An exploratory analysis approach for understanding variation in stochastic textured surfaces

Stochastic textured surface data are increasingly common in industrial quality control and other settings. Although there are a number of recently developed methods for understanding variation (e.g., due to manufacturing inconsistency) across a set of profiles or other multivariate quality control data, these existing methods are not applicable to stochastic textured surfaces due to their stochastic nature. One challenge is that it is not straightforward how to define distances or dissimilarities between surface samples. An approach is developed for understanding variation in stochastic textured surfaces by deriving a new pairwise dissimilarity measure between surface samples and using these dissimilarities within a manifold learning framework to discover a low-dimensional parameterization of the surface variation patterns. Visualizing how the stochastic nature of the surfaces changes as the manifold parameters are varied helps build an understanding of the individual physical characteristic of each variation pattern. The approach is demonstrated with simulation and textile examples, in which the physical characteristics of the variation patterns are clearly revealed. The computer codes for implementing the approach are available in the spc4sts R package.