## 3 Design of Experiment
### Design of Experiment Steps
#### 3.1.5 Execute Design of Experiment and Analysis Data  
* Screening test  
In the screening test, 10 independent design parameters were selected as two factor levels that distinguish only the maximum and minimum values, and the test was constructed with the fractional factorial design of experiments. In the fractional factorial design of experiments, a total of 65 experiments were conducted. Using the JMP statistical program [19], a fractional factorial design of experiments was conducted. The fractional factorial design of experiments is expressed by dividing the factor into two levels, the maximum value and the minimum value denoted by 1 and \(-1\). In order to use the fractional factorial design of experiments method using the JMP statistical program, the values expressed as 1 and \(-1\) must be converted into actual values. Therefore, the maximum and minimum values of the independent design parameters were converted to fit the partial factor notation, and the corresponding data are shown in Figure 11.  
The suitability of the model obtained through the screening test can be judged using the graph in Figure 12--the narrower it is, the better the modeling. After the regression analysis, a Pareto plot and a \(p\)-Value were used to classify design independent parameters that have a great influence on design target parameters using the fractional factorial design of experiments. The Pareto graph shown in Figure 13 illustrates which factors affect the target design parameters more. The factors distributed over the upper side are factors that have a greater influence on the target design parameter. Figure 11: Converting fractional values to design parameter values. The regression coefficient, which is the result of the regression analysis, represents the relationship between the target design parameter and the independent design parameter. The \(p\)-value shown in Table 15 is used to determine whether the regression coefficient representing this relationship is an  
Figure 12: Screening test graph. Figure 13: Screening test Pareto plot. appropriate value. The \(p\)-value is expressed as a value between 0 and 1, and the closer to 0, the better the relationship. In general, the null hypothesis is considered rejected when the significance level has a value of 0.05 or less, and represents the relationship between the target design parameter and the independent design parameter well. In the present study, using the \(p\)-value of the regression coefficients and the results obtained from the regression analysis, five design independent parameters that greatly affect the design target parameters were selected, which are cruise speed, cruise altitude, passengers, baggage, and stall speed. * Response surface method  
In the response surface method (RSM), which is a statistical analysis method, when constructing a model in which design independent parameters have multiple effects on target design parameters, the response surface of the independent design parameters is estimated using a regression equation to optimize the model with minimum experiments. In this paper, the following equation, which is the central composite design (CCD) method among the response surface methods, was used as the second regression model [22]. \[y=\beta_{0}+\sum_{l=1}^{k}\beta_{i}x_{i}+\sum_{l=1}^{k}\beta_{i}x_{i}^{2}+\sum _{l=1}^{k-1}\sum_{j=i+1}^{k}\beta_{ij}x_{i}x_{j}, \tag{23}\]  
where \(y\) is the response, \(x_{i}\) and \(x_{j}\) are the design parameters, and \(\beta_{0}\), \(\beta_{i}\), \(\beta_{ii}\), and \(\beta_{ij}\) are the regression coefficients. As independent design parameters, five factors selected through screening tests were used. The CCD was used in the JMP statistical software and conducted 43 experiments. The graph of the result of the response surface method obtained using the central composite design is shown in Figure 14. The narrower the graph, the better the modeling.