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Traditional Statistical Process Control methodologies face several challengeswhen monitoring defects in complex geometries, such as those of productsobtained via Additive Manufacturing techniques. Many approaches cannot beapplied in these settings due to the high dimensionality of the data and thelack of parametric and distributional assumptions on the object shapes.Motivated by a case study involving the monitoring of egg-shaped trabecularstructures, we investigate two recently-proposed methodologies to detectdeviations from the nominal IC model caused by excess or lack of material. Ourstudy focuses on the detection of both isolated large changes in the geometricstructure, as well as persistent small deviations. We compare the approach ofScimone et al. (2022) with Zhao and del Castillo (2021) for monitoring defectsin a small Phase I sample of 3D-printed objects. While the former control chartis able to detect large defects, the latter allows the detection ofnonconforming objects with persistent small defects. Furthermore, we addressthe fundamental issue of selecting the number of eigenvalues to be monitored inZhao and del Castillo's method by proposing a dimensionality reductiontechnique based on kernel principal components. This approach is shown toprovide a good detection capability even when considering a large number ofeigenvalues. By leveraging the sensitivity of the two monitoring schemes todifferent magnitudes of nonconformities, we also propose a novel jointmonitoring scheme that is capable of identifying both types of defects in theconsidered case study. Computer code in R and Matlab that implements thesemethods and replicates the results is available as part of the supplementarymaterial.

Statistical Process Monitoring of Isolated and Persistent Defects in Complex Geometrical Shapes