Optimal statistical design of the double sampling np chart based on expected median run length

Double sampling (DS) control charts are widely regarded as an effective process monitoring tool owing to their remarkable properties, such as the ability to detect small and moderate process shifts efficiently with the reduced sample size. Since the shape of the run length distribution is highly right-skewed for the process small shift size and becomes almost symmetric when the process shift size is large, the use of median run length (MRL) as a performance measure is therefore more representative. Existing works on the DS np chart construction were performed by taking an approach that the shift size of the process fraction nonconforming is assumed to be known. However, the shift size of the fraction nonconforming is usually unknown by the quality practitioners in practice. Herein, to address this issue, the expected median run length (EMRL) has been suggested as a performance measure for the unknown shift size. This paper suggests an optimal design procedure for the DS np chart based on the EMRL criterion. An example is provided to illustrate the construction of the EMRL-based DS np chart. The DS np chart is compared with a competing chart based on the EMRL criterion. Findings obtained reveal that when the shift size is unknown, the EMRL is an alternative performance measure for the DS np chart, with greater sensitivity observed for the DS np chart in contrast to the standard np chart for detecting a wide range of shifts.