Shewhart Median Scheme with Estimated Process Parameters Using Median Run Length for Smart Manufacturing

The exclusive reliance on the average run length (ARL) as a control scheme's performance metric has drawn a lot of criticisms in the literature. This is because the form and skewness of the run length distribution changes depending on the amount of the mean shift in any process, making interpretation based only on the ARL potentially inaccurate. Therefore, when the process parameters are estimated (U-Case), we take into account the median run length (MRL) performance metric for the Shewhart median scheme. To demonstrate how to apply the U-Case Shewhart median scheme, we provide an example for smart manufacturing using a dataset related to the forged piston ring manufacturing process.