ROBUSTIFICATION OF MULTIVARIATE CONTROL CHART √|S| IN CONTROL PHASE I

Abstract

This article, chart robustification based on the square root of the sample generalized variance √|S|, is studied to control the variability of a bivariate normal process in stage 1 of Phase I control, built with observations for rational subgroups, and using the robust estimators, MVE, MCD and estimator S. These charts, are being compared with the usual chart, based on unbiased sample estimator, S, of the covariance matrix, ∑_0, in the presence of outliers from perturbation schemes such as, ∑_0 inflation contamination, and contamination affecting only the correlation. We use as performance measure, the mean squared error in estimating ∑_0, and absolute bias in the estimate, used √(|∑_0 | ), about the unbiased estimators for each one of the parameters respectively built with the rational subgroups that remain after the purification process undertaken in Phase 1 and are consider as the data group that represent the stage of the stable variation process.

Keywords

• Control estadístico multivariado
• estimación robusta
• fase I de control
• matriz de covarianzas