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.

翻译：传统统计过程控制方法在监测复杂几何形状（如增材制造技术所得产品）中的缺陷时面临诸多挑战。由于数据的高维性及物体形状缺乏参数化假设与分布假设，许多方法在此类场景下难以适用。受一项涉及蛋形小梁结构监测的案例研究启发，我们探究了两种近期提出的方法，以检测因材料过量或缺失导致的标称IC模型偏差。本研究聚焦于两类缺陷的检测：几何结构中的孤立大幅变化与持续性小幅偏差。我们对比了Scimone等（2022）与Zhao和del Castillo（2021）的方法，用于监测3D打印物体的小规模第一阶段样本缺陷。前者控制图能检测大幅缺陷，而后者可发现存在持续性小幅缺陷的不合格物体。此外，针对Zhao与del Castillo方法中需监测特征值数量的基本问题，我们提出了一种基于核主成分的降维技术。该技术即使在考虑大量特征值的情况下仍展现出良好的检测能力。通过利用两种监测方案对不同程度非合规性的灵敏度差异，我们还提出了一种新型联合监测方案，能够在所述案例研究中识别两类缺陷。实现这些方法并复现结果的R语言与Matlab计算机代码作为补充材料提供。