In this paper, we provide a review of statistical methods that are useful in conducting computer experiments. Our focus is on the task of metamodeling, which is driven by the goal of optimizing a complex system via a deterministic simulation model. However, we also mention the case of a stochastic simulation, and examples of both cases are discussed. The organization of our review first presents several engineering applications, it then describes approaches for the two primary tasks of metamodeling: (i) selecting an experimental design; and (ii) fitting a statistical model. Seven statistical modeling methods are included. Both classical and newer experimental designs are discussed. Finally, our own computational study tests the various metamodeling options on two two-dimensional response surfaces and one ten-dimensional surface.

Purpose: The dimensional accuracy of three‐dimensional (3D) printed anatomical models is essential to correctly understand spatial relationships and enable safe presurgical planning. Most recent accuracy studies focused on 3D printing of a single pathology for surgical planning. This study evaluated the accuracy of medical models across multiple pathologies, using desktop inverted vat photopolymerization (VP) to 3D print anatomic models using both rigid and elastic materials.Methods: In the primary study, we 3D printed seven models (six anatomic models and one reference cube) with volumes ranging from ~2 to ~209 cc. The anatomic models spanned multiple pathologies (neurological, cardiovascular, abdominal, musculoskeletal). Two solid measurement landing blocks were strategically created around the pathology to allow high‐resolution measurement using a digital micrometer and/or caliper. The physical measurements were compared to the designed dimensions, and further analysis was conducted regarding the observed patterns in accuracy. All of the models were printed in three resins: Elastic, Clear, and Grey Pro in the primary experiments. A full factorial block experimental design was employed and a total of 42 models were 3D printed in 21 print runs. In the secondary study, we 3D printed two of the anatomic models in triplicates selected from the previous six to evaluate the effect of 0.1 mm vs 0.05 mm layer height on the accuracy.Results: In the primary experiment, all dimensional errors were less than 1 mm. The average dimensional error across the 42 models was 0.238 0.219 mm and the relative error was 1.10 1.13%. Results from the secondary experiments were similar with an average dimensional error of 0.252 0.213 mm and relative error of 1.52% 1.28% across 18 models. There was a statistically significant difference in the relative errors between the Elastic resin and Clear resin groups. We explained this difference by evaluating inverted VP 3D printing peel forces. There was a significant difference between the Solid and Hollow group of models. There was a significant difference between measurement landing blocks oriented Horizontally and Vertically. In the secondary experiments, there was no difference in accuracy between the 0.10 and 0.05 mm layer heights.Conclusions: The maximum measured error was less than 1 mm across all models, and the mean error was less than 0.26mm. Therefore, inverted VP 3D printing technology is suitable for medical 3D printing if 1 mm is considered the cutoff for clinical use cases. The 0.1 mm layer height is suitable for 3D printing accurate anatomical models for presurgical planning in a majority of cases. Elastic models, models oriented horizontally, and models that are hollow tend to have relatively higher deviation as seen from experimental results and mathematical model predictions. While clinically insignificant using a 1 mm cutoff, further research is needed to better understand the complex physical interactions in VP 3D printing which influence model accuracy.

Fused filament fabrication (FFF) is one of the most popular additive manufacturing (AM) techniques used to fabricate polymeric structures. However, these polymeric structures suffer from an inherent deficiency of weak inter-laminar tensile strength. Because of this weak inter-laminar strength, these parts fail prematurely and exhibit only a fraction of the mechanical properties of those fabricated using conventional means. In this paper, we study the effect of thermal annealing in the presence of an initially applied static uniaxial load on the ultimate tensile strength of parts fabricated using FFF. Tensile specimens or dogbones were fabricated from an acrylonitrile butadiene styrene (ABS) filament with a glass transition temperature (T_g) of 105 °C; these specimens were then isothermally annealed, post manufacture, in a fixture across a given range of temperatures and static loads. Tensile testing was then performed on these specimens to gauge the effect of the thermal annealing and static loading on inter-laminar tensile strength by measuring the ultimate tensile strength of the specimens. A design of experiments (DOE) approach was followed to calculate the main and interaction effects of the two factors (temperature and static loading) on the ultimate tensile strength, and an analysis of variance was conducted. Cross-sectional images of the specimens were studied to observe the changes in the mesostructure of the specimens that led to the increase in inter-laminar strength of the parts. The results show that temperature plays a dominant role in increasing the ultimate tensile strength and an 89% increase in the average ultimate tensile strength was seen corresponding to an annealing temperature of 160 °C. A change in the mesostructure of the parts is seen, which is characterized by an increase in bond length and void coalescence. These results can be helpful in studying the structural strength of 3D printed parts, and thus could eventually guide the fabrication of components with strength comparable to those of conventional manufacturing techniques.

Statistical analyses of time-series or spatial data have been widely used to investigate the behavior of ambient air pollutants. Because air pollution data are generally collected in a wide area of...