Eficiência entre os gráficos de controle T² de Hotelling e os gráficos de X̅ univariados simultâneos para a média em processos multivariados

Abstract

This study aims to compare the performance in detecting changes in the mean vector of the process , when subjected to disturbances in one or more characteristics of two types of control charts for bivariate and trivariate processes, being these the Control Chart multivariate (GCM) T² Hotelling and graphs X univariate concurrent (SU X ). For this, an algorithm was developed by the R software, which uses the Monte Carlo method, able to generate multivariate data and make the whole analysis procedure for calculating the average run length to the occurrence of a signal (NMA0), which is used for measuring the graphics performance. Estimates of the mean vector and the covariance of a real process of a paint industry, which had 44 samples collected in July 2013 by the company itself matrix were used. The analysis took place in two stages, where the first process is trivariate and only two features are significantly correlated in this case Density and Viscosity and pH does not correlate with any of them, where only the second of these correlated variables are analyzed, with a coefficient correlation equal to 0,5. The results show that for the trivariate case, if the disturbance occurs in the density or viscosity characteristics, T² Hotelling has become more efficient, but when pH undergoes displacement, in general, the graphic SU X has better performance, especially for large displacements. When viscosity and pH or pH and density suffer displacement, the graph T has better performance, while in the case of the Density and Viscosity SU X is more efficient. If the three characteristics are exposed to disturbances, there is almost no difference between the two graphs. When the process is bivariate, if only one of the features suffers displacement T² is the best option when the two characteristics are altered, the SU X is more efficient. Applications of the techniques discussed in this study were presented. Through the GCM T² Hotelling, both the trivariate process as bivariate presented under control, the same happened when applied graphics SU X , whereas with the current methodology of the company, traditional Shewhart charts, the Density variable is out of control points, which does not occur when taken into account the correlation with Viscosity. In this study, we conclude that when all the variables are not correlated strategy of grouping them into a graph T² is not the best, thus the use of graphs, univariate and multivariate, jointly is seen as more appropriate.