Control charts based on randomized quantile residuals

In practice, quality characteristics do not always follow a normal distribution, and quality control processes sometimes generate non-normal response outcomes, including continuous non-normal data and discrete count data. Thus, achieving better results in such situations requires a new control chart derived from various types of response variables. This study proposes a procedure for monitoring response variables that uses control charts based on randomized quantile residuals obtained from a fitted regression model. Simulation studies demonstrate the performance of the proposed control charts under various situations. We illustrate the procedure using two real-data examples, based on normal and negative binomial regression models, respectively. The simulation and real-data results support our proposed procedure.