*3.2. Cost Estimation Tool Validation*

The developed cost estimation tool was validated according to the procedure in Section 2.3. The average percentual deviations were registered for each of the production steps and are presented in Figure 10. Additionally, an influence of part complexity level in these deviations was noticed. Furthermore, this influence behaved slightly differently depending on the analyzed production step. A graph that depicts the variation in absolute percentual deviation of each production step, over the different part complexity levels can be observed in Figure 11.

**Figure 10.** Average percentual deviation for each part production step.

**Figure 11.** Absolute percentual deviation variation of each part production step, over different part complexity levels.

Cost Estimation Tool Validation: Case Study 2

An additional case study was conducted, as the tool can be adapted to different machines. Tests were conducted for CNC milling machines with vacuum tables. These machines conduct mainly: side-milling; end-milling; drilling and face-milling operations, which meant that the equations are presented in Section 2.1 could be used to estimate machining operations. It was noted that the parts usually produced in these machines did not exhibit much variability in terms of shape or complexity. This enabled a more accurate time prediction based on the equations, especially for the step regarding machining and finishing operations, without the need to define part complexity levels. One of the produced parts can be observed in Figure 12, as well as its technical drawing.

**Figure 12.** Produced part for Case Study 2 in a CNC milling center with vacuum table.

Regarding machining time operation for these parts, it was quite accurate for all the tested ones; however, regarding the performance of CAM software for the machining, it was the step that had the biggest deviation (this is depicted in Figure 13). This is due to the number of holes that these parts have, inducing delays from the developers of the CAM for these parts. Although some of these parts imply complex programming, it was noted that the average percentual deviation registered for this step (−19%) is not as accentuated as that registered for Case Study 1 (38%), this is because the complexity of some the part's machined in machines of this case study is considerably higher, especially in terms of geometry.

**Figure 13.** Average percentual deviation values for each of the production steps, for parts produced in milling centers with vacuum tables (Case Study 2).

A total of 10 parts were estimated and produced using these machines, registering the average percentual deviation values from the real production times, as presented in Figure 13.

#### **4. Discussion**

In Figure 10, it can be observed that the percentual deviations are mostly positive. This is quite satisfactory, as a positive percentual deviation is preferred since there will be no direct revenue loss from the production of the parts (associated with negative percentual deviations). For this case, the higher percentual deviation is for the "Finishing operations" step, exhibiting a −71% percentual deviation. This value is quite high, due to the complexity of these types of operations, and the fact that these are usually carefully performed, and are dependent on human work. The second highest percentual deviation is for the "CAM" step, at about 38%. The most influential production step on the overall production cost is the "Machining operations", due to the influence of machining time [34]. This step registered an acceptable percentual deviation of about 14%.

The part's complexity level was also found to influence the percentual deviation error, increasing this error for higher levels. This can be observed in Figure 11, where the highest values for all the considered production steps are registered for higher part complexity levels. Additionally, the error of "Finishing operations" tends to be higher when compared to the other production steps. Again, this is due to the difficulty in predicting these times, as there are many variables that cannot be controlled directly, such as finishing and inspection operations that are performed outside the machine [44]. This is corroborated by the data obtained from Case Study 2, presented in Figure 13. A side-by-side comparison of the average percentual deviation values for each of the production steps, for both case studies, can be observed in Table 9.


**Table 9.** Average percentual deviations for each of the production steps, for both case studies.

In Case Study 2, the produced parts were of similarly low complexity, with finishing operations being conducted inside the machine. This is reflected in the obtained results, as the values for percentual deviation are quite consistent and low when compared to the values for Case Study 1. For the second case study, the highest percentual deviation was −19%, for the "CAM" step, with all the other values being positive deviations.
