Optimal Design of One-Sided Exponential Truncated EWMA Control Charts Based on Median Run Length

One-sided exponential exponentially weighted moving average (EWMA) control charts are widely used in the Statistical Process Control (SPC) as an effective tool for monitoring high-quality manufacturing processes. To improve the efficiency of monitoring process degradation, the optimal design of the one-sided exponential EWMA chart using the truncation method is developed in this paper. Considering that the run length distribution of the exponential EWMA chart is skewed, especially for the process stays in-control. The median run length (MRL) metric is employed as a more meaningful alternative to the average run length (ARL), which is commonly used in existing studies. To enhance parameter optimisation efficiency, a Markov chain model is established for the one-sided exponential truncated EWMA charts, enabling parameter optimisation under in-control MRL constraints. To facilitate the implementation of the proposed control chart, control limits based on the $M R L$ are tabulated, and extensive comparative studies with existing one-sided schemes are conducted to validate the effectiveness of the proposed chart for monitoring high-quality manufacturing processes.