A study of the Shewhart Median Scheme with Estimated Process Parameters based on Expected Median Run Length for Sustainable Manufacturing

The exclusive dependence on the average run length (ARL) as a measure of performance for control schemes has faced considerable criticism in literature. The skewness and form of the run length distribution vary depending on the extent of the mean shift in a given process, rendering interpretations based only on the ARL possibly erroneous. Consequently, for estimated process parameters (Case-U), the previous study considered the median run length (MRL) indicator for the Shewhart median scheme. However, the MRL framework requires the assumption that the exact shift size is known in advance. In numerous practical applications, the exact magnitude of the shift is frequently indeterminate. To address this limitation, we investigated the construction of the Case-U Shewhart median scheme utilizing the expected MRL (EMRL) approach, which only requires the shift size to fall within a specified interval. We provide an example of the Case-U Shewhart median scheme applied to smart manufacturing, utilizing a dataset pertaining to the manufacturing of forged piston rings.