robust phase i monitoring of poisson regression profiles in multistage processes

The challenge of monitoring and controlling processes where the response variable follows a poisson distribution, rather than a normal distribution, is addressed in this paper. the significant impact of outliers on model estimators, which subsequently affects the performance of control charts, is also highlighted. to overcome these challenges, the use of robust estimators for monitoring profiles and enhancing control chart efficiency is proposed. furthermore, as industries increasingly adopt multistage processes in manufacturing instead of a single stage, monitoring these processes becomes essential. therefore, two robust control charts, namely the  and  control charts, designed for poisson regression profiles in multistage processes, are proposed. the efficiency of the proposed control chart is assessed using the signal probability criterion and its performance is compared to that of a classic control chart in phase i. extensive simulation studies are conducted to appraise the performance of these monitoring schemes under different shifts and stages, considering contamination scenarios as well. based on the simulation results, it is found that the control chart using robust estimators provides better performance compared to the classic control chart, demonstrating the effectiveness of the proposed method. additionally, a real example is presented to further evaluate the performance of this approach.