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.