Guaranteed conditional performance of the median run length based EWMA X¯ chart with unknown process parameters.

Exponentially weighted moving average (EWMA) type charts are very popular and efficient in monitoring various kind of statistics. Much researches have been done on the EWMA X ¯ chart with known process parameters. But, in practice, the process parameters used to set the control chart limits are often unknown and they need to be estimated from different Phase I samples. Moreover, because the shape of the run length distribution for the EWMA X ¯ chart changes with the mean shift, the median run length (MRL) can serve as a good alternative to evaluate the performance of the EWMA X ¯ chart. In this article, we will investigate the conditional properties of the EWMA X ¯ chart with unknown process parameters based on the MRL metric. In order to investigate the chart's properties, the average MRL (AMRL) and the standard deviation of MRL (SDMRL) will be used together when the process parameters are unknown. To prevent too many lower in-control MRL values, the adjusted control limits of the MRL based EWMA chart are obtained by using a bootstrap type approach and the results show that the adjusted control limits can give a good tradeoff between the in-control and out-of-control MRL performances. [ABSTRACT FROM AUTHOR]