## 3 Case Study
### System Modelling and Availability Analysis  
#### 3.3.1 Fuzzy Probability of Basic Events  
In this study, due to unknown failure data for the wellhead connector, the failure and repair data are mainly obtained from the offshore and onshore reliability data (OREDA) [39] and the well activity reports (WARs) in the e-Well system [40]. However, the unknown data needs to be determined through fuzzy comprehensive evaluation. Twelve experts from different companies, as listed in Table 3, were invited to judge the failure modes rating based on their experiences and reports from [PERSON] and TechnipFMC.  
Based on the expert scoring procedure, a basic events level evaluation table is as shown in Table 4. Table 4 lists an expert's scoring results for \"Failure Effect Severity\" and \"Failure Cause Probability\" of failure modes of the wellhead connector as an example. The expert is a professor-level senior engineer from CNOOC(CNOOC Research Institute CO. LTD,) and has been in this field for 30 years. The position of the \"\(\surd\)\" marks the scoring level of the expert.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Event** & **Fault Name** & **Event** & **Fault Name** \\
**Codes** & & **Codes** & **Codes** \\ \hline T & Wellhead connector failure & X5 & Upper and lower cylinder wall weld seam cracking \\ M1 & Bottom hub failure & X6 & Upper and lower cylinder wall crack \\ M2 & Top hub failure & X7 & Upper and lower cylinder wall bending and deformation \\ M3 & Bottom flange failure & X8 & Fitting face of top flange and collet collapse \\ M4 & Upper and lower cylinder & X9 & Fitting face of top flange and seal ring collapse \\  & wall failure & X10 & Fitting face of top flange and bottom flange collapse \\ M5 & Top flange failure & X10 & Fitting face of collet and top flange deformation \\ M6 & Collet failure & X11 & Fitting face of collet and top flange deformation \\ M7 & Pressure ring failure & X12 & Fitting face of collet and bottom flange deformation \\ M8 & Seal ring failure & X13 & Pressure ring deformation \\ M9 & Collet structure failure & X14 & Pressure ring fracture \\ X1 & Collet supporting plate bend & X15 & Seal ring surface wear \\ X2 & Fitting face of bottom flange & X16 & Seal ring deformation seriously \\  & and collet collapse & & \\ X3 & Fitting face of bottom flange & & \\  & and seal ring collapse & & \\ X4 & Fitting face of bottom flange & & \\  & and top flange collapse & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Fault name of the basic events.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Serial** & **Job Title** & **Education** & **Service Time** & **Score** & **Weight** \\
**Number** & **Job Title** & **Level** & **(Year)** & **Score** & **(W\({}_{\text{i}}\))** \\ \hline E1 & Senior Engineer & Bachelor & 13 & 14 & 0.064 \\ E2 & professor-level & Bachelor & 30 & 20 & 0.091 \\ E3 & Senior Engineer & Master & 15 & 18 & 0.082 \\ E4 & professor-level & Bachelor & 37 & 20 & 0.091 \\ E5 & Associate Professor & PhD & 10 & 19 & 0.087 \\ E6 & Senior Engineer & Master & 9 & 14 & 0.064 \\ E7 & Senior Engineer & Master & 10 & 16 & 0.073 \\ E8 & Senior Engineer & Bachelor & 23 & 18 & 0.082 \\ E9 & Senior Engineer & Bachelor & 16 & 16 & 0.073 \\ E10 & Associate Professor & PhD & 8 & 17 & 0.078 \\ E11 & professor-level & Master & 27 & 22 & 0.100 \\ E12 & Professor & PhD & 30 & 25 & 0.115 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Experts’ information.  
This paper refers to OREDA to take \(E_{rM}\) as \(0.3455\times 10^{-7}\). Finally, the basic events of the wellhead connector are calculated as shown in Table 5.