Using VSI EWMA charts to monitor dependent process steps with incorrect adjustment

The article considers the variable process control scheme for two dependent process steps with incorrect adjustment. Incorrect adjustment of a process may result in shifts in process mean, ultimately affecting the quality of products. We construct variable sampling interval (VSI) EWMA Z X and EWMA Z e control charts to effectively monitor the quality variable produced by the first process step with incorrect adjustment and the quality variable produced by the second process step with incorrect adjustment. The performance of the proposed VSI control charts is measured by the adjusted average time to signal (AATS) derived using a Markov chain approach. An example of the automobile braking system with incorrect adjustment shows the application and performance of the proposed VSI EWMA Z X and EWMA Z e control charts in detecting shifts in process mean. Furthermore, the performance of the proposed VSI EWMA Z X and EWMA Z e control charts and the fixed sampling interval (FSI) EWMA Z X and EWMA Z e control charts are compared by numerical analysis results. These demonstrate that the former is much faster in detecting small and median shifts in mean. The optimum VSI EWMA Z X and EWMA Z e control charts are also proposed using optimization technique to minimize AATS when quality engineers cannot specify the values of variable sampling intervals. It has been found that the optimum VSI EWMA Z X and EWMA Z e control charts always work better than the VSI EWMA Z X and EWMA Z e control charts.