A novel control chart employing curtailed inspection

This article presents an optimal algorithm for the design of the SX (sum of Xs) control chart. The objective is to maximize the effectiveness of the SX control chart in detecting the process mean shifts, on condition that the false alarm rate is held at a specified level. The optimal SX chart can be used in 100% inspection, and in some sampling inspections as well. The effectiveness of the SX chart is measured by the out-of-control average time to signal (ATS) under the random-shift mode. The effectiveness of the optimal SX chart is further enhanced by the curtail technique. The results from many numerical studies have shown that the optimal SX chart with curtailment is able to reduce the out-of-control ATS by half, on average, compared to the conventional Shewhart X¯ chart. It even outperforms the EWMA chart and the joint X¯-EWMA chart for mean shift δ of any sizes