# 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)  
TOPSIS, which is one of the classical multi-criteria decision-making methods, was developed by [PERSON] and [PERSON] (1981). According to the weighted normalized fuzzy decision matrix, we know that the elements \(v_{nl}\forall n,\ l\) are normalized positive numbers, and their ranges belong to the closed interval [0, 1]. Then, we can define the positive-ideal solution A\({}^{+}\) and negative-ideal solution A\({}^{-}\) as  
\[\mathrm{A}^{+}=(1,1,1), \tag{14}\]  
\[\mathrm{A}^{-}=(0,0,0) \tag{15}\]The distance of each failure mode from A\({}^{+}\) and A\({}^{-}\) can be currently calculated as  
\[d_{n}^{+}=\sqrt{\sum_{l=\,1}^{3}(v_{nl}-1)^{2}}, \tag{16}\]  
\[d_{n}^{-}=\sqrt{\sum_{l=\,1}^{3}(v_{nl}-0)^{2}} \tag{17}\]  
where \(d_{n}^{+}\) is the Euclidean distance from the failure mode \(FM_{n}\) to the positive-ideal solution; \(d_{n}^{-}\) is the Euclidean distance from the failure mode \(FM_{n}\) to the negative-ideal solution. The closeness coefficient of each failure mode \(C_{n}\) can be calculated as follows:  
\[C_{n}=\frac{d_{n}^{-}}{d_{n}^{+}+d_{n}^{-}},\ n=\ 1,2,\cdots,N, \tag{18}\]  
Obviously, a failure mode \(FM_{n}\) is closer to A\({}^{+}\) and farther from A\({}^{-}\) as \(C_{n}\) approaches to 1. Therefore, according to the closeness coefficient, we can determine the ranking order of all failure modes. **4. Risk Identification of FPSO Oil and Gas Processing System Leakage**  
Taking the 150,000-ton \"OFFSHORE-111\" FPSO as the study subject, this module is classified to simplify the FMEA analysis of the FPSO leakage risk. The International and European Standard IEC EN 60079-10-2 \"Classification of areas-explosive gas atmospheres\" pointed out that hazardous areas shall be classified in zones based on the frequency of occurrence and persistence of the dangerous atmosphere, as reported in Table 4.  
The oil and gas processing module includes equipment and facilities, such as oil and gas storage tanks, transfer devices, protected fire containers, etc. Due to the high concentration and release of explosive gas, this area should be classified as Zone 0. There are 12 main failure modes in total, which were identified by an FMEA team and are presented together with their causes and effects on the systems in Table 5.  
The FMEA team consists of five cross-functional experts. The selection of experts and their weight distribution have a significant impact on the accuracy and stability of the evaluation results. In this research, the experts fulfill three significant criteria: (1) have more than ten years' experience in FPSO design, building, and inspection; (2) still working in the offshore engineering industry; and (3) have high-level knowledge of and experience in FPSO systems. Keeping in mind the above criteria, the expert team, which consists of one professor of Harbin Engineering University with a major in offshore oil and gas security, one senior chief engineer of China National Offshore Oil Corporation (CNOOC), one senior designer of China International Marine Containers (CIMC Raffles), one senior designer engaged in marine engineering design in a university, and one platform engineer of China National Offshore Oil Corporation (CNOOC). Different scores and weights are given to team experts, as shown in Table 6. \begin{table}
\begin{tabular}{c c} \hline \hline
**Zones** & **Characteristics** \\ \hline Zone 0 & An explosive atmosphere is present continuously or for long periods or frequently \\ Zone 1 & An explosive atmosphere is likely to occur in normal operation occasionally \\ Zone 2 & An explosive atmosphere is not likely to occur in normal operation but, if it does \\  & occur, will persist for a short period only \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Zone types. The FMEA team functions to prioritize these 12 failure modes in terms of their failure risks, such as the probability of occurrence, severity, and detectability, so that high-risk failure modes are corrected with top priority.