Detecting shifts in Conway–Maxwell–Poisson profile with deviance residual-based CUSUM and EWMA charts under multicollinearity

Monitoring profiles with count responses is a common situation in industrial processes and for a count distributed process, the Conway–Maxwell–Poisson (COM-Poisson) regression model yields better outcomes for under- and overdispersed count variables. In this study, we propose CUSUM and EWMA charts based on the deviance residuals obtained from the COM-Poisson model, which are fitted by the PCR and r–k class estimators. We conducted a simulation study to evaluate the effect of additive and multiplicative types shifts in various shift sizes, the number of predictor, and several dispersion levels and to compare the performance of the proposed control charts with control charts in the literature in terms of average run length and standard deviation of run length. Moreover, a real data set is also analyzed to see the performance of the newly proposed control charts. The results show the superiority of the newly proposed control charts against some competitors, including CUSUM and EWMA control charts based on ML, PCR, and ridge deviance residuals in the presence of multicollinearity.