Variable sampling interval Shewhart-Lepage scheme with an application in monitoring hard-baking process

This study proposes an enhanced nonparametric Shewhart-Lepage (SL) scheme with the variable sampling interval (VSI) feature to collectively surveil both the location and scale characteristics of the process. The suggested approach is distribution-free, meaning that it can be widely used irrespective of the underlying process’s density. The proposed method differs from current nonparametric SL-type schemes with fixed sampling intervals by integrating adaptive inspection intervals determined by a warning region, leading to a stochastic time-to-signal framework. A Monte Carlo-based iterative search algorithm is suggested to quantitatively ascertain the control and warning limits. We validate the effectiveness of the proposed scheme over the SL, 2-of-3 runs rules Lepage, and synthetic Lepage schemes using computer-intensive simulations. We demonstrate the practical application of the proposed methodology in tracking the flow width measurements. In conclusion, we suggest using the VSI SL method because it is efficient and superior to other schemes under comparison.