Process control using VSI cause selecting control charts

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, process variance, or both, ultimately affecting the quality of products. We construct the variable sampling interval (VSI) Z_{`(X)]</sub>-Z<sub>SX<sup>2</sup></sub>{Z_{\overline{X}}-Z_{S_X^2}} and Z<sub>`(e)]}-Z_Se²{Z_{\bar{{e}}}-Z_{S_e^2}} 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, respectively. The performance of the proposed VSI control charts is measured by the adjusted average time to signal derived using a Markov chain approach. An example of the cotton yarn producing system shows the application and performance of the proposed joint VSI Z_{`(X)]</sub> -Z<sub>SX<sup>2</sup></sub> {Z_{\overline{X}} -Z_{S_X^2 }} and Z<sub>`(e)]} -Z_Se² {Z_{\bar{{e}}} -Z_{S_e^2 }} control charts in detecting shifts in mean and variance for the two dependent process steps with incorrect adjustment. Furthermore, the performance of the VSI Z_{`(X)]</sub>-Z<sub>SX<sup>2</sup></sub> {Z_{\overline{X}}-Z_{S_X^2 }} and Z<sub>`(e)]} -Z_Se² {Z_{\bar{{e}}} -Z_{S_e^2 }} control charts and the fixed sampling interval Z_{`(X)]</sub> -Z<sub>SX<sup>2</sup></sub> {Z_{\overline{X}} -Z_{S_X^2 }} and Z<sub>`(e)]} -Z_Se² {Z_{\bar{{e}}} -Z_{S_e^2 }} control charts are compared by numerical analysis results. These demonstrate that the former is much faster in detecting small and median shifts in mean and variance. When quality engineers cannot specify the values of variable sampling intervals, the optimum VSI Z_{`(X)]</sub>-Z<sub>SX<sup>2</sup></sub> {Z_{\overline{X}}-Z_{S_X^2 }} and Z<sub>`(e)]} -Z_Se² {Z_{\bar{{e}}} -Z_{S_e^2 }} control charts are also proposed by using the Quasi-Newton optimization technique.