## 4 Discussion
### Uncertainty and Cumulative Error  
Table 10 lists accuracy measurement studies [81; 82; 83; 84; 85; 86; 87; 88; 89; 90; 91; 92] of additively manufactured constructs using various anatomical models, imaging medium and modality, measurement principles, AM technologies, and measurement instruments. Most studies have used CT imaging technology to image a dry skull. Though imaging a dry skull can account for an approximated error analysis, this is almost never the case in clinical practice and can yield unrealistic values. Several studies have imaged the skull in water to simulate close to realistic cases. However, the tissue surrounding the bone can certainly vary in  
density. Due to ethical concerns, only few studies have used human skull with and without soft tissue for accuracy analysis, but they can still be limited to manual contact measurements. In fact, majority of the studies have employed a contact measurement principle of repeated measurements between anatomical landmarks using calipers to estimate the overall error of the process chain. However, this principle can easily induce error in pinpointing the exact location of the freeform anatomical surface points in multiple models for linear measurements. This error was mitigated by introducing artificial reference features, i.e., grooved holes [84] or markers [58,90], into the 3D model of the specimens before manufacturing. Though this has provided an ease of pinpointing the regions of interest on the freeform geometry, the measurement principle is often laborious and is limited in terms of number of measurements. Further in literature, human error has been mitigated using CMM for data collection.  
In the present case study, the prescribed methodology aims to overcome the limitations. Principles of GUM are exploited to develop a systematic approach to evaluate overall cumulative error propagating from each process step. The use of animal model simulates a realistic case that also enables tissue removal and measurements of the dry skull to obtain a gold standard. Contact measurements are conducted on a tailor-made QA Phantom through controlled experiments that take advantage of the impeccable accuracy of the tactile-CMM. Optical measurements are conducted on freeform geometry of the dry skull and the additively manufactured implant without geometric manipulation. Subsequent mean difference is evaluated through an adequate number of measurements in the order of 500,000. The method also traces the measurements to the SI units using calibrated instruments. The prescribed methodology has potential of being a standard quality control and assurance protocol that can be applicable to various imaging, thresholding, modeling, and AM processes.  
The LD and NLD components of combined uncertainty can yield a reliable measure of possible error of the end-use implant including resolution, non-linearity, and magnification error of CT imaging, segmentation error of 3D thresholding, resolution of 3D modeling, and resolution, non-linearity, and magnification error of AM including heat treatment and support removal. Further, uncertainty in terms of LD and/or NLD can also be calculated for each individual process step. The LD component allows for evaluating error as a function of length for the implant.  
Worst-case cumulative error is calculated for the maximum length of the freeform implant which takes into account intricate features of the shape as a result of each process step. Evidently, a smaller dimension would yield a smaller error. Further, boundary surface plays a critical role to the length measurement of the implant which is dictated by the NLD component of thresholding.  
Uncertainty results for both one and two boundary surfaces are comparable to those reported in the literature. However, when considering the worst-case cumulative error, in particular for two boundary surfaces, the error peaks compared to the reported mean differences.