## 3 Results  
Considering the muscle force values that are provided in Table 1 and the value of bite force at the maximum capability of a normal mandible (un-fractured), the components of the forces as regards the chosen coordinate system are provided in Table 2, which represent the current design. Considering that the fracture indicator can be regarded as the maximum von Mises stress [29], the maximum value of von Mises stress is located at the cortical bone tissues, specifically at the right part with a value of \(\sigma_{max}^{Corleft}\approx 71\) MPa (cf. Figure 4a). Consequently, the maximum displacement is found at the right part of the cortical bone tissue (cf. Figure 4b), with a value of \(\delta_{max}^{CorLeftBack}\approx 0.3\) mm. Figure 3: Improvement in process output, where \(\times\) symbols represent the location of the data. The initial step of SSA is the Design Of Experiments (DOE), to build a Response Surface (RS) over the design space. The next step is to describe the variation range of the selected input parameters. The mean values are the forces applied to the current design with standard deviations of 5% (Table 2). All input parameters are normally distributed. Minimum and maximum values of forces are presented in Table 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Input Parameters**} & **Number** & **MP** & **SD** & **Min** & **Max** \\ \hline \(F^{Right}\) (N) & \(F_{y}^{Right}\) & \(P_{1}\) & \(-104\) & \(5.2\) & \(-200\) & \(-50\) \\ \hline \(F^{Left}\) (N) & \(F_{y}^{Left}\) & \(P_{2}\) & \(-104\) & \(5.2\) & \(-200\) & \(-50\) \\ \hline \multirow{4}{*}{\(M^{Right}\) (N)} & \(M_{x}^{Right}\) & \(P_{3}\) & \(26\) & \(1.3\) & \(2.6\) & \(26\) \\ \cline{2-7}  & \(M_{y}^{Right}\) & \(P_{4}\) & \(431.6\) & \(21.58\) & \(43.16\) & \(431.6\) \\ \cline{2-7}  & \(M_{z}^{Right}\) & \(P_{5}\) & \(27.7\) & \(1.39\) & \(2.77\) & \(27.7\) \\ \hline \multirow{4}{*}{\(M^{Left}\) (N)} & \(M_{x}^{Left}\) & \(P_{6}\) & \(-26\) & \(1.3\) & \(-26\) & \(-2.6\) \\ \cline{2-7}  & \(M_{y}^{Left}\) & \(P_{7}\) & \(431.6\) & \(21.58\) & \(43.16\) & \(431.6\) \\ \cline{2-7}  & \(M_{z}^{Left}\) & \(P_{8}\) & \(27.7\) & \(1.39\) & \(2.77\) & \(27.7\) \\ \hline \multirow{4}{*}{\(T^{Right}\) (N)} & \(T_{x}^{Right}\) & \(P_{9}\) & \(-28.3\) & \(1.42\) & \(-28.3\) & \(-2.83\) \\ \cline{2-7}  & \(T_{y}^{Right}\) & \(P_{10}\) & \(147.9\) & \(7.40\) & \(14.79\) & \(147.9\) \\ \cline{2-7}  & \(T_{z}^{Right}\) & \(P_{11}\) & \(-133.9\) & \(6.70\) & \(-133.9\) & \(-13.39\) \\ \hline \multirow{4}{*}{\(T^{Left}\) (N)} & \(T_{x}^{Left}\) & \(P_{12}\) & \(28.3\) & \(1.42\) & \(2.83\) & \(28.3\) \\ \cline{2-7}  & \(T_{y}^{Left}\) & \(P_{13}\) & \(147.9\) & \(7.40\) & \(14.79\) & \(147.9\) \\ \cline{2-7}  & \(T_{z}^{Left}\) & \(P_{14}\) & \(-133.9\) & \(6.70\) & \(-133.9\) & \(-13.39\) \\ \hline \multirow{4}{*}{\(p^{Right}\) (N)} & \(p_{x}^{Right}\) & \(P_{15}\) & \(187.4\) & \(9.37\) & \(18.74\) & \(187.4\) \\ \cline{2-7}  & \(p_{y}^{Right}\) & \(P_{16}\) & \(325.1\) & \(16.26\) & \(32.51\) & \(325.1\) \\ \cline{2-7}  & \(p_{z}^{Right}\) & \(P_{17}\) & \(-76.5\) & \(3.83\) & \(-76.5\) & \(-7.65\) \\ \hline \multirow{4}{*}{\(p^{Left}\) (N)} & \(p_{x}^{Left}\) & \(P_{18}\) & \(-187.4\) & \(9.37\) & \(-187.4\) & \(-18.74\) \\ \cline{2-7}  & \(p_{y}^{Left}\) & \(P_{19}\) & \(325.1\) & \(16.26\) & \(32.51\) & \(325.1\) \\ \cline{1-1} \cline{2-7}  & \(p_{z}^{Left}\) & \(P_{20}\) & \(-76.5\) & \(3.83\) & \(-76.5\) & \(-7.65\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of forces as well as related probabilistic parameters. MP: Mean Point and SD: Standard Deviation. Figure 4: Distribution of (**a**) von Mises stresses in MPa, and (**b**) total displacements in mm. The minimum and maximum points regarding each parameter from the output parameters were roughly established through Min-Max search on the RS (cf. Table 3).