# A DMAIC Integrated Fuzzy FMEA Model: A Case Study in the Automotive Industry
## 2 Fuzzy FMEA  
Although the present work falls within the scope of visual inspections in the automotive industry, the use of fuzzy FMEA is present in the most varied sectors of activity. The fuzzy FMEA, an improvement over classical FMEA, is a general method that can be employed to fuzzify the risk indexed parameters S, O, and D with suitable membership functions. Several studies proposed the implementation of an FIS to improve the efficiency of FMEA and to overcome its limitations [12; 13; 14; 15; 16; 17]. In most applications, the results achieved revealed the advantages of this methodology to deal with the risk associated with failure modes. In particular, they proved beneficial for the problems indicated in [10; 18]. As a way to prioritize the problems associated with healthcare, in [18] was implemented a fuzzy FMEA inference system. He applied FMEA with linguistic variables and fuzzy inference rules, \"IF-THEN\". Inputs S and O were defined according to five linguistic terms and exclusively trapezoidal membership functions. Input D and output RPN were defined by six linguistic terms and trapezoidal and triangular functions. Taking into account the vast modes of failure that can occur in health care institutions, their prioritization is of great importance. FMEA is efficient for this purpose, allowing identification of the causes and effects of potential failures. However, the implemented fuzzy FMEA analysis proved to be a more flexible alternative of assessment, providing the capture of the uncertainty associated with the variables. In [19] addresses an extended FMEA approach by employing fuzzy best-worst method and multi-objective optimization by ratio analysis based on the Z-number theory (Z-MOORA) method. These methods in the proposed approach are utilized to surmount several traditional RPN shortcomings. This approach was applied in the automotive spare parts industry, and the results have shown a full prioritization of the failures when compared with other traditional methods. While in [10] applied the fuzzy FMEA inference system to the hydraulic system of a paper mill. Specifically, the system was applied to the supply structure due to the high levels of saturation and the increase in the number of maintenance interventions, as a result of constant breakdowns. The FIS was applied to prioritize the causes associated with malfunctions. Causes that previously were not of high importance, showed, through the fuzzy FMEA analysis, to be critical to the problem. Thus, thanks to the contribution of fuzzy logic, it was possible to improve the understanding of the dynamics of complex problems, characterized by inaccurate and subjective information. Fuzzy FMEA has been applied to many distinct industries and for different applications. A risk-based fuzzy evidential approach is proposed in [20] by employing interval-valued Dempster-Shafer theory and fuzzy axiomatic design in order to assess the risk of failure modes with fuzzy belief structures. The efficiency of the proposed model was researched through an example and the results were compared with riskless evaluations. An FMEA risk management approach is proposed in [16] through fuzzy rule based interface system with the intention of mitigating the failures of a load, haul, dump machine (LHD). The risk assessment in a green supply chain using the fuzzy approach to FMEA was addressed in [21] and was applied in an Indian plastic industrial unit. In other areas of application in knowledge management failure factors were evaluated in [22] through an intuitionistic fuzzy environment as a case study in an Iranian oil and gas company. The results of this study have shown that the lack of leadership and management commitment was the most significant factor that affected the failure of knowledge management in the company. In [11] a fuzzy numerical method for FMEA was proposed that addresses the drawbacks of crisp FMEA and fuzzy rule based FMEA approaches.