Support vector regression based residual control charts

Abstract

Control charts for residuals, based on the regression model, require a robust fitting technique for minimizing the error resulting from the fitted model. However, in the multivariate case, when the number of variables is high and data become complex, traditional fitting techniques, such as ordinary least squares (OLS), lose efficiency. In this paper, support vector regression (SVR) is used to construct robust control charts for residuals, called SVR-chart. This choice is based on the fact that the SVR is designed to minimize the structural error whereas other techniques minimize the empirical error. An application shows that SVR methods gives competitive results in comparison with the OLS and the partial least squares method, in terms of standard deviation of the error prediction and the standard error of performance. A sensitivity study is conducted to evaluate the SVR-chart performance based on the average run length (ARL) and showed that the SVR-chart has the best ARL behaviour in comparison with the other residuals control charts.