A Study of Synthetic Double Sampling np Chart Based on Median Run Length

The Markov chain method has been adopted in this work to evaluate the performance of the synthetic double sampling (SynDS) np chart, which combines the double sampling (DS) np sub-chart and the conforming run length (CRL) sub-chart. In the literature, the performance of the existing SynDS np chart is investigated using average run length (ARL). It is found that the skewness of the run length (RL) distribution varies depending on the size of shift in the process fraction nonconforming, from being significantly right-skewed when the process is in-control (IC) or small shift to being nearly symmetric when the process shift is large. As a result, the true performance of the chart may differ from what the ARL displays. Thus, median run length (MRL) is recommended to represent the central tendency associated with the varying shapes of the RL distribution in accordance to the process shift sizes. This work suggests an optimal design approach for SynDS np chart based on MRL to monitor the process fraction nonconforming, under zero-state and steady-state modes.