## 3 TIES Method
### Determine System Feasibility and Viability  
In order to determine the feasibility and viability of the system, the MCS results were fed into the CDF and the feasibility of the system was assessed through a comparison with the target values. The desirability function was then used for the results of the RSM. A schematic of the feasibility and viability of the system is presented in Figure 6.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Regression Coefficient** & \multirow{2}{*}{**MTOW**} & \multirow{2}{*}{**Wing Span**} & \multicolumn{1}{c}{**Wing Root**} & \multicolumn{1}{c}{**Wing Loading**} & \multicolumn{1}{c}{**Power-to-Weight**} & \multicolumn{1}{c}{**Fuel Efficiency**} \\ \cline{1-1} \cline{5-6} \multicolumn{1}{c}{**of Design Variables**} & & & **Chord** & **(W/S)** & **(P/W)** & **Efficacy** \\ \hline Intercept & 2562.3 & 33.843 & 5.8205 & 17.0 & 0.0705 & 13.544 \\ Range & 51.260 & 0.3290 & 0.0572 & 0.0 & \(-\)0.0002 & 0.2355 \\ Maximum speed & 67.907 & 0.4568 & 0.0786 & 0.0 & 0.0055 & \(-\)0.4008 \\ Cruising speed & 101.58 & 0.6595 & 0.1140 & 0.0 & 0.0002 & \(-\)0.7820 \\ Cruising altitude & \(-\)31.397 & \(-\)0.2044 & \(-\)0.0352 & 0.0 & \(-\)0.0014 & 0.1483 \\ Passengers & 223.24 & 1.4355 & 0.2467 & 0.0 & \(-\)0.0026 & \(-\)0.7584 \\ Takeoff ground roll & \(-\)0.0724 & \(-\)0.0005 & \(-\)0.0002 & 0.0 & 0.0000 & 0.0001 \\ Stall speed & \(-\)104.99 & \(-\)2.7368 & \(-\)0.4712 & 2.0 & 0.0008 & 0.1836 \\ \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\ Passengers \(\times\) Passengers & 41.641 & 0.2436 & 0.0444 & 0.0 & \(-\)0.0005 & \(-\)0.0983 \\ Takeoff ground roll \(\times\) & 1.6614 & 0.0086 & \(-\)0.0006 & 0.0 & \(-\)0.0005 & 0.0067 \\ Stall speed \(\times\) Stall speed & 22.2014 & 0.3486 & 0.0594 & 0.0 & \(-\)0.0005 & \(-\)0.1433 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Regression coefficients of a response surface model.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Design Target Variables** & \(R^{2}\) & \(AR^{2}\) \\ \hline MTOW & 0.99 & 0.99 \\ Wing span & 0.99 & 0.99 \\ Wing root chord & 0.99 & 0.99 \\ Wing loading (W/S) & 1 & 1 \\ Power-to-weight (P/W) & 0.92 & 0.90 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Coefficient of determination and adjusted R-squared of response surface equation (RSE).  
Based on the results generated by the MCS, it was observed that the feasible design space for MTOW is from 2238 to 3219 lbs. and the target value for the MTOW is less than 2500 lbs. A probability that is capable of satisfying the target value for MTOW is 26.7%. In a similar way, the feasible design space for wing span is from 29 to 40 ft and a probability that is capable of satisfying the target value for wind span is 100%. The feasible design space for wing root chord is from 5.1 to 6.9 ft and a probability that is capable of satisfying the target value for wind root chord is 2.5%. The feasible design space for W/S is from 15 lb/\(ft^{2}\) to 19 lb/\(ft^{2}\) and a probability that is capable of satisfying the target value for W/S is 50%. The feasible design space for the P/W ratio is from 0.061 hp/lb to 0.089 hp/lb and a probability that is capable of meeting the target value for the wind span is 50%. With regard to fuel efficiency, it is a qualitative variable, and the feasible design space is from 9.36 to 14.84 mpg. Although the wing root chord design variable appears to show a low probability that meets the target value, it was confirmed that all design variables could be used for the optimization process. Hence, this indicates that it is possible to optimize the baseline design values in the feasible design space.