Uma avaliação do desempenho de núcleos-estimadores no controle de processos multivariados

Abstract

The purpose of this dissertation is to evaluate the performance of kernel estimators and the empirical distribution function when applied in quality control of multivariate processes with and without autocorrelation with Normal and non-normal distributions. Three estimators were considered: T2 Hotellings statistic (1947), Hayter and Tsuis statistic (1994) and principal components analysis (Jackson, 1959). Kernels estimators and the empirical distribution function were used to determine the distribution function of these statistics. Two methods were used to obtain the optimal window (h) for kernel estimators: Polansky e Bakers (2000) and Bessegatos (2001). These results from Monte Carlo simulation showedthat in general the M statistic had a better performance than the other statistics presenting a smaller rates of false alarms (higher ARL in control values) and higher rates of true alarms (lower ARL out of control values) even for small sample sizes when kernel estimators are used for estimate this distribution. The Hayter and Tsuis M statistic had better performance for normal and non-normal process with and without autocorrelation. The empirical distribution function had bad performance in all cases considered. As far as the method to estimate the windowh is considered the plug-in multi-stage from Polansky and Bakers (2000) with b=5 and Bessegatos (2001) presented similar results and were very adequate in the estimation of the control limits for multivariate process.