Expanded fraction defective chart using cornish-fisher terms with adjusted control limits to improve in-control performance

The number of nonconforming items in a sample is monitored using the fraction defective known as the np-chart. The performance of the np-chart in Phase II depends on the accuracy of the estimated parameter in Phase I. Although taking large sample sizes ensures the accuracy of the estimated parameter, it can be impractical for attributes in some cases. Recently, the traditional c-chart and the np-chart with some adjustments have been studied to guarantee the in-control performance. Due to technology progresses, researchers have faced high-quality processes with a very low rate of nonconformity, for which traditional control charts are inadequate. To ameliorate such inaccuracy, this study develops a new method for designing the np-chart, such that the in-control performance is guaranteed with a pre-defined probability. The proposed method uses Cornish-Fisher expansions and the bootstrap method to guarantee the desired conditional in-control average run length. Through a simulation study, this study shows that the proposed adjustments improve the np-charts' in-control performance.