Evaluating the Performance of Synthetic Double Sampling np Chart Based on Expected Median Run Length

Abstract

To keep an eye on the status of high-quality processes for fraction nonconforming, the synthetic double sampling (SDS) np chart is a helpful tool. The SDS np chart is a hybrid between the double sampling (DS) np chart and the conforming run length (CRL) chart. The performance of a control chart is typically judged solely using the average run length (ARL). However, as the shape of the run length (RL) distribution varies with the magnitude of the shift in the process fraction nonconforming, the ARL no longer provides clear interpretation of a chart’s performance. Subsequently, enhanced DS np charts that use median run length (MRL) and expected median run length (EMRL) measures, including SDS np with MRL have recently been proposed for addressing this setback. To broaden the functionality of SDS np, in this work, the unexplored use of EMRL as alternative performance measure is developed by means of Markov chain model. Additionally, in both the zero-state (ZS) and steady-state (SS) modes, the novel optimal designs algorithms are described for computing the optimal charting parameters of the SDS np chart, for both MRL1 and EMRL1 minimizations, without any unfavourable feature of bilateral sensitivity. Both the MRL and EMRL performances of SDS np, synthetic np, and DS np charts are compared. Optimal designs charting parameters and sensitivity analyses are provided to aid the practical application of SDS np chart.