Multivariate control charts with a bayesian network

The purpose of this article is to present an approach allowing the fault detection of a multivariate process with a bayesian network. As a discriminant analysis is easily modeled with a bayesian network, we will show that we we can consider the multivariate T² and MEWMA control charts as particular cases of the discriminant analysis. So, we give the structure of the bayesian network as well as the parameters of the network in order to detect faults in the multivariate space in the same manners as if we used multivariate control charts. The resulting bayesian network, with a computed threshold, is similar to the multivariate control charts.

[1]  Richard D. Braatz,et al.  Fault Detection and Diagnosis in Industrial Systems , 2001 .

[2]  Peter E. Hart,et al.  Nearest neighbor pattern classification , 1967, IEEE Trans. Inf. Theory.

[3]  Charles W. Champ,et al.  A multivariate exponentially weighted moving average control chart , 1992 .

[4]  Theodora Kourti,et al.  Statistical Process Control of Multivariate Processes , 1994 .

[5]  Douglas C. Montgomery,et al.  Introduction to Statistical Quality Control , 1986 .

[6]  Pat Langley,et al.  An Analysis of Bayesian Classifiers , 1992, AAAI.

[7]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[8]  H. Hotelling,et al.  Multivariate Quality Control , 1947 .

[9]  Pedro Larrañaga,et al.  Supervised classification with conditional Gaussian networks: Increasing the structure complexity from naive Bayes , 2006, Int. J. Approx. Reason..

[10]  Manabu Kano,et al.  Comparison of multivariate statistical process monitoring methods with applications to the Eastman challenge problem , 2002 .

[11]  Kevin M. Bodden,et al.  A Program for Approximating the In-Control ARL for the MEWMA Chart , 1999 .

[12]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[13]  Nir Friedman,et al.  Bayesian Network Classifiers , 1997, Machine Learning.

[14]  Lakhmi C. Jain,et al.  Introduction to Bayesian Networks , 2008 .

[15]  Igor Kononenko,et al.  Semi-Naive Bayesian Classifier , 1991, EWSL.

[16]  David G. Stork,et al.  Pattern classification, 2nd Edition , 2000 .

[17]  B. Bakshi.  Multiscale PCA with application to multivariate statistical process monitoring , 1998 .

[18]  Vladimir Vapnik,et al.  The Nature of Statistical Learning , 1995 .

[19]  George C. Runger,et al.  Comparison of multivariate CUSUM charts , 1990 .

[20]  Theodora Kourti,et al.  Multivariate SPC Methods for Process and Product Monitoring , 1996 .

[21]  A. R. Crathorne,et al.  Economic Control of Quality of Manufactured Product. , 1933 .