# Failure Mode and Effects Analysis Considering Consensus and Preferences Interdependence
## 5 Case Study
### Comparisons and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Failure Modes**} & \multicolumn{2}{c}{**\(\mathbf{t=0.84}\)**} & \multicolumn{2}{c}{**\(\mathbf{t=0.86}\)**} & \multicolumn{2}{c}{**\(\mathbf{t=0.88}\)**} & \multicolumn{2}{c}{**\(\mathbf{t=0.90}\)**} \\ \cline{2-9}  & **Scores** & **Ranking** & **Scores** & **Ranking** & **Scores** & **Ranking** & **Scores** & **Ranking** \\ \hline \(FM_{1}\) & \(-0.0604\) & 6 & \(-0.0801\) & 7 & \(-0.0723\) & 7 & \(-0.0544\) & 6 \\ \(FM_{2}\) & \(0.1437\) & 2 & \(0.1415\) & 2 & \(0.1276\) & 2 & \(-0.1181\) & 2 \\ \(FM_{3}\) & \(0.0782\) & 3 & \(0.0742\) & 3 & \(0.0744\) & 4 & \(0.0622\) & 3 \\ \(FM_{4}\) & \(-0.2074\) & 9 & \(-0.2014\) & 9 & \(-0.1944\) & 9 & \(-0.1995\) & 9 \\ \(FM_{5}\) & \(-0.1129\) & 8 & \(-0.1266\) & 8 & \(-0.1304\) & 8 & \(-0.0853\) & 7 \\ \(FM_{6}\) & \(0.0106\) & 5 & \(0.0293\) & 5 & \(0.0422\) & 5 & \(0.0375\) & 5 \\ \(FM_{7}\) & \(0.2140\) & 1 & \(0.1821\) & 1 & \(0.1781\) & 1 & \(0.1900\) & 1 \\ \(FM_{8}\) & \(0.0563\) & 4 & \(0.0657\) & 4 & \(0.0856\) & 3 & \(0.0618\) & 4 \\ \(FM_{9}\) & \(-0.0800\) & 7 & \(-0.0573\) & 6 & \(-0.0570\) & 6 & \(-0.0989\) & 8 \\ \(n(\text{E})\) & 0 & 2 & 4 & 5 & 5 & \\ \(n(\text{FM})\) & 0 & 13 & 27 & & 38 & \\ \hline \hline \end{tabular}  
* \(n(\text{E})\) is the number of modified expert evaluations, and \(n(\text{FM})\) is the number of modified failure modes.  
\end{table} 
Table 5: Ranking of different threshold values \(\zeta\). departments, and have different professional backgrounds, practical experiences, and knowledge structures. Therefore, they should be assigned different importance during risk assessments. We can see that there are some differences between the priority of failure modes determined by the proposed method and the fuzzy VIKOR approach. The ranking results determined by the fuzzy VIKOR method may be unreasonable because the consensus-reaching process and the experts' judgments dependencies were not considered in the risk assessment. For example, \(FM_{9}\) was the least important failure mode using the fuzzy VIKOR method, whereas it ranked sixth using the proposed method. Interestingly, \(FM_{6}\) ranked before \(FM_{3}\) with the fuzzy VIKOR approach, however, the latter is more important in reality. Therefore, \(FM_{3}\) was merited a higher priority in comparison with \(FM_{6}\) in our proposed method. Furthermore, the solution obtained through the fuzzy VIKOR method compared with the proposed approach is a set of compromise solutions. Apart from \(FM_{1}\), \(FM_{4}\), and \(FM_{6}\), the ranking orders of the failure modes obtained by the fuzzy MULTIMOORA approach are totally different from those determined through the proposed method. These inconsistent ranking results may be expressed by the fact that the subjective weights of risk factors were not taken into account in the fuzzy MULTIMOORA method, which may result in irrational rankings of failure modes. For example, \(FM_{8}\) is given to be a more important failure mode than \(FM_{7}\) according to the fuzzy MULTIMOORA approach. However, in the proposed approach, it ranks only the fourth position; \(FM_{7}\) has the top risk priority, which also can be validated by the IFHWED-based and the fuzzy VIKOR methods. In addition, the consensus-reaching process is not considered in the fuzzy MULTIMOORA approach, which may be another reason that leads to the biased ranking results. As shown in Table 5, the failure modes for \(FM_{3}\), \(FM_{5}\), \(FM_{6}\), \(FM_{8}\), and \(FM_{9}\) have different ranking orders between the proposed approach and IFHWED-based method. Interestingly, the sorting positions of \(FM_{5}\) and \(FM_{9}\) have been interchanged in the proposed method comparing with the IFHWED-based approach. There are many different types of interdependent relationships between the experts' preferences in the real world because of the mutual influences of FMEA team experts.