Optimal Design of One-Sided Exponential EWMA Charts With Estimated Parameters Based on the Median Run Length

One-sided exponential exponentially weighted moving average (EWMA) charts are useful tools for monitoring high-quality processes. Average run length ($ARL$ ) is usually used as the only criterion to evaluate the performance of a control chart. However, the shapes of the run length ($RL$ ) distributions of the one-sided exponential EWMA charts are highly skewed, and furthermore, are affected by the number of Phase I samples used to estimate the process parameters. This results in some confusion in the interpretation of control charts based on $ARL$ for practitioners. Fortunately, the median run length ($MRL$ ), which is more intuitional for users, could be employed as a good alternative measure. Based on these, the $MRL$ -based one-sided exponential EWMA charts are investigated in this paper, by taking the effect of estimated parameters into account. The performances of control charts are investigated through a Markov chain approach. An optimal design procedure is developed for the one-sided exponential EWMA charts with estimated parameters based on $MRL$ . Finally, an illustrative example is presented to show the implementation of the exponential EWMA chart when process parameters are estimated.