The effects of parameter estimation on minimising the in-control average sample size for the double sampling X chart

The double sampling (DS) X chart, one of the most widely-used charting methods, is superior for detecting small and moderate shifts in the process mean. In a right skewed run length distribution, the median run length (MRL) provides a more credible representation of the central tendency than the average run length (ARL), as the mean is greater than the median. In this paper, therefore, MRL is used as the performance criterion instead of the traditional ARL. Generally, the performance of the DS X chart is investigated under the assumption of known process parameters. In practice, these parameters are usually estimated from an in-control reference Phase-I dataset. Since the performance of the DS X chart is significantly affected by estimation errors, we study the effects of parameter estimation on the MRL-based DS X chart when the in-control average sample size is minimised. This study reveals that more than 80 samples are required for the MRL-based DS X chart with estimated parameters to perform more favourably than the corresponding chart with known parameters.