Optimal X~ chart for concentrated sampling inspection

This article presents an optimal algorithm for the design of the X~ control chart. The objective is to search the optimal sample size and sampling interval which maximize the effectiveness of the X~ control chart in detecting the process mean shifts, on condition that the false alarm rate is held at a specified level. The design of this chart is applicable for the concentrated sampling inspection, where the allowed number of inspections within a given period is predefined. The effectiveness of the X~ chart is measured by the out-of-control average time to signal (ATS). The results from the numerical studies have shown that the optimal X~ chart is able to reduce the out-of-control ATS for the process mean shifts of any size compared to the conventional Shewhart X~ chart.