## 5 An Example of the Application of the Method  
Assume that we have generated a service composition expressed by FRCPN for the calculation process for CAE simulation in SCP prototype, as shown in Figure 7. According to the reliability calculation method, we will calculate the reliability value of the FRCPN. We get all kinds of parameters of Web services, as shown in Table 1. The reliability value _ReliabilityValue_ is required for the calculation, so we use the method in this paper to calculate the reliability value. Firstly, we use Algorithm 1 to get the reliability values of the transitions in the FRCPN. We use _frcpn_.getTransitionSet() to get the transition sequence, which is \(\{t_{4}\),\(t_{7}\),\(t_{5}\),\(t_{6}\),\(t_{8}\),\(t_{11}\),\(t_{9}\),\(t_{10}\),\(t_{3}\),\(t_{2}\),\(t_{1}\). We set the semantic similarity threshold \(k=0.8\), \(m_{1}=0.8\), and \(m_{2}=0.2\) in all the formulas. All of the conditions in \(P\), \(Q\) are satisfied. All the transitions in the FRCPN are shown in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Web Services’**} & \multirow{2}{*}{**IRS (Immediate** **Reachability Set)**} & **PRTS** & **POTS** & **PIRS (Prepositional** **(P)stpositional** & **Immediate** **Reachability Set)** \\ \hline \(WS_{1}\) & \(\{WS_{2}\), \(WS_{3}\), \(WS_{4}\), \(WS_{5}\)} & \(\emptyset\) & \(\{t_{1}\}\) & \(\emptyset\) \\ \(WS_{2}\) & \(\{WS_{6}\}\) & \(\{t_{1}\}\) & \(\{t_{2}\}\) & \(\{WS_{1}\}\) \\ \(WS_{3}\) & \(\{WS_{6}\}\) & \(\{t_{1}\}\) & \(\{t_{2}\}\) & \(\{WS_{1}\}\) \\ \(WS_{4}\) & \(\{WS_{6}\}\) & \(\{t_{1}\}\) & \(\{t_{2}\}\) & \(\{WS_{1}\}\) \\ \(WS_{5}\) & \(\{WS_{6}\), \(WS_{7}\}\) & \(\{t_{1}\}\) & \(\{t_{3}\}\) & \(\{WS_{1}\}\) \\ \(WS_{6}\) & \(\{WS_{4}\), \(WS_{5}\), \(WS_{6}\), \(WS_{7}\}\) & \(\{t_{2}\}\),\(t_{3}\}\) & \(\{t_{4}\),\(t_{5}\),\(t_{6}\),\(t_{7}\}\) & \(\{WS_{2}\),\(WS_{3}\),\(WS_{4}\),\(WS_{5}\}\) \\ \(WS_{7}\) & \(\{WS_{11}\}\) & \(\{t_{3}\}\) & \(\{t_{7}\}\) & \(\{WS_{5}\}\) \\ \(WS_{8}\) & \(\{WS_{15}\}\) & \(\{t_{4}\}\) & \(\{t_{11}\}\) & \(\{WS_{6}\}\) \\ \(WS_{9}\) & \(\{WS_{12}\), \(WS_{13}\}\) & \(\{t_{5}\}\) & \(\{t_{8}\),\(t_{9}\}\) & \(\{WS_{6}\}\) \\ \(WS_{10}\) & \(\{WS_{14}\}\) & \(\{t_{6}\}\) & \(\{t_{10}\}\) & \(\{WS_{6}\}\) \\ \(WS_{11}\) & \(\{WS_{14}\}\) & \(\{t_{7}\}\) & \(\{t_{10}\}\) & \(\{WS_{6}\),\(WS_{7}\}\) \\ \(WS_{12}\) & \(\{WS_{15}\}\) & \(\{t_{8}\}\) & \(\{t_{11}\}\) & \(\{WS_{9}\}\) \\ \(WS_{13}\) & \(\{WS_{15}\}\) & \(\{t_{9}\}\) & \(\{t_{11}\}\) & \(\{WS_{9}\}\) \\ \(WS_{14}\) & \(\{WS_{15}\}\) & \(\{t_{10}\}\) & \(\{t_{11}\}\) & \(\{WS_{10}\),\(WS_{11}\}\) \\ \(WS_{15}\) & \(\varnothing\) & \(\{t_{11}\}\) & \(\varnothing\) & \(\{WS_{6}\),\(WS_{12}\),\(WS_{13}\),\(WS_{14}\}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters of Web services in FRCPN (Fuzzy Reasoning Colored Petri Net). Figure 7: The FRCPN generated. According to the sequence \(\{t_{4}\),\(t_{7}\),\(t_{5}\),\(t_{6}\),\(t_{8}\),\(t_{11}\),\(t_{9}\),\(t_{10}\),\(t_{3}\),\(t_{2}\),\(t_{1}\}\) and Algorithm 1, we calculate the reliability values of the transitions. Let us start with a look at the calculation of \(t_{4}\)'s reliability value. We know from Table 2 that \(t_{4}\) is of the fifth type.