Industrial statistics and manifold data

Complex and not only big data exist everywhere in industry and how to control and optimize systems based on these data types is an important aspect of modern Quality Engineering. One fundamental type of complexity occurs when data lies on a lower dimensional, curved subspace or manifold. We review a new approach for statistical process monitoring of point cloud, mesh and voxel data based on intrinsic geometrical features of the 2-D manifold (surfaces) of scanned manufactured parts. Monitoring intrinsic properties avoids computationally expensive registration pre-processing of the data sets. We also present a review of recent approaches for analyzing and designing experiments where either the response or the covariates lie on manifolds.