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Exponential type charts are useful tools to monitor the time between events in high-quality processes with a low defect rate. Most studies on exponential charts are designed with the average run length ( ARL ) metric. The only use of  ARL  in the design of control charts is sometimes criticized because the shape of the run length ( RL ) distribution of control charts changes with the shift size. In fact, the  RL  distribution of the exponential exponentially weighted moving average (EWMA) chart is skewed, especially when the process is in-control. Hence, the median run length ( MRL ) serves as a more meaningful indicator. Moreover, in some situations, the shift size in the process is unknown in advance. Under this case, the expected median run length ( EMRL ) can be used as the metric. In this paper, the  RL  properties of both the upper- and lower-sided exponential EWMA charts are studied through a Markov chain approach. Two optimal design procedures are developed for one-sided exponential EWMA charts based on the  MRL  and  EMRL , respectively. The choices of reflecting boundaries for one-sided exponential EWMA charts are discussed through many numerical studies. The  MRL  and  EMRL  performances of the one-sided exponential EWMA charts are investigated.

Optimal design of one-sided exponential EWMA charts based on median run length and expected median run length