On the Monitoring of AR(1) Auto-Correlated Simple Linear Profiles in Multistage Processes

If the quality of a process is described using a linear functional relationship between the response variable and independent variables, such a relationship is called the profile. Today, with the development of manufacturing technologies, multistage processes have found a special position in manufacturing companies and industries. In the present paper, we consider a multistage process with AR(1) auto-correlated simple linear profile in each stage and address the effect of both auto-correlation and cascade property on the efficiency of common monitoring procedures. To eliminate the effect of auto-correlation, we used a transformation method as a remedial measure at first. Then, an approach based on the U statistic is applied to eliminate the cascade effect. Next, a modified T² control chart is proposed to monitor the process in the second stage. The performance of the proposed control chart is evaluated in terms of the average run length criterion. The simulation studies show that the proposed control chart perform satisfactorily.