Beta regression residuals-based control charts with different link functions: an application to the thermal power plants data

In industries, quality monitoring tools are necessary for producing good quality products. Control charts are the most important tools for monitoring a single variable. Sometimes, there exists the explanatory variable (s) along with the study variable, which is linearly related, and monitoring them is called linear profiling. However, there is a strong assumption that the response is normally distributed in linear profiling. When the response variable is in the form of ratio/rates, restricted to interval (0,1), and follows the beta distribution, then beta profiling is a more appropriate approach. In this study, we introduce the control charts based on weighted residuals under various link functions associated with the beta regression model. To check the performance of the proposed control charts, we considered a Monte Carlo simulation study and an Angolan thermal power plant application. Further, the three criteria are used for performance checking: the average of the run length, the standard deviation of the run length, and the median of the run length. We also evaluate the performance of the proposed control chart in two ways: by monitoring the intercepts and by monitoring the slope coefficients. After analyzing the intercept, the outcomes reveal that the log–log link function with weighted residuals and the probit link function with deviance residuals, by monitoring the slope coefficients, detect shift quickly for the comparison of other link functions. Similarly, in monitoring the average response, the log–log link function with the weighted residuals performs better than the deviance residuals with all other considered link functions.