Árboles de clasificación para el análisis de gráficos de control multivariantes

• Gámez Martínez, Matías ^[1] ; Alfaro Cortés, Esteban ^[1] ; Alfaro Navarro, José Luis ^[1] ; García Rubio, Noelia ^[1]
  1. [1] Universidad de Castilla, Facultad de Ciencias Económicas y Empresariales de Albacete
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 16, Nº. 1, 2009, págs. 30-42
• Idioma: español
• DOI: 10.15517/rmta.v16i1.1417
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    En control estad´?stico de la calidad, una de las herramientas m´as utilizadas son losgr´aficos de control. El principal problema de los gr´aficos de control multivariantesradica en que s´olo indican que se ha producido un cambio en el proceso, pero nodice cu´al o cu´ales de las variables son las que originan este cambio. En la literaturaespecializada existen muchas aproximaciones para solucionar este problema, si bien,la m´as utilizada consiste en la descomposici´on del estad´?stico T2. En este trabajo sepropone un m´etodo alternativo mediante la aplicaci´on de ´arboles de clasificaci´on. Losresultados obtenidos muestran que estos ´arboles de clasificaci´on constituyen una buenaherramienta para completar la interpretaci´on de los gr´aficos de control multivariantes.Palabras clave: Control estad´?stico de la calidad, T2 de Hotelling, ´Arboles de clasificaci´on.

  • English

    In statistical quality control, one of the most widely used tools are the controlcharts. The main problem of the multivariate control charts lies in that they onlyindicate that a change in the process has happened, but they do not show whichvariable or variables are the source of this change. In the specialized literature thereare many approaches to tackle this problem, although the most usual consists on thedecomposition of the T2 statistic. In this research, we propose an alternative methodthrough the application of classification trees. The results show that this methodconstitutes a good tool to help to interpret the multivariate control charts.Keywords: Statistic Process Control, T2 Hotelling, Classification trees.

• Referencias bibliográficas
  • Alt, F.B. (1985) ”Multivariate quality control” , en: N.L. Johnson & S. Kotz (Eds.) Encyclopedia of Statistical Sciences vol. 6, John...
  • 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...
  • Cheng, C.S. (1995) “A multi-layer neural network model for detecting changes in the process mean”, Computers and Industrial Engineering 28(1):...
  • Cheng, C.S. (1997) “A neural network approach for the analysis of control chart patterns”, International Journal of Production Research 35(3):...
  • Doganaksoy, N.; Faltin, F.W.; Tucker W.T. (1991) “Identification of out of control quality characteristics in a multivariate manufacturing...
  • Guh, R.S. (2003) “Integrating artificial intelligence into on-line statistical process control” , Quality and Reliability Engineering International...
  • Guh, R.S. (2007) “On-line identification and quantification of mean shifts in bivariate processes using a neural network-based approach”,...
  • Guh, R.S.; Tannock, J.D.T. (1999) “A neural network approach to characterize pattern parameters in process control charts”, Journal of Intelligent...
  • Hayter, A.J.; Tsui, K.L. (1994) “Identification and quantification in multivariate quality control problems”, Journal of Quality Technology...
  • 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...
  • Mason, R.L.; Tracy, N.D.; Young, J.C. (1995) “Decomposition of T 2 for multivariate control chart interpretation”, Journal of Quality Technology...
  • Murphy, B.J. (1987) “Selecting out of control variables with the T 2 multivariate quality control procedure” , Journal of the Royal Statistical...
  • Niaki, S.T.A.; Abassi, B. (2005) “Fault diagnosis in multivariate control charts using artificial neural networks”, Quality and Reliability...
  • Noorossana, R.; Farrokhi, M.; Saghaei, A. (2003) “Using neural networks to detect and classify out-of-control signals in autocorrelated processes”,...
  • 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:...
  • Zorriassatine, F.; Tannock, J.D.T. (1998) “A review of neural networks for statistical process control”, Journal of Intelligent Manufacturing...