## 5 Numerical Experiments  
Modelling the fuzzy constraints including cost, weight and volume under consideration of uncertainty for the four benchmarks of RRAP aiming to maximize the system reliability, the experimental results are solved by the adopted SSO algorithm. The similar literature does not exist resulting our work cannot be compared to the other in literature. However, the performance is compared with the state-of-the-art algorithms including PSO, hybrid of PSO and SSO (named PSSO), and GA. Thus, the parameters of these algorithms are defined as following:  
SSO: Cg = 0.4, Cp = 0.7, Cw = 0.9  
PSO: C1 = C2 = 2, W = 0.9  
GA: Cr = 0.8 (crossover rate), Cm = 0.2, elite selection  
For fairness, the following conditions and data settings of the four algorithms including the adopted SSO, PSO, PSSO, and GA are consistent. While performing the experiments, the algorithms are coded using DEV C++ with 64-bit Windows 10, implemented on an Intel Core i7-6650U CPU @ 2.20 GHz 2.21-GHz notebook with 64 GB of memory. Total 1000 generations are ran and 50 solutions are obtained for each algorithm. The confidence level for the credibility constraints of weight and volume in Equations (30)-(37) has been defined as \(\varepsilon\) = 0.95, and also \(\lambda\) = 0.95. The data, which the weight and volume of components have been converted to the triangular fuzzy number, used in the four benchmarks of RRAP is shown in following Tables 1-3. The system reliability and running time are obtained to compare the performance of the adopted SSO algorithm with PSO, PSSO and GA for the four benchmarks of RRAP. The statistics of experimental results including minimum (Min), maximum (Max), average, and standard deviation (STD) of the system reliability and running time and also the convergent generation number for the best solution (denoted as \(\text{Gen}_{\text{convergent}}\)) of the system reliability and running time are analyzed and shown in following Tables 4-11. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Subsystem \(i\)** & \(\mathbf{10^{5}a_{i}}\) & \(\beta_{i}\) & \(w_{i}v_{i}^{2}\) & \(w_{i}\) & \(V\) & \(C\) & \(W\) \\ \hline
1 & 2.330 & 1.5 & (0.8, 1, 1.2) & (6.5, 7, 7.5) & & & \\
2 & 1.450 & 1.5 & (1.8, 2, 2.2) & (7.5, 8, 8.5) & & & \\
3 & 0.541 & 1.5 & (2.8, 3, 3.2) & (7.5, 8, 8.5) & 110 & 175 & 200 \\
4 & 8.050 & 1.5 & (3.8, 4, 4.2) & (5.5, 6, 6.5) & & & \\
5 & 1.950 & 1.5 & (1.8, 2, 2.2) & (8.5, 9, 9.5) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data for benchmark 1 and benchmark 3[24; 34; 37]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Subsystem \(i\)** & \(\mathbf{10^{5}a_{i}}\) & \(\beta_{i}\) & \(w_{i}v_{i}^{2}\) & \(w_{i}\) & \(V\) & \(C\) & \(W\) \\ \hline
1 & 2.500 & 1.5 & (1.8, 2, 2) & (3, 3.5, 4) & & & \\
2 & 1.450 & 1.5 & (3.8, 4, 4) & (3.5, 4.0, 4.5) & & & \\
3 & 0.541 & 1.5 & (4.8, 5, 5.2) & (3.5, 4.0, 4.5) & 180 & 175 & 100 \\
4 & 0.541 & 1.5 & (7.8, 8, 8.2) & (3, 3.5, 4) & & & \\
5 & 2.100 & 1.5 & (3.8, 4, 4.2) & (4, 4.5, 5) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Data for benchmark 2[24; 34; 37]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Subsystem \(i\)** & \(\mathbf{10^{5}a_{i}}\) & \(\beta_{i}\) & \(w_{i}v_{i}^{2}\) & \(w_{i}\) & \(V\) & \(C\) & \(W\) \\ \hline
1 & 1 & 1.5 & (0.8, 1, 1.2) & (5.5, 6, 6.5) & & & \\
2 & 2.3 & 1.5 & (1.8, 2, 2.2) & (5.5, 6, 6.5) & & & \\
3 & 0.3 & 1.5 & (2.8, 3, 3.2) & (7.5, 8, 8.5) & & & \\
4 & 2.3 & 1.5 & (1.8, 2, 2.2) & (6.5, 7, 7.5) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Data for benchmark 4[24; 34; 37].