Optimal Design of One-sided Synthetic Exponential Charts with Known and Estimated Parameters Based on the Median Run Length

The one-sided synthetic exponential chart is used to improve the performance of exponential Shewhart chart, which includes two sub-chart: an exponential Shewhart X̅ sub-chart and a conforming run length (CRL) sub-chart. It is noticed that the shape of the run length distribution of the one-sided synthetic exponential chart is highly skewed, which makes the median run length (MRL) as a better alternative performance measure. Hence, MRL-based one-sided synthetic exponential charts with known and estimated parameters are focused in this article. Furthermore, an optimal procedure is developed to obtain the optimal parameter combinations for minimizing the out-of-control MRL based on a desired in-control MRL, and several optimal parameter combinations are presented for practitioners.