An Intrinsic Geometrical Approach for Statistical Process Control of Surface and Manifold Data
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This paper presents a new method for statistical process control (SPC) of a discrete part manufacturing system based on intrinsic differential-geometric properties of the parts. The approach estimates the spectrum of the Laplace-Beltrami (LB) operator of the scanned parts and uses a multivariate nonparametric control chart for on-line process control. An intrinsic method has the computational advantage of avoiding the difficult part registration problem. Our proposal brings SPC closer to computer vision and computer graphics methods, but the SPC problem differs in that small changes in shape or size of the parts need to be detected without completely filtering noise, which, if incremented, can be a signal to detect as well, while keeping a controllable false alarm rate. Both an on-line or "phase II" method and a scheme for starting up in the absence of prior data ("phase I") are presented, both based on recent work on permutation-based SPC methods. The run length and detection performance of the phase II and phase I methods are investigated. Comparison with a simpler SPC method based on registration of parts shows the LB spectrum methods to be much more sensitive to rapidly detect small changes in shape and size, including the practical case when the sequence of part surface datasets is in the form of large, unequal size meshes. A post-alarm diagnostic method to investigate the location of defects on the surface of a part is also presented. The methods can be applied to point cloud, mesh, and even voxel metrology data.
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