Deviance and Pearson residuals-based control charts with different link functions for monitoring logistic regression profiles: an application to COVID-19 data

In statistical process control, the control charts are an effective tool to monitor the process. When the process is examined based on an exponential family distributed response variable along with a single explanatory variable, the generalized linear model (GLM) provides better estimates and GLM-based charts are preferred. This study is designed to propose GLM-based control charts using different link functions (i.e., logit, probit, c-log-log, and cauchit) with the binary response variable. The Pearson residuals (PR)- and deviance residuals (DR)-based control charts for logistic regression are proposed under different link functions. For evaluation purposes, a simulation study is designed to evaluate the performance of the proposed control charts. The results are compared based on the average run length (ARL). Moreover, the proposed charts are implemented on a real application for COVID-19 death monitoring. The Monte Carlo simulation study and real applications show that the performance of the model-based control charts with the c-log-log link function gives a better performance as compared to model-based control charts with other link functions.