Adaptive control schemes for two dependent process steps

The article considers the statistical adaptive process control for two dependent process steps. We construct adaptive sample size and sampling interval (ASSI) ZX¯ and Ze¯ control charts to monitor the quality variables produced by the first process step and the second process step at the end of the second process step and effectively distinguish which process step is out-of-control. The performance of the proposed ASSI control charts is measured by adjusted average time to signal (AATS) using Markov chain approach. An example of automobile braking system shows the application and performance of the proposed ASSI ZX¯ and Ze¯ control charts in detecting shifts in process mean. Furthermore, the performance of the ASSI ZX¯ and Ze¯ control charts and the nonadaptive sample size and sampling interval ZX¯ and Ze¯ control charts are compared by some numerical analysis results. It demonstrates that the former is much faster than the latter in detecting small shifts in mean.