# A DMAIC Integrated Fuzzy FMEA Model: A Case Study in the Automotive Industry
## 4 The Case Study
### DMAIC Cycle
#### 4.1.3 Analyze  
In the analyze phase the proposed fuzzy FMEA system was implemented. After developing an FMEA table with all the failure modes, effects, occurrence, and respective indexes, the indices were fed into the fuzzy FMEA system and a fuzzy RPN index was generated for each set. Table 6 contains the comparative study between the RPN values of the two methodologies, classic FMEA and fuzzy FMEA. By observing Table 6, it is possible to verify that the difference in the results of the models is not significant. However, given the small differences, it is important to distinguish the approach of the proposed model. One of the main limitations of the classic FMEA corresponds to the tie that occurs in the RPN value for failure modes with different values of S, P, and D. In the classic FMEA (see column \"RPN\" in Table 6) the failure modes \"Lost thread (6)\", \"High shot (7)\" and \"High shot (8)\" have a total RPN value of 72, despite differences in the risk implications of the three failure modes. With the fuzzy FMEA analysis, the draws referred to did not happen. On the contrary, the fuzzy RPN values are relatively dispersed from one another. The classic FMEA proves to be insensitive in the tiebreaker criterion since events with different parameters are given the same priority. Consequently, it can imply a waste of resources in mitigation actions, or even cause an event with a high degree of risk to go unnoticed.  
On the other hand, the classification of failure modes according to their priority has undergone some changes, as shown in Table 7. The most critical failure modes remain the same, however, with a different prioritization. This change in the prioritization of failure modes, although not very significant, demonstrates FMEA's inconsistencies in the face of the specialists' real desire. Therefore, classic FMEA can result in preventive and corrective actions in failure modes with less implicit risk, contrary to the desire to act on those who really represent a greater risk for the process.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Component** & **\#** & **Failure Mode** & **Cause** & **S** & **P** & **D** & **RPN** & **FMEA** & **Fuzzy RPN** & **Fuzzy FNEA** & **Fuzzy RPN** \\  & & & & & & & & & & & & & & \\ \hline Cast transformer & 1 & Bubbles in epoxy & C1, C2 \& C3 & 9 & 6 & 4 & 216 & 1 st & 665 & 2 nd & Important \\ Secondary & 2 & Conical spool & C1, C2 \& C3 & 9 & 5 & 4 & 180 & 2 nd & 673 & 1 st & Important \\ \hline \multirow{3}{*}{Cast transformer} & 3 & Epoy contamination & C3 & 7 & 6 & 4 & 168 & 3 rd & 591 & 4 th & Average \\  & 4 & Epoy contamination & C2 & 7 & 2 & 8 & 112 & 4 th & 648 & 3 rd & Average \\ \hline Primary & 5 & Unreadable D2 code & C2 \& C3 & 5 & 5 & 3 & 75 & 5 th & 450 & 6 th & Low Importance \\ Secondary & 6 & Lost thread & C1,C2 \& C3 & 9 & 2 & 4 & 72 & 6 th & 513 & 5 th & Average \\ \hline \multirow{3}{*}{Cast transformer} & 7 & High shot & C1 \& C2 & 6 & 6 & 2 & 72 & 6 th & 382 & 8 th & Low Importance \\  & 8 & High shot & C4 & 6 & 4 & 3 & 72 & 6 th & 366 & 9 th & Low Importance \\  & 9 & Shot uneven & C2 & 6 & 5 & 2 & 60 & 7 th & 334 & 10 th & Very Low Importance \\  & 10 & Shot uneven & C3 & 6 & 5 & 2 & 60 & 7 th & 335 & 10 th & Very Low Importance \\  & 11 & Epoy contamination & C1 & 6 & 2 & 4 & 48 & 8 th & 382 & 8 th & Low Importance \\ \hline Secondary & 12 & Unreadable marking & C1 \& C6 \& C2 & 5 & 3 & 45 & 9 th & 250 & 12 th & Very Low Importance \\ Primary & 13 & Unreadable D2 code & C1 & 6 & 2 & 3 & 36 & 10 th & 426 & 7 th & Low Importance \\  & 14 & Shot uneven & C2 & 6 & 2 & 3 & 36 & 10 th & 426 & 7 th & Low Importance \\  & 15 & High shot & C3 & 6 & 2 & 2 & 24 & 11 th & 303 & 11 th & Very Low Importance \\ \hline Assembled & 16 & Poorly inserted core & C1 \& C2 & 3 & 1 & 3 & 9 & 12 th & 75.2 & 13 th & Not Important \\ transformer & 17 & Damaged crossbar & C3 & 5 & 1 & 1 & 5 & 13 th & 75.2 & 13 th & Not Important \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison between classic RPN and fuzzy RPN.