# Evaluating 3D Printers Using Data Envelopment Analysis
## 4 Results and Discussion  
Before proceeding to the actual evaluation of the 3D printers with DEA, a correlation analysis of the 11 output parameters was performed in order to identify the minimum number of parameters that could be efficiently employed in DEA, i.e., investigate whether some of the initial selected parameters could be ignored without affecting the evaluation results. A reduction in the number of parameters is desirable because it lowers the associated computational burden and generally reduces the time required for the analysis. The results of the correlation analysis of output parameters, performed with Minitab 17, are presented in Table 3. It can be observed that no strong correlation between any two of the output parameters exists. Nevertheless, there are pairs of parameters which seem to be somewhat correlated, as indicated by the fact that the corresponding \(p\)-values are lower than 0.05, but weakly, as indicated by the corresponding correlation coefficient values. Among the initial set of output parameters, four seem to be more often correlated with others: build volume, nominal power, X-Y resolution, and speed. In order to check whether some of these parameters could be omitted from the analysis, a preliminary DEA evaluation of the printers' set was conducted. This evaluation involved two sets of computations, the first taking into account all eleven outputs while the second only seven of them, excluding the four correlated parameters. The sole input parameter in both evaluations was the printers' price and both CCR and BCC, input-oriented DEA was performed. The corresponding preliminary evaluation results are presented in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Pinter**} & **Build** & **Num. ** & **Layer** & **Nozzle** & & **X-Y** & **No of** & **Nominal** & **Printing** & **Open** & **Weight** & **Price** \\
**\#** & **Volume** & **of Ex-** & **Trick-** & **Inness** & **(mm)** & **Plate** & **(tim)** & **als** & **(W)** & **(mm/s)** & **Source** & **(kg)** & **(USD)** \\ \hline
1 & 1459 & 1 & 50 & 0.35 & No & 15 & 4 & 20 & 60 & No & 1.00 & 315.00 \\
2 & 2627 & 1 & 150 & 0.40 \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Printer \#**} & \multicolumn{2}{c}{**CCR**} & \multicolumn{2}{c}{**BCC**} \\
**11 Outputs** & **7 Outputs** & **11 Outputs** & **7 Outputs** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 4: Results of CCR and BCC DEA evaluation of printers, considering all eleven output parameters and only seven of them. Examining the values in Table 4 is quite obvious that when taking into account all output parameters the BCC model leads to a very high number of efficient systems (28 out of 30), i.e., almost all printers are evaluated as efficient. The CCR model, on the other hand, provided a broader distribution of efficiency scores that permits a more useful assessment of printer efficiency. This was, to some extent, expected since the BCC frontier is more flexible and envelops the data in a tighter manner. Another observation is that omitting the four output parameters (build volume, nominal power, X-Y resolution, and speed) leads to a reduction of efficiency scores for most printers in both models. This reduction affects also the number of efficient units identified for both models; something that is exhibited more vividly in the case of BCC DEA where efficient units are reduced from 28 to 16. A possible explanation for this deterioration of scores for some of the efficient printers is that these systems have relatively high values for the omitted output parameters. Since the exclusion of all four parameters led to significant changes in the initially obtained scores, it has been decided to further explore whether some of the four output parameters under investigation could be excluded from further analysis.