# Evaluating 3D Printers Using Data Envelopment Analysis
## 4 Results and Discussion
The test was implemented in R program language and employed the bootstrapping method for testing the following hypotheses:  
**Hypothesis 0 (H0). **: 3_D Printers excibit constant returns to scale (CCR)._
**Hypothesis 1 (H1). **: 3_D Printers excibit variable returns to scale (BCC)._  
As indicated by the test results, H0 can be accepted at a 5% confidence level; hence the CCR model has been employed for further evaluation. Having excluded the BCC model from further analysis and reduced the number of outputs to nine (building volume, number of extruders, layer thickness, nozzle diameter, presence of heated bed, number of materials, printing speed, open-source character, and weight) the analysis proceeded to the evaluation of an extended sample of 3D printers. The extended sample included eight additional 3D printers, numbered as printers 31-38 (see Table 7), which were highly rated and received favorable reviews from experts at specialized web sites (all3 dp.com, www.aniwana.com, 3 dforged.com; all web sites accessed on various dates between July 2018-October 2019). The actual number of highly rated printers in the sample was nine, since printer 24, which was randomly included in the initial sample, received favorable reviews, also. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{11}{c}{**(a)**} \\ \hline
**Printer \#** & **A** & **B** & **C** & **D** & **AB** & **AC** & **AD** & **BC** & **BD** & **CD** \\ \hline  
0.2028 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Evaluated efficiency of 3D printers, according to the CCR (**a**) and the BCC (**b**) model, for the output combinations of Table 5.  
The DEA evaluation results for the extended sample, according to the CCR model, are presented in the second column of Table 8. The results of the analysis show a wide distribution of efficiency scores among printers and a rather clear distinction between efficient and less efficient units. In an effort to further reduce the number of output parameters to simplify the data collection and analysis process, the influence of nozzle diameter and open-source character on the evaluation results was examined. The evaluated efficiencies, excluding both and each of the above parameters are presented also in Table 8. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{10}{c}{**(b)**} \\ \hline
**Printer \#** & **A** & **B** & **C** & **D** & **AB** & **AC** & **AD** & **BC** & **BD** & **CD** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 7: Technical specifications/parameters and price of the additional top-rated 3D printers. Comparing the results considering all nine parameters (second column) to those obtained without considering nozzle diameter (third column), hardly any difference is observed. This is definitely not the case for the efficiency ratings evaluated when the open-source character (fourth column) or both parameters are ignored. Interestingly enough, the efficiency scores in the last two columns of Table 8 are almost identical. These two observations indicate that ignoring the nozzle diameter does not notably alter the overall 3D printer evaluation results and implies that the specific parameter could be also omitted. Such a behavior could be probably attributed to the fact that there is only a very limited variation of this particular output/specification among the 38 3D printers examined (the great majority of printers is equipped with nozzles of 0.40 mm diameter). Examining the efficiency scores for the nine top-rated printers in the sample (printers 31-38 and printer 24), we observe that only five of them were evaluated as highly efficient. These are printers 35, 32, and 31, which display maximum efficiency, as well as printers 33 and 38, which achieve efficiency scores close to one. The remaining four top-rated systems (printers 24, 34, 36, and 37), on the other hand, failed to achieve high efficiency scores in the DEA evaluation. It should also be noted that all other printers, which were not considered