## 3 Methodology
### Design of Experiments  
The DOE of this study was planned to statistically analyze the FFF parameters significantly affecting the manufacturing performance changes. In addition, it identified the process parameter settings that optimized the individual and overall manufacturing performance of the FFF for the CFR-PEEK. For this, three critical process parameters for FFF (i.e., layer thickness, build orientation, and printing speed) were considered as the input parameters for the experiments. First, layer thickness was the measure of each layer height deposited by a nozzle tip. Layer thickness determined the number of layers deposited for a printed part, and thus printing time and precision could be affected by this process parameter. Two values (i.e., 0.2 mm and 0.3 mm) were considered as the levels of layer thickness for the experimental design. It was noted that the 0.2 mm layer thickness was a reference parameter level recommended by the manufacturer for CFR-PEEK printing. Second, the build orientation represented the direction of a printed part that stood on a build plate. Since the movement directions of the material deposition were varied depending on the build orientation of a fabricated part, it could critically affect the operational performance of the outputs. Two main directions on the \(x\) axis (i.e., 0\({}^{\circ}\) and 90\({}^{\circ}\)) were considered for the build orientation of each design type (see Figure 3). The last input parameter was the printing speed defined as the nozzle's movement speed at which the material was deposited. Printing speed was another key process parameter for FFF that may have needed adjusting in practice to decrease the production lead-time. However, this may have led to poor product quality due to unstable polymer extrusion caused by fast nozzle movements. Based on the recommended printing speed of the machine (i.e., 1200 mm/min), 1000 mm/min and 1400 mm/min (a range of \(\pm\)200 mm/min) were additionally considered to define three printing speed levels. Table 4 shows all the input parameters and their levels considered in the experimental design of this study. All the combinations of these parameters were applied to each design sample through Simplify3D. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Unit** & **Value** \\ \hline Bed temperature & \({}^{\circ}\)C & 120 \\ Nozzle temperature & \({}^{\circ}\)C & 510 \\ Perimeters & Layers & 3 \\ Number of top layers & Layers & 0 \\ Number of bottom layers & Layers & 0 \\ Infill pattern & - & Rectilinear \\ Infill angle & \({}^{\circ}\) & + 45/\(-\) 45 \\ Infill rate & \% & 100 \\ Extrusion with first layer & \% & 96 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fixed process parameters. Figure 3: Illustration of the build orientation for the experiments. (**a**) 0\({}^{\circ}\) on x-axis; (**b**) 90\({}^{\circ}\) on x-axis. Printing time, dimensional accuracy, and material cost were selected for the response variables of the DOE. Each performance measurement is summarized in Table 5, and more detailed information is described below. The printing time was measured by the duration in minutes between the start-time of the fabrication and the end-time of fabrication recorded by the machine. The start-time and end-time were recorded when the machine started fabrication after the completion of all the set-up processes and when the machine finished fabrication and started a cooling-down process, respectively. It was evident that an increase in printing speed led to a decrease in the total printing time. Moreover, the previous study reporting that layer thickness and build orientation were critical factors to minimize printing time [51] suggested that the different level combinations of the process parameters for CFR-PEEK may distinctively affect the printing time for each design. Dimensional accuracy is measured by the mean squared error (MSE) between the measured specifications and the actual dimensional specifications of a fabricated part (see Equation (1)).