The article considers the variable process control scheme for two dependent process steps. We construct variable sample size (VSS) ZX̄ and Zē control charts to effectively monitor the quality variable produced by the first process step and the quality variable produced by the second process step 2, respectively. The performance of the proposed VSS control charts is measured by the adjusted average time to signal (AATS) using a Markov chain approach. An example of producing cotton yarn system shows the application and performance of the proposed VSS ZX̄ and Zē control charts in detecting shifts in process mean. Furthermore, the performance of the VSS ZX̄ and Zē control charts and the fixed sample size (FSS) ZX̄ and Zē control charts are compared by numerical analysis results. These demonstrate that the former is much faster in detecting small shifts in mean.
Applied Stochastic Models in Business and Industry 22,503-517