A Ridge-Regression based Control Chart in the presence of Multicollinearity

Cause-selecting charts (CSCs) are the main tool for statistical quality control in multistage processes. The establishment of these control charts, which use regression models and residuals to remove the effect of previous stages from current stage, needs some critical assumptions like the linear independence among incoming quality variables. When this assumption is violated, which is quite common in real practice and called multicollinearity, the variance inflation in regression parameters occurs. Subsequently, this leads to some crucial problems in the performance of traditional CSCs. To tackle the mentioned problem, there exist some statistical and practical methods and the application of ridge regression is one of the most efficient approaches. In this paper, modeling and designing a novel control chart based on ridge regression has been addressed and extensive simulation studies have been conducted to investigate the performance of the suggested monitoring procedure compared with the traditional control chart in the literature. The results reveal that the proposed control chart outperforms the existing control chart in the presence of multicollinearity.