## Experiments: Statistical Conformity

While determining the quality of the 3D printed objects, it was important to make sure that all the prints conformed to the specification. The two measurements of interests were the height of the object and the diameter, as they are required to determine surface area of the objects. When the right-circular cone and right-circular cylinder were modeled, they were designed to have a height and base diameter of 30 mm each. The statistical software, Minitab was used to analyze the data. Three factors were considered.

The first was pigmentation. It is important because it has an influence on the final print-shape. The user always has an option to use colored PLA filament. Adding colored pigments to natural PLA will give it different properties ^{[25]}. For an extruder temperature above 493 K (219.85 °C), the pigmentation becomes relevant as it affects the roughness of the final print ^{[23]}, hence a lower optimal temperature was chosen. The temperature can also alter the printing material’s crystallinity, depending on its color ^{[25]}, which will, in turn, affect the appearance of the printed object. In this experiment, the colors used were natural (translucent), pink, and blue.

The second factor was the amount of infill. The amount of infill has a range of 0 to 100%. An infill level of 20% and 80% are commonly used ^{[23]}, and on top of that, the two extreme levels of 0 (hollow) and 100% (solid) were chosen along with them. For a shorter print duration, a lower infill is chosen, for better stability, a higher infill is chosen ^{[23]}.

Finally, the third was the type of shape/deformation of the object, i.e., whether it gradually tapered (cone), or didn’t (cylinder). There are several other factors which can contribute to the quality of print such as the temperature of the nozzle, size of the nozzle, rate of filament retraction and many more ^{[9,20,21,26]}. They are not considered in this experiment.

Once the prints were complete, they were measured using a digital Vernier caliper for accurate measurements, and the grand averages of the values of the height and base diameter were obtained. The area of the base was also calculated. Each experiment was replicated to check for bias. The test used to perform the analysis was Anderson-Darling test using Minitab. The collected data was confirmed to be normal with a 95% confidence interval, as shown in Fig. 2 for cones of 80% infill. Similar data for other infill levels of all objects also exists and is made available in the supplementary material.

**Fig. 2** Graphs showing normality of the measurement data in the case of 80% infill level.

In Fig. 2, the factor that determines the significance of the result of the normality test is p-value. Since the p-values were higher than 0.05, the data collected is normal and does not have false-positives. The closer the p-value to 1, the more normally distributed is the data ^{[18,19]}. It also shows the standard deviation of the data.

Experiment-1 was a 2^{k} factorial design, where k is the number of factors; each factor has two levels. The pigmentation factors were selected to be natural (translucent) and pink, and the shape was tapered or none. Each time the experiment was performed, only a pair of the infill factors was chosen to keep the levels consistent. i.e., a combination of two among hollow, 20%, 80%, and solid were chosen. Depending upon the combination, an appropriate level was chosen to be the lower infill and higher infill level. This was done to determine the optimum levels of infill if the choice were among the combinations. The shape/deformation factor were tapered and none.

Experiment-2 was the same as the first, except the pigmentation was changed from pink to blue. Finally, Experiment-3 factored the colored PLAs (pink and blue) for analysis. Table 1 shows the factors and their associated levels. For simplicity, they are labelled as factors A, B, and C in the table and henceforth.

Factor |
Level 1 |
Level 2 |

Factor A (Pigmentation) | Color 1 | Color 2 |

Factor B (Infill) | Lower Infill | Higher Infill |

Factor C (Shape) | None | Tapered |

**Table 1.** Factors and their levels

## References

References can be found in the Introduction section.