## 5 Reliability and Sensitivity Analysis Results  
From the above procedure, the reliability is analyzed based on the Kriging + TLFF + MCS, and the correctness of the reliability analysis results is verified by using the MCS method. \begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Type** \\ \hline \(\rho_{\text{BPN}}\) & Input variable \\ \(d\) & Input variable \\ \(\rho_{\text{CMDB}}\) & Input variable \\ \(t_{\text{CMDB}}\) & Input variable \\ \(I_{\text{min}}\) & Input variable \\ MATLAB\_input.m & MATLAB input script file \\ MATLAB\_output & MATLAB output file \\ MATLAB & MATLAB execution commands \\ \(I(x)\) & Output variable \\ \(\hat{G}(x)\) & Display function of the ignition \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Nodes in the simulation workflow. Figure 8: Ignition simulation workflow of the pyrotechnic igniter. Figure 7: Reliability simulation flow chart of the pyrotechnic igniter. The reliability results are presented in Table 5. The results, which are gained by the above methods, and the relative error, are 1.2%. The Kriging + TLFF + MCS method requires 81 samples to construct the initial Kriging model. However, the MCS sampling requires about \(10^{6}\) performance function evaluations. Therefore, the Kriging + TLFF + MCS method is suitable for the functional reliability analysis of the pyrotechnic igniter. According to the ignition reliability simulation program of the pyrotechnic igniter, the Kriging response surface model of some random variables, \(\mathbf{x}\), is shown in Figure 9.  
Table 6 shows the results of sensitivity analysis of ignition of the pyrotechnic igniter based on Equation (32). Among these, \(\rho_{\text{BPN}}\), \(n_{\text{CMDB}}\) and \(\rho_{\text{CMDB}}\) have a positive influence on the results of the mean sensitivity analysis; that is, increasing the mean value of these parameters improves the ignition reliability of the pyrotechnic igniter. Parameter \(d\) has a negative effect on the mean sensitivity; in other words, reducing the mean value of its parameters improves the ignition reliability of the igniter. The sensitivity results of the standard deviation indicate that reducing the standard deviation of each variable aids in improving the reliability. From the perspective of the design, the decrease in \(d\) is what mainly leads to the higher ignition reliability. As for the pyrotechnic igniter, it has a high reliability requirement, usually with 0.999 at least for the igniter device. Then, it should take some measures for reliability improvement according to the sensitivity results in Table 6. The straightest way towards improvement may be by decreasing the mean of the nozzle diameter \(d\). The reliability results with different mean values of nozzle diameter \(d\) are shown in Figure 10, which reveals that the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Mean Sensitivity** & **Standard Deviation Sensitivity** \\ \hline \(\rho_{\text{BPN}}\) & 0.03 & \(-\)0.001 \\ \(n_{\text{CMDB}}\) & 0.411 & \(-\)0.011 \\ \(d\) & \(-\)0.900 & \(-\)0.006 \\ \(\rho_{\text{CMDB}}\) & 0.136 & \(-\)0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Sensitivity results for the pyrotechnic igniter. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Reliability** & **Reliability Index** \\ \hline Kriging + TLFF + MCS (81 samples) & 0.8383 & 0.0719 \\ MCS (\(10^{6}\) samples) & 0.8281 & 0.0706 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results for the ignition reliability of the pyrotechnic igniter. Figure 9: Response surface of the Kriging model. (**a**) \(l\)–(\(d\), \(\rho_{\text{CMDB}}\)), (**b**) \(l\)–(\(d\), \(n_{\text{CMDB}}\)). igniter can meet its reliability requirement once the mean values of nozzle diameter \(d\) are controlled to be lower than 3.5 mm.