Variable control scheme in the cascade processes

The article considers the variables process control scheme for cascade processes. We construct variable sample sizes and sampling intervals (VSSI) control charts to effectively monitor the input variable and the output variable produced by a cascade process. The performance of the proposed VSSI control charts is measured by the adjusted average time to signal derived by a Markov chain approach. An example of the metallic film thickness of the computer connectors system shows the application and the performance of the proposed VSSI control charts in detecting shifts in means of the cascade process. Furthermore, the performance of the proposed VSSI control charts and the fixed sample sizes and sampling intervals control charts are compared by numerical analysis results. These demonstrate that the former is much faster in detecting small and medium shifts. The optimum VSSI control charts are also proposed using optimization technique when quality engineers cannot specify the values of the variable sample sizes and sampling intervals. It has been found that the optimum VSSI control charts work and are thus suggested whenever quality engineers cannot specify the values of variable sample sizes and sampling intervals. Furthermore, the impacts of misusing Shewhart charts to monitoring the process means on the cascade process are also investigated.