## 4 Case Study
### Case Study Results  
The results obtained show that the control strategy proposed has notably improved the quality of the parts produced, observing a generalized decrease in the maximum deviations detected. Figure 11 shows the graphical representation of the mean values and the standard deviations of the maximum deviations detected at Stage_4. The dark blue line represents Case 1 data (Scenario_0). Red and purple lines represent Case 2 and 3, respectively, showing considerable improvements compared to Case 1. However, this improvement is even greater in Cases 4 and 5, represented with green and light blue lines, respectively.  
Considering the results related to productivity, every simulation has been run for the same simulation time (50,000 s) to compare the total number of finished products. Moreover, the throughput (finished products per hour) is also calculated. Likewise, with regard to the analysis of geometric quality, a limit of 3 mm (in absolute value) has been established for the maximum allowed deviation, obtaining the number of finished products that meet the specifications and being able to calculate the failure percentage with respect to total production (defect index). All these results are summarized in Table 1.  
The main conclusions based on the analysis of the results of Table 1 are presented below:  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Case 1** & **Case 2** & **Case 3** & **Case 4** & **Case 5** \\ \hline F.P. & 214 & 164 & 203 & 153 & 180 \\ Throughput & 15.41 & 11.81 & 14.61 & 11.01 & 12.96 \\ F.P.M.S. & 155 & 132 & 164 & 136 & 156 \\ D.I. & 27.57 & 19.51 & 19.21 & 11.11 & 13.33 \\ F.P.M.S.H. & 11.17 & 9.51 & 11.81 & 9.80 & 11.24 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results table. Six results are summarized: finished products (F.P); finished products that meet specifications (FPMS); finished products per hour (throughput); defect index (D.I); finished products that meet specifications per hour (FPMSH).  
Figure 11: Statistical analysis of maximum deviation detected at final inspection (Stage_4). (**a**) Mean; (**b**) standard deviation.  
* Case 1 presents the highest throughput. However, this case also has the highest D.I.
* The introduction of the feed-forward control (Cases 2 and 3) allows for improvement of the quality of the finished products and to reduce the D.I.
* In Cases 4 and 5, a backward control is also incorporated, observing a greater improvement in the quality results and obtaining the minimum D.I.
* The consideration of manual and automatic actuators in locator positioning considerably reduces the number of finished products. This effect is greater in the cases with manual actuators (Cases 2 and 4).
* In the cases where manual actuators are considered (Cases 2 and 4), the improvement in quality is not enough to offset the reduction of throughput.
* In Case 3, the results show that, despite reducing the total number of products produced, the improvement in quality causes an increase in the number of finished products that meet specifications, obtaining the best result.  
As expected, the introduction of measurement and adjustment operations causes a reduction in the units produced. However, if we combine these data with the quality results, we can see that the total number of finished products that meet specifications is notably higher in Case 3 (automatic feed-forward control). However, it would be interesting to develop other types of analysis, such as a cost study, to cross-check with the results obtained and to be able to perform a more complete multi-domain analysis.  
Beyond the analysis of the results of the case study, it is important to highlight that the implementation and simulation of the models for each scenario has been satisfactorily completed, obtaining results consistent with the conditions set out.