## 4 Results
### Application of the Monte Carlo Method
#### 4.1.3 Range of the Input Parameters  
As mentioned in Section 3.3, the range of the input parameters was initially defined by modifying their nominal values in a 10%. However, the results might vary if that range is modified for some of the parameters, or if their nominal values are changed.  
First, the effect of modifying the ranges of all the inputs was analysed. Figure 3 shows the comparison of the total-effect indices when using different range sizes.  
It can be seen that if the range of all the input parameters is modified equally, there are no significant differences in the results. Thus, the robustness of the method is proven, as the same effect is obtained for all the input parameters regardless of the variation of the range size.  
The effect of modifying the range of only one specific input was also analysed. Two different cases were analysed, \(D_{\text{ri}}\) and \(g\), as they are the two inputs that have the highest effect considering both the torque and the vibrations.  
Figures 4 and 5 show the total-effect indices when the range of \(D_{\text{ri}}\) is reduced to a 5% of its nominal value, and when the range of \(g\) is increased to a 20% of its nominal value, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & \(D_{\text{ri}}\) & \(h_{\text{sy}}\) & \(h_{\text{m}}\) & \(g\) & \(L_{\text{s}}\) & \(w_{\text{t}}\) & \(w_{\text{sl}}\) & \(h_{\text{t}}\) & Total \\ \hline Vibration & \(S_{i}\) & 0.179 & 0.258 & 0.002 & 0.118 & 0.007 & 0.122 & 0.114 & 0.254 & 1.055 \\  & \(S_{i}^{\text{tot}}\) & 0.083 & 0.251 & 0.004 & 0.119 & 0.007 & 0.012 & 0.012 & 0.144 & 0.631 \\ \hline Torque & \(S_{i}\) & 0.490 & 0.000 & 0.018 & 0.017 & 0.493 & 0.000 & \(-\)0.008 & \(-\)0.008 & 1.002 \\  & \(S_{i}^{\text{tot}}\) & 0.492 & 0.000 & 0.017 & 0.017 & 0.493 & 0.000 & 0.000 & 0.000 & 1.020 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Sensitivity indices—Dependent inputs.  
Figure 3: Total-effect indices for several input range sizes, (**a**) Vibration, (**b**) Torque.  
It can be observed that the nominal value of the parameters also modifies the results of the sensitivity analysis. In both cases, a lower nominal value results in a higher influence of that input, even though the changes are not as substantial as when modifying the range.  
Therefore, if a sensitivity analysis is performed for a certain machine, the conclusions that are obtained can be extrapolated to other similar machines. Even though the values of the indices will not be correct, the trends will be very similar.  
Nevertheless, when performing a sensitivity analysis, it is important to be aware of the influence of the ranges selected for the input parameters. The most correct approach would be to select the ranges considering the design restrictions of each particular case. From a theoretical point of view, as in this work, where no particular restrictions exist, the fairest approach is to set all the inputs within the same percentage. The value of that percentage is not relevant, as long as the same value is applied to all of the inputs, and feasible values are obtained for all the dependent parameters.