## 5 Results and Discussion
### Experimental Validation of Quantitative Reliability Calculations
#### 5.2.1 Quantitative Calculation of Reliability of Sea to Air Missions  
The cumulative state probability algorithm of the GO method is used for quantitative calculation, and the result is the probability of success of the sea-to-air mission. For the challenge of inaccurate calculation results due to the existence of common cause failure in the system, the common cause failure correction algorithm is employed to address this issue. All units in the ship electronic information system are simplified into two states, namely state 1 (normal working state) and state 2 (failure state). The ship electronic information system unit operator numbers for the sea-to-air mission are shown in Table 14. The first column is the name of the AADL unit contained in the ship electronic information system for sea-to-air missions, and the second column is the type of GO method operator that is converted to a GO diagram model pair. Operator 3 is a type 2 operator and operators 1 and 2 are type 5 operators, so according to the previous formula, operator 3 calculates the state accumulation probability as shown below. \[A_{R3}(1)=1-[1-A_{R1}(1)]\times[1-A_{R2}(1)]=1-[1-P_{S1}(1)]\times[1-P_{S2}(1)] \tag{30}\]  
Operator 4 is a type 6 operator and is calculated according to the previous formula as indicated below. \[A_{R4}(1)=A_{R3}(1)A_{R22}(1)P_{C4}(1) \tag{31}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Population** & **Crossover** & **Scale** & **Inertia** & **Learning Factor** & **Learning Factor** & **Iterations** & **Average** \\
**Size** & **Rate** & **Factor \(F\)** & **Weight w** & **C1** & **C2** & **C2** & **Calculation** \\ \hline
200 & 0.5 & 0.5 & 0.5 & 2 & 2 & 200 & 1.9709 \\ \hline
100 & 0.7 & 0.5 & 0.5 & 2 & 2 & 200 & 1.9804 \\ \hline
100 & 0.5 & 0.7 & 0.5 & 2 & 2 & 200 & 1.9773 \\ \hline
100 & 0.5 & 0.5 & 0.7 & 2 & 2 & 200 & 1.9732 \\ \hline
100 & 0.5 & 0.5 & 0.5 & 4 & 2 & 200 & 1.9791 \\ \hline
100 & 0.5 & 0.5 & 0.5 & 2 & 4 & 200 & 1.9788 \\ \hline
100 & 0.5 & 0.5 & 0.5 & 2 & 2 & 500 & 1.9717 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: The solution results of SMA-DE hybrid optimization algorithm under parameter-changing conditions. Operators 5, 6, 7, 9, 10, 11, and 12 are also type 6 operators, so the output of operator 12 can be introduced as follows:  
\[ \begin{array}{l}A_{R12}(1)=A_{R11}(1)A_{R28}(1)P_{C12}(1)\\ =A_{R10}(1)A_{R25}(1)P_{C11}(1)A_{R28}(1)P_{C12}(1)\\ =A_{R9}(1)A_{R22}(1)P_{C10}(1)A_{R25}(1)P_{C11}(1)A_{R28}(1)P_{C12}(1)\\ =A_{R6}(1)A_{R31}(1)P_{C9}(1)A_{R22}(1)A_{R4}(1)P_{C7}(1)P_{C8}(1)\\ P_{C10}(1)A_{R25}(1)P_{C11}(1)A_{R28}(1)P_{C12}(1)\\ =[P_{S1}(1)+P_{S2}(1)-P_{S1}(1)P_{S2}(1)]^{2}A_{R22}(1)P_{C4}(1)^{2}A_{R25}(1)P _{C5}(1)P_{C6}(1)\\ A_{R28}(1)A_{R31}(1)P_{C9}(1)A_{R22}(1)P_{C7}(1)P_{C8}(1)P_{C10}(1)A_{R25}(1)P _{C11}(1)A_{R28}(1)P_{C12}(1)\end{array}  \tag{32}\]  
Operators 13, 14, and 15 are two-state units, and operator 32 is a linear combination generator, so the output of operator 32 can be introduced as the following:  
\[A_{R32}(1)=0.5A_{R12}(1)P_{C13}(1)+0.3A_{R12}(1)P_{C14}(1)+0.2A_{R12}(1)P_{C15 }(1) \tag{33}\]  
Operator 22 is a type 2 operator, and according to the formula for or gate calculation, the formula for the cumulative probability of the output signal of operator 22 can be derived as follows:  
\[A_{R22}(1)=1-[1-A_{R20}(1)]\times[1-A_{R21}(1)] \tag{34}\]  
Operators 20, 21, 22; 23, 24, 25; 26, 27, 28; 29, 30, and 31 form a parallel redundant common cause failure structure, which is denoted as common cause component group 1, common cause failure group 2, common cause failure group 3, and common cause failure group 4, respectively. The probability of accumulation of states for signals 22, 25, 28, and 31, as derived from the previously described common cause failure modification algorithm, is shown below.