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 EWMAX 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 EWMAX chart changes with the mean shift, the median 1 run length (M RL) can serve as a good alternative to evaluate the performance of the EWMAX chart. In this article, we will investigate the conditional properties of the EWMAX chart with unknown process parameters based on the M RL metric. In order to investigate the chart's properties, the average M RL (AM RL) and the standard deviation of M RL (SDM RL) will be used together when the process parameters are unknown. To prevent too many lower in-control M RL values, the adjusted control limits of the M RL 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 M RL performances.