Gráficos de controle de regressão beta robustos

Abstract

Control charts are the main tool of the statistical control process (SPC) to monitor and extract information about a certain process. The usual control charts are built under the normality assumption of the data or approximation by normal. However, fractional-type data generally presents asymmetry, becoming the normal assumption inappropriate. Another common characteristic in production lines is a main characteristic can be affected by control variables, which requires a regression model to adjust their influence. The beta regression control chart (BRCC) fulfills these two needs, being useful for monitoring fraction type variables and incorporating control variables that influence the response variable. BRCC is based on maximum likelihood inference, which is seriously affected by outliers. Considering that in Phase I, the parameters estimates are obtained, not treating the aberrant values can cause distortions in the model. Consequently, the control limits determination can be compromised, providing misinformation about the process stability. In this work, we propose robust beta regression control charts based on weighted maximum likelihood estimators. This method uses robust inference, decreasing outliers influence in the parameters estimation, without losing all information os those observations. Thus, the control limits determination is not affected by distant observations of the data bulk, which may hinder the correct model specification. Through Monte Carlo simulations, we evaluated the breakdown point and sensitivity curve of the estimators and the adaptive measures of the ARL to analyze the performance of the control charts. Finally, in order to demonstrate the performance of the proposed charts, an application in real data was made, comparing the proposed graphs results with the competitors control charts. The proposed control charts show better performance, demonstrating the need for robust control charts in real data.