Design and evaluation of a synthetic-X control chart

Abstract

This project studies the efficiency of the Synthetic-x control chart to detect the process mean shift, δ, when compared to the Shewhart control chart. The Synthetic-x control chart is an integration of the characteristics of the Shewhart x ̅ control chart and the Conforming Run Length (CRL) control chart. This report documents the procedures to validate the superiority of the Synthetic-x control chart to detect the process mean shift compared to the x ̅ control chart.

During the course of the project, investigation and studies were done on the two charts. The x ̅ control chart and the Synthetic-x control chart are designed, the out-of-control Average Run Length (ARL) calculated and validated by simulation.

To validate the robustness of the Synthetic-x control chart to detect shift in the process mean, performance tests were conducted on the two charts. The ARLs of the two charts were compared by plotting it against the mean shift, δ. It was found that the ARL of the Synthetic-x chart was constantly smaller than that of the x ̅ chart for any mean shift when the false alarm rate is held at a specific value.

In order to better show the advantages of the Synthetic-x control chart, hypothetical examples were used to illustrate the superiority to detect shifts in the process mean of the Synthetic-x control chart for quality control for variables.