# Risk Identification of FPSO Oil and Gas Processing System Based on an Improved FMEA Approach
## 3 The Proposed Approach
### 3.3. Topsis-Based Risk Prioritization (Step3)
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Risk Factors** & **FMEA Experts** & **Factors Weights** & **FM1** & **FM2** & **FM3** & **FM4** & **FM5** & **FM6** \\ \hline \multirow{8}{*}{Occurrence} & DE1(0.35) & VSI & H33 & H33,0.5 & \multirow{8}{*}{H22} & H12,0.9 & H23,0.5 & \multirow{8}{*}{H33,0.1} \\  & DE1(0.35) & VSI & H33 & H44,0.5 & & & & \\  & DE2(0.20) & MI & H44 & H23 & H22 & H22 & H12 & H34,0.8 \\  & DE3(0.15) & SI & & & & & & \\  & DE4(0.20) & SI & H34 & H23 & H33 & H12 & H23,0.5 & H33 \\  & DE5(0.10) & MI & H25 & H22 & H22 & H22,0.9 & & & \\  & DE1(0.35) & MI & H35,0.9 & H45,0.9 & & & & \\  & DE2(0.20) & VSI & H55 & H45 & H33 & H33 & H35 & \\ Severity & DE3(0.15) & SI & H45 & H34 & H45 & H33,0.9 & H23,0.5 & H34 \\  & DE4(0.20) & SI & H55 & H44 & H33 & H33 & H44 & H35 \\  & DE5(0.10) & VSI & H44 & H45 & H44 & H34 & H33 & H44 \\  & DE1(0.35) & SI & H33 & H33 & H22 & H22 & H23 \\  & DE2(0.20) & UI & H34 & H44,0.9 & H22 & H23 & H22 & H22 \\ Detectability & DE3(0.15) & MI & H33 & H24 & H23 & H12,0.8 & H23 & H22 \\  & DE4(0.20) & UI & H22 & H34 & H22 & H33 & & H12 \\  & DE5(0.10) & UI & H23 & H33,0.9 & H24 & H22 & H14 & H12 \\ \hline Risk factors & FMEA experts & Factors weights & FM7 & FM8 & FM9 & FM10 & FM11 & FM12 \\ \hline \multirow{8}{*}{Occurrence} & DE1(0.35) & VSI & H22 & H22,0.9 & \multirow{8}{*}{H33} & H22,0.7 & \multirow{8}{*}{H33,0.5} & \multirow{8}{*}{H22} \\  & DE2(0.20) & MI & H33 & H23 & H34 & & & \\  & DE3(0.15) & SI & H33,0.9 & H33 & H23 & H33 & H33 & H23 \\  & DE4(0.20) & SI & H34 & H34 & H33 & H33 & H34 & H22 \\  & DE5(0.10) & MI & H22 & H22 & H33 & H23 & H34 & H12 \\  & DE1(0.35) & MI & H22,0.4 & & & & & \\  & DE2(0.20) & VSI & H33,0.5 & & & & & \\  & DE2(0.20) & VSI & H44 & H33 & H44 & H33 & H34 & H13 \\ Severity & DE3(0.15) & SI & H44 & H33 & H44 & H33 & H34 & H13 \\  & DE3(0.15) & SI & H44 & H33 & H44 & H33 & H33 & H22 \\  & DE4(0.20) & SI & H34 & H23 & H44 & H44 & H44 & H23 \\  & DE5(0.10) & VSI & H44 & H33 & H44 & H34 & H34 & H22 \\  & DE1(0.35) & SI & H23 & H23 & H33 & H33 & H33 & H33 \\ Detectability & DE2(0.20) & UI & H33,0.9 & H22 & H23,0.8 & H23 & H33 & H23 \\  & DE3(0.15) & MI & H22 & H23 & H33 & H22 & H22 & H33 \\  & DE4(0.20) & UI & H22 & H22 & H23 & & & & \\  & DE5(0.10) & UI & H22 & H12 & H33 & H22 & H33 & H24 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Assessment information on 12 failure modes by five FMEA experts. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Failure Modes** & **Occurrence** & **Severity** & **Detect-Ability** & **Occurrence** & **Severity** & **Detect Ability** \\ \hline FM\({}_{1}\) & 1.190 & 1.280 & 1.063 & 0.109 & 0.083 & 0.067 \\ FM\({}_{2}\) & 0.877 & 1.215 & 1.380 & 0.080 & 0.079 & 0.088 \\ FM\({}_{3}\) & 0.943 & 1.333 & 1.223 & 0.086 & 0.087 & 0.078 \\ FM\({}_{4}\) & 0.785 & 1.2 The weighted normalization matrix is calculated by Equation (13), and then, based on the TOPSIS method, Euclidean distance to the positive-ideal solution \(d_{n}^{+}\), Euclidean distance to the negative-ideal solution \(d_{n}^{-}\) and the closeness coefficient \(C_{n}\) of all failure modes can be obtained by Equations (14)-(18). Finally, as shown in Table 9, the scores are ranked, and results show that the most important failure mode is \"Fuel gas scrubber\" (FM9).