  Traditional Statistical Process Control methodologies face several challenges
when monitoring defects in complex geometries, such as those of products
obtained via Additive Manufacturing techniques. Many approaches cannot be
applied in these settings due to the high dimensionality of the data and the
lack of parametric and distributional assumptions on the object shapes.
Motivated by a case study involving the monitoring of egg-shaped trabecular
structures, we investigate two recently-proposed methodologies to detect
deviations from the nominal IC model caused by excess or lack of material. Our
study focuses on the detection of both isolated large changes in the geometric
structure, as well as persistent small deviations. We compare the approach of
Scimone et al. (2022) with Zhao and del Castillo (2021) for monitoring defects
in a small Phase I sample of 3D-printed objects. While the former control chart
is able to detect large defects, the latter allows the detection of
nonconforming objects with persistent small defects. Furthermore, we address
the fundamental issue of selecting the number of eigenvalues to be monitored in
Zhao and del Castillo's method by proposing a dimensionality reduction
technique based on kernel principal components. This approach is shown to
provide a good detection capability even when considering a large number of
eigenvalues. By leveraging the sensitivity of the two monitoring schemes to
different magnitudes of nonconformities, we also propose a novel joint
monitoring scheme that is capable of identifying both types of defects in the
considered case study. Computer code in R and Matlab that implements these
methods and replicates the results is available as part of the supplementary
material.
