Optimal np control chart with curtailment

This article presents an algorithm for the optimization design of the np control chart with curtailment. The objective is to maximize the effectiveness of the np chart, while holding the false alarm rate at a specified level and maintaining its simplicity for understanding and operation to a large degree. The optimization algorithm can be applied to a 100% inspection as well as a general random sampling inspection. The effectiveness of the chart is measured by the out-of-control average time to signal (ATS) under the steady-state mode. This mode allows a shift in fraction nonconforming, p, to occur at any time during the inspection of a sample and, therefore, provides more realistic results than the zero-state mode. According to several performance studies and an illustrative example that are conducted in this research, the optimal np chart with curtailment may reduce the out-of-control ATS by nearly half, on average, compared to the conventional np charts.