# Failure Mode and Effects Analysis Considering Consensus and Preferences Interdependence
## 5 Case Study
### Implement the Proposed Method
**Step 2.6:** Based on Equations (16)-(18), the elements of failure modes that need to be modified are determined to be:  
\(AES=\{\)(2,1,1), (2,1,3), (2,4,1), (2,4,2), (2,4,3), (2,5,1), (2,5,2), (2,5,3), (2,6,3), (2,7,2), (2,8,1), (2,8,2), (2,8,3), (3,2,2), (3,2,3), (3,3,1), (3,3,2), (3,4,1), (3,4,2), (3,4,3), (3,6,1), (3,6,2), (3,7,1), (3,7,2), (3,7,3), (3,8,2), (3,9,1), (3,9,2)). **Step 2.7:** According to Equation (19), the personalized suggestions for experts are obtained. The modified assessment information on the nine failure modes is shown in Table 4. Then, let \(\gamma=2\), go back to step 2.2. Next is the second round of the consensus-reaching process. **Step 2.2:** Convert all linguistic variables in each linguistic evaluation matrix \(L^{2}\) and \(L^{3}\) into the IVPFNs according to Table 2 to construct assessment matrices \(A^{2}\) and \(A^{3}\). **Step 2.3:** Based on the IVPFWA operator, the comprehensive matrix \(C\) is obtained as follows:  
\[C=\left( \begin{array}{ccccccccccccc}([0.4639,0.5640],[0.4373,0.5378])&([0.5117,0.6119],[0.3887,0.4890])&([0.4173,0.5173],[0.4835,0.5838])\\ ([0.6528,0.7545],[0.2470,0.3492])&([0.5870,0.6873],[0.3132,0.4136])&([0.5492,0. 6497],[0.3514,0.4522])\\ ([0.5542,0.6547],[0.3464,0.4472])&([0.4441,0.5442],[0.4573,0.5578])&([0.6645,0.7656 ],[0.2352,0.3366])\\ ([0.5000,0.6000],[0.4000,5.0000])&([0.4330,5.5209],[0.4700,0.5708])&([0.2604,0. 3594],[0.6431,0.7434])\\ ([0.5592,0.6596],[0.3415,0.4423])&([0.5000,0.6000],[0.4000,5.000])&([0.2507,0. 3496],[0.6531,0.7533])\\ ([0.6916,0.7920],[0.2083],[0.3088])&([0.5927,0.6941],[0.3077,0.4096])&([0.3112, 0.4096],[0.5954,0.6960])\\ ([0.6900,0.7000],[0.3000,0.4000])&([0.7105,0.8132],[0.1877,0.2905])&([0.5173, 0.6176],[0.3831,0.4835])\\ ([0.8434,1.0000],[0.0000,0.1578])&([0.4000,0.5000],[0.5000,0.6000])&([0.3176, 0.4173],[0.5838,0.6840])\\ ([0.4780,0.5780],[0.4229,0.5233])&([0.5000,0.6000],[0.4000,5.0000])&([0.4639, 0.5640],[0.4373,0.5378])\\ \end{array} \right).\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Failure Modes**} & \multicolumn{4}{c}{**Severity(S)**} & \multicolumn{4}{c}{**Occurrence(O)**} & \multicolumn{4}{c}{**Detection(D)**} \\ \cline{2-13}  & \(E_{1}\) & \(E_{2}\) & \(E_{3}\) & \(E_{4}\) & \(E_{5}\) & \(E_{1}\) & \(E_{2}\) & \(E_{3}\) & \(E_{4}\) & \(E_{5}\) & \(E_{1}\) & \(E_{2}\) & \(E_{3}\) & \(E_{4}\) & \(E_{5}\) \\ \hline \(FM_{1}\) & ML & M & ML & M & M & M & M & M & MH & MH & M & ML & ML & ML \\ \(FM_{2}\) & MH & MH & H & M &  
**Step 2.4** Compute the consensus degree. Based on Equations (11) and (12), the \(CDF\) value is determined as follows. \[CDF=\left( \begin{array}{ccccc}0.8456&0.9162&0.8967&0.8560&0.8919\\ 0.8120&0.8695&0.8756&0.8266&0.8860\\ 0.8570&0.8511&0.8570&0.8252&0.8193\\ 0.8469&0.9129&0.9129&0.8849&0.8428\\ 0.8834&0.8965&0.8998&0.8965&0.8238\\ 0.8929&0.8973&0.9668&0.7994&0.8608\\ 0.8489&0.9594&0.9594&0.8897&0.8989\\ 0.8896&0.9087&0.9410&0.8729&0.8401\\ 0.8847&0.9042&0.9263&0.8653&0.8917\end{array} \right).\]  
Then, according to Equation (13), the \(CDM\) value is calculated as follows. \[CDM=(0.8623,0.9042,0.9150,0.8574,0.8939).\]  
Finally, using Equation (14), the \(CDT\) value is obtained as \(CDT=0.8929\). **Step 2.5:** Due to \(CDT>\zeta\), go to step 2.8. **Step 2.8:** Output the adjusted IVPFN assessment matrix. **Step 3:** The comprehensive evaluation matrix \(D\) is obtained by considering the weights of experts and applying the IVPFWGBM operator. The result is as follows. \[D=\left(