367–385.
Guh, R.S.; Tannock, J.D.T. (1999) “A neural network approach to characterize pattern parameters in process control charts”, Journal of Intelligent Manufacturing 10(5): 449–462.
Hayter, A.J.; Tsui, K.L. (1994) “Identification and quantification in multivariate quality control problems”, Journal of Quality Technology 26: 197–208.
Jackson, J.E. (1980) “Principal components and factor analysis: Part I – Principal components”, Journal of Quality Technology 12: 201–213.
Mason, R.L.; Young, J.C. (2002) “Multivariate statistical process control with industrial applications” , American Statistical Association and the Society for Industrial and Applied Mathematics (ASA-SIAM): Philadelphia.
Mason, R.L.; Tracy, N.D.; Young, J.C. (1995) “Decomposition of T 2 for multivariate control chart interpretation”, Journal of Quality Technology 27: 109–119.
Murphy, B.J. (1987) “Selecting out of control variables with the T 2 multivariate quality control procedure” , Journal of the Royal Statistical Society 36 Serie D (The Statistician): 571–581.
Niaki, S.T.A.; Abassi, B. (2005) “Fault diagnosis in multivariate control charts using artificial neural networks”, Quality and Reliability Engineering International 21: 825–840.
Noorossana, R.; Farrokhi, M.; Saghaei, A. (2003) “Using neural networks to detect and classify out-of-control signals in autocorrelated processes”, Quality and Reliability Engineering International 19: 1–12.
Quinlan, J.R. (1986) “Induction on decision trees”, Machine Learning 1: 81–106.
Quinlan, J.R. (1993) C4.5 Programs for Machine Learning. Morgan Kaufmann, San Mateo, CA.
Tracy, N.D.; Young, J.C.; Mason, R.L. (1992) “Multivariate control charts for individual observations”, Journal of Quality Technology 24: 88–95.
Zorriassatine, F.; Tannock, J.D.T. (1998) “A review of neural networks for statistical process control”, Journal of Intelligent Manufacturing 9(3): 209–224.