# Reliability Analysis of C\({}^{4}\)ISR Systems Based on Goal-Oriented Methodology
## 4 Results  
In this paper, the unit reliability is calculated under the service time of 100 h, see in Table 4. Units of the C\({}^{4}\)ISR system in this paper are two-state, that are, working (0) and failed (1). The reliability computation of the GO model follows a designed procedure. First, the success probability of signal flow 7 and 9 can be calculated as:  
\[ \begin{array}{c}A_{7}(0)=A_{1}(0)P_{2}(0)P_{4}(0)P_{5}(0)P_{6}(0)\\ A_{9}(0)=A_{7}(0)A_{8}(0)\end{array}  \tag{14}\]  
According to the system structure, the signal flows to 10 and 16, respectively at the same time. Obviously, the operator is affected by a common cause. Therefore, in combination with the common cause failure, the output signal flow 22 is corrected by the \(\beta\)-factor model. Note that the common cause failure rate is set to be \(C=\beta\lambda=0.000236\). Hence, the success probability of signal flow 10 is reached by:  
\[ \begin{array}{c}A_{10}(0)=A_{9}(0)P_{9}(0)\\ A_{22}(0)=A_{10}(0)[P_{10}(0)P_{12}(0)P_{13}(0)P_{15}(0)+P_{16}(0)P_{17}(0)P_{ 19}(0)P_{20}(0)\\ -P_{10}(0)P_{12}(0)P_{13}(0)P_{15}(0)P_{16}(0)P_{17}(0)P_{19}(0)P_{20}(0)]\\ -A_{10}(0)[P_{15}(0)+P_{20}(0)-P_{15}(0)P_{20}(0)]\,C\end{array}  \tag{15}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Unit** & **Failure Rate** & **Unit** & **Failure Rate** \\ \hline Communication module & 0.0001477323 & Network module & 0.0002001001 \\ \hline Communication module & 0.0001716049 & Network module application software & 0.0002684325 \\ \hline Power supply & 0.0000079940 & Signal receiver & 0.0002394779 \\ \hline Server & 0.0001998801 & Server application software & 0.0002251758 \\ \hline Information exchange module & 0.0002967919 & Integrated Information & \\ application software & 0.0002967919 & Management Module & 0.0002389058 \\ \hline Information Exchange Module & 0.0001999200 & Data storage module & 0.0000800336 \\ \hline RAID controller & 0.0001331071 & Hard disk & 0.0000799472 \\ \hline Data storage module & 0.0001878982 & Data loading module & 0.000208103 \\ application software & 0.0001598977 & Data load module & 0.0001596233 \\ \hline EDID reader & 0.0001999200 & Motherboard module & 0.0001335425 \\ \hline EDID reader application software & 0.0002357298 & Comprehensive decompression module & 0.0001595660 \\ \hline Comprehensive information & & Comprehensive decompression module & 0.0002160759 \\  management module & 0.0002722646 & application software & 0.0002160759 \\ application software & & & \\ \hline CPEX main processor module & 0.0002077888 & USB interface expansion module & 0.0001332711 \\ \hline CPEX main processor module & 0.0001999500 & Display processing module & 0.0001335425 \\ \hline USB interface extension module & 0.0002038553 & Display processing module & 0.0001601643 \\ application software & & & \\ \hline Touch display & 0.0000666867 & Monitor & 0.0000666867 \\ \hline Multifunctional information & 0.0001353867 & Control exterior parts & 0.0001598977 \\ demodulation module & & & \\ \hline Multifunctional information & & & \\ demodulation module & 0.0001771930 & Control keyboard, Remote control unit, & \\ application software & & Communication telephone & 0.0000266386 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Failure rates of the C\({}^{4}\)ISR system units. Subsequently, the success probability of the signal flow 23 and 30 are computed, see Equation (16), which are a comment (shared) signal of operators 23 and 26. Accordingly, the output signal 30 needs to be corrected and the common cause rate is set to be \(C=\beta\lambda=0.000236\). \[ \begin{array}{c}A_{23}(0)=A_{22}(0)P_{22}(0)\\ A_{30}(0)=A_{23}(0)[P_{23}(0)P_{25}(0)+P_{26}(0)P_{28}(0)-P_{23}(0)P_{25}(0)P_{ 26}(0)P_{28}(0)]\\ -A_{23}(0)[P_{25}(0)+P_{28}(0)-P_{25}(0)P_{28}(0)]C\end{array}  \tag{16}\]  
Similarly, a common signal 40 and 47 are corrected and the common cause rate is set to be \(C=\beta\lambda=0.000236\) as a basis of that the success probabilities of the signal flow 40, 47, 54, 58, 74, and 82 are computed by Equations (17)-(19):