Hypothesis tests with functional data for surface quality change detection in surface finishing processes

This work is concerned with providing a principled decision process for stopping or tool-changing in a surface finishing process. The decision process is supposed to work for products of non-flat geometry. The solution is based on conducting hypothesis testing on the bearing area curves from two consecutive stages of a surface finishing process. In each stage, the bearing area curves, which are in fact the nonparametric quantile curves representing the surface roughness, are extracted from surface profile measurements at a number of sampling locations on the surface of the products. The hypothesis test of these curves informs the decision makers whether there is a change in surface quality induced by the current finishing action. When such change is detected, the current action is deemed effective and should thus continue, while when no change is detected, the effectiveness of the current action is then called into question, signaling possibly some change in the course of action. Application of the hypothesis testing-based decision procedure to both spherical and flat surfaces demonstrates the effectiveness and benefit of the proposed method and confirms its geometry-agnostic nature.