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) Z X EWMA and Ze EWMA control charts to effectively monitor the quality variable produced by the first process step with incorrect djustment and the quality variable produced by the second process step with incorrect djustment. 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 pplication and performance of the proposed VSI Z X EWMA and Ze EWMA control charts in detecting shifts in process mean. Furthermore, the performance of the proposed VSI Z X EWMA and Ze EWMA control charts and the fixed sampling interval (FSI) Z X EWMA and Ze EWMA control harts are compared by numerical analysis results. These demonstrate that the former is much faster in detecting small and median shifts in mean. The ptimum VSI Z X EWMA and Ze EWMA control charts are also proposed using optimization technique when quality engineers cannot specify the values of variable sampling intervals. It has been found that the optimum VSI Z X EWMA and Ze EWMA control charts always work better than the VSI Z X EWMA
and Ze EWMA control charts.
