## 3 Parameters Studies and Discussions
### Orthogonal Design Test
#### 3.2.3 Selection of Active Factors
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Factors**} & \multicolumn{3}{c}{**The Mean Square Errors**} \\ \cline{2-5}  & \(F_{z}\) & \(F_{x}\) & \(F_{y}\) & \(A_{c}\) \\ \hline \(x_{1}\) & 15.70742 & 0.02138 & 0.60160 & 44.53319 \\ \(x_{2}\) & 196.36442 & 2.11052 & 2.69865 & 115.39593 \\ \(x_{3}\) & 0.24615 & 0.13753 & 0.21154 & 69.21850 \\ \(x_{4}\) & 0.05153 & 1.91301 & 1.04544 & 1557.16874 \\ \(x_{5}\) & 0.24876 & 0.27282 & 0.08978 & 161.02762 \\ \(x_{6}\) & 0.05817 & 0.88098 & 0.08544 & 13.81811 \\ \(x_{7}\) & 0.02298 & 0.98206 & 0.25764 & 1.50246 \\ \(x_{8}\) & 0.46019 & 0.61019 & 0.15663 & 16.25891 \\ \(x_{9}\) & 0.22571 & 0.08459 & 0.41872 & 1.14816 \\ \(x_{10}\) & 0.20981 & 0.02352 & 0.62467 & 219.01455 \\ \(x_{11}\) & 0.09366 & 0.11422 & 0.12611 & 9.55418 \\ \(x_{12}\) & 0.26766 & 0.12900 & 0.25309 & 320.33627 \\ \(x_{13}\) & 4.48885 & 31.47385 & 47.28643 & 9.62576 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The mean square errors of 13 analysis factors for various observation objectives. (2) \(P\) statistic value  
When the \(P\) statistic is adopted for selecting active factors, \(l\) = 7 is set according to the calculation principle of \(l\) in this paper. The given global significance level is \(\alpha\) = 0.05. Table 5 shows the \(P\) statistic of all analysis factors calculated according to Equation (13). Figure 12 shows the \(P\) statistic positions of the observation parameters corresponding to different analysis factors in contrast with those of the critical value. As shown in Figure 12, for \(F_{z}\), the \(P\) statistic values of 3 analysis factors are higher than the critical value, namely \(x_{1}\), \(x_{2}\) and \(x_{13}\) are the significant influence factors of \(F_{z}\). Similarly, \(x_{13}\) is the significant influence factor of \(F_{x}\) and \(F_{y}\), \(x_{4}\), \(x_{5}\), \(x_{10}\) and \(x_{12}\) are the significant influence factors of \(A_{c}\). Figure 11: Selection results of \(H\) statistic values. Figure 12: Selection results of \(P\) statistic values. (3) \(B\) statistic value  
According to Equation (16) and the \(B\) statistic calculation process, the \(B\) statistics of 13 analysis factors can be obtained, see Table 6. As shown in Table 6, for \(F_{z}\), the \(B\) statistic values of 3 analysis factors are higher than the critical value, namely \(x_{1}\), \(x_{2}\) and \(x_{13}\) are the significant influence factors of \(F_{z}\). Similarly, \(x_{13}\) is the significant influence factor of \(F_{x}\) and \(F_{y}\), \(x_{4}\), \(x_{10}\) and \(x_{12}\) are the significant influence factors of \(A_{c}\). According to the selected active factors of \(H\)/\(P\)/\(B\) statistical values, the factors significantly influencing turnout rail surface initiated RCF are \(x_{1}\), \(x_{2}\), \(x_{4}\), \(x_{10}\), \(x_{12}\) and \(x_{13}\), referring to train speed, axle load of vehicle, wheel profile, stock rail cant, integral vertical track stiffness and wheel-rail friction coefficient, respectively. In the previous work [1], [PERSON] and [PERSON] presented axle load, wheel-rail friction coefficient, and wheel/rail profiles as the parameters which could affect the performance of railway turnout significantly. The results of this paper are basically the same with previous conclusions, and the previous results could be corroborated by this paper. In addition, the previous work is investigated based on an ordinary railway turnout which has a significant difference with the high-speed railway turnout, such as the structure, wheel/rail contact relationship and so on. Therefore, there are some different results, such as the integral vertical track stiffness. The outcome of this work could provide a theoretical guidance for the simulation and prediction of surface initiated RCF of high-speed railway turnouts.