Pearson and Deviance Residual-Based Control Charts for the Inverse Gaussian Ridge Regression Process: Simulation and an Application to Air Quality Monitoring - Muhammad Amin; Samra Rani; Sadiah M. A. Aljeddani (Axioms)
In manufacturing and service industries, monitoring processes with correlated input variables and inverse Gaussian (IG)-distributed quality characteristics is challenging due to the limitations of maximum likelihood estimator (MLE)-based control charts. When input variables exhibit multicollinearity, traditional MLE-based inverse Gaussian regression model (IGRM) control charts become unreliable. This study introduces novel Shewhart control charts using Pearson and deviance residuals based on the inverse Gaussian ridge regression (IGRR) model to address this issue. The proposed IGRR-based charts effectively handle multicollinearity, offering a robust alternative for process monitoring. Their performance is evaluated through Monte Carlo simulations using average run length (ARL) as the main criteria, demonstrating that Pearson residual-based IGRR charts outperform deviance residual-based charts and MLE-based methods, particularly under high multicollinearity. A real-world application to a Pakistan air quality dataset confirms their superior sensitivity in detecting pollution spikes, enabling timely environmental negotiations. These findings establish Pearson residual-based IGRR control charts as a practical and reliable tool for monitoring complex processes with correlated variables.