# New Possibilities of Using DEMATEL and ERPN in the New PFMEA Hybrid Model
## 3 Results and Discussion
### Model DEMATEL
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & **FM1** & **FM2** & **FM3** & **FM4** & **FM5** & **FM6** & **FM7** & **FM8** & **FM9** & **FM10** & **FM11** & **FM12** \\ \hline
**FM1** & 0 & 0.056 & 0.028 & 0.083 & 0.028 & 0 & 0 & 0 & 0.028 & 0 & 0 & 0.028 \\
**FM2** & 0.139 & 0 & 0.111 & 0.139 & 0.083 & 0.028 & 0 & 0.083 & 0.056 & 0.083 & 0.083 & 0.028 \\
**FM3** & 0.139 & 0.167 & 0 & 0.139 & 0.083 & 0.083 & 0.028 & 0.083 & 0.056 & 0.083 & 0.083 & 0.056 \\
**FM4** & 0.111 & 0.111 & 0.056 & 0 & 0.028 & 0 & 0 & 0.028 & 0.028 & 0.028 & 0 \\
**FM5** & 0.083 & 0.056 & 0.167 & 0.028 & 0 & 0.111 & 0.083 & 0.028 & 0.083 & 0.028 & 0.111 \\
**FM6** & 0.083 & 0 & 0 & 0.056 & 0.056 & 0 & 0.056 & 0 & 0 & 0 & 0 & 0 \\
**FM7** & 0 & 0 & 0.111 & 0 & 0.056 & 0.028 & 0 & 0.028 & 0 & 0.028 & 0 & 0.083 \\
**FM8** & 0 & 0.083 & 0.111 & 0 & 0 & 0 & 0 & 0 & 0.028 & 0.167 & 0.167 & 0.056 \\
**FM9** & 0.056 & 0.083 & 0.111 & 0.028 & 0.167 & 0 & 0 & 0.167 & 0 & 0 & 0.167 & 0 \\
**FM10** & 0 & 0.083 & 0.111 & 0 & 0 & 0 & 0 & 0.167 & 0.028 & 0 & 0.167 & 0 \\
**FM11** & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.139 & 0.139 & 0.139 & 0 & 0 \\
**FM12** & 0.083 & 0.111 & 0.139 & 0.083 & 0.056 & 0 & 0 & 0.083 & 0 & 0.083 & 0.028 & 0 \\ \hline \hline \end{tabular} The overall relation matrix T was determined from Equation (5) and is given in Table 7. It is an n \(\times\) n matrix.  
\end{table} 
Table 6: Normalized direct-relation matrix N. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & **FM1** & **FM2** & **FM3** & **FM4** & **FM5** & **FM6** & **FM7** & **FM8** & **FM9** & **FM10** & **FM11** & **FM12** \\ \hline
**FM1** & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
**FM2** & 0.257 & 0.150 & 0.255 & 0.237 & 0.166 & 0 & 0 & 0.227 & 0.149 & 0.206 & 0.228 & 0 \\
**FM3** & 0.282 & 0.318 & 0.181 & 0.259 & 0.184 & 0.129 & 0 & 0.247 & 0.161 & 0.224 & 0.246 & 0 \\
**FM4** & 0.178 & 0.182 & 0.134 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
**FM5** & 0.215 & 0.199 & 0.308 & 0.146 & 0 & 0.157 & 0 & 0.167 & 0.161 & 0.144 & 0.161 & 0.170 \\
**FM6** & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
**FM7** & 0 & 0.184 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
**FM8** & 0 & 0.195 & 0.227 & 0 & 0 & 0 & 0.155 & 0 & 0.282 & 0.301 & 0 \\
**FM9** & 0.175 & 0.222 & 0.266 & 0.129 & 0.243 & 0 & 0 & 0.313 & 0 & 0.154 & 0.316 & 0 \\
**FM10** & 0 & 0.184 & 0.214 & 0 & 0 & 0 & 0 & 0.288 & 0 & 0.130 & 0.293 & 0 \\
**FM11** & 0 & 0 & 0 & 0 & 0 & 0 & 0.244 & 0.186 & 0.217 & 0.126 & 0 \\
**FM12** & 0.198 & 0.241 & 0.267 & 0.183 & 0.129 & 0 & 0 & 0.209 & 0 & 0.197 & 0.162 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Total-relation matrix T. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **R** & **D** & **D + R** & **D - R** \\ \hline FM1 & 1.758 & 0.686 & 2.444 & \(-\)1.071 \\ FM2 & 1.993 & 2.058 & 4.051 & 0.066 \\ FM3 & 2.258 & 2.407 & 4.665 & 0.148 \\ FM4 & 1.475 & 1.09 & 2.565 & \(-\)0.384 \\ FM5 & 1.319 & 2.041 & 3.36 & 0.723 \\ FM6 & 0.65 & 0.535 & 1.185 & \(-\)0.116 \\ FM7 & 0.375 & 0.966 & 1.341 & 0.591 \\ FM8 & 2.122 & 1.652 & 3.774 & \(-\)0.47 \\ FM9 & 1.277 & 2.092 & 3.369 & 0.815 \\ FM10 & 1.796 & 1.519 & 3.316 & \(-\)0.277 \\ FM11 & 2.072 & 1.148 & 3.22 & \(-\)0.925 \\ FM12 & 0.886 & 1.787 & 2.674 & 0.901 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Summary of the prominence and relation of the 12 FM. In terms of degree of importance, FM3 is ranked in first place, followed by FM2, FM8, FM9, FM5, FM10, FM11, FM12, FM4, FM1, FM7, and FM6. In this study, FM2, FM3, FM5, FM7, FM9, FM12 are regarded as causal variables, and FM1, FM4, FM6, FM8, FM10, FM11 are regarded as an effect. The division of failure modes according to their significance (Figure 3):  
1. High significance and high correlation: This quadrant include failure modes FM3, FM2, FM9 and FM5. These failure modes are the main causal factors influencing the other items. They are therefore triggers for problem-solving. 2. Failure modes FM12 and FM7 were in the second quadrant. These are characterized by low significance and high relation.