Conditional design of the Shewhart X chart with unknown process parameters based on median run length

International audienceNumerous researches have been done on the Shewhart X chart based on the average run length (ARL) metric. Since the shape of the run length (RL) distribution changes with the mean shift size, the median run length (M RL) is argued to be a better criterion for evaluating the performance of the Shewhart X chart. Moreover, when the process parameters are unknown, the Phase II properties of the Shewhart X chart are conditioned on the parameter estimates arising from different practitioners in Phase I. This variability among the estimated process parameters is usually called as the between-practitioners variability. In order to investigate this variability in the conditional M RL values, both the average M RL (AM RL) and the standard deviation of M RL (SDM RL) will be used together in our article. The performance analyses of the M RL base