# Failure Mode and Effects Analysis Considering Consensus and Preferences Interdependence
## 2 Literature Review
### Failure Mode Ranking  
The risk assessment of failure modes in FMEA is a typical multiple-criteria decision-making (MCDM) problem [33], which needs an MCDM technique to obtain the risk priority of failure modes. To obtain a reasonable result, many MCDM methods, which have been extensively used in various fields, have been utilized to determine the risk priority of failure modes. These methods can be divided into two categories according to the independence and the interdependence of failure modes. For the first category, a multi-expert MCDM approach was introduced into the FMEA method by [PERSON] and [PERSON] [34] to identify the risk priority of failure modes without requiring an arbitrary numerical conversion. In their approach, risk factors were defined as the evaluation criteria, whereas failure modes were interpreted as the alternatives. Since then, improvements in FMEA approaches based on various MCDM technologies have been proposed by many researchers. For example, [PERSON] et al. [22] developed a new risk priority method that utilized the complex proportional assessment (COPRAS) method to determine the ranking of failure modes. [PERSON] et al. [24]presented a new FMEA approach under the interval 2-tuple linguistic environment and used the Elimination and choice expressing reality (ELECTRE) method to rank the risk priority of failure modes. For reflecting the psychological character of decision-makers, [PERSON] et al. [21] presented a new method for FMEA, which combines the linguistic distribution evaluation and TODIM (an acronym in Portuguese of interactive and multi criteria decision-making) approaches. In addition, the technique for order preference by similarity to ideal solution (TOPSIS) [3; 18], VIKOR (VIsekriterijumskaoptimizacijaiKOmpromisnoResenje) [16; 35; 36; 37], PROMETHEE (Preference ranking organization methods for enrichment evaluations) [33], and MULTIMOORA (MOORA plus Full Multiplicative Form) [20; 38] methods have also been introduced by many researchers into FMEA to determine the risk priority of failure modes. On the other hand, many methods have been presented to reflect the effects of the interdependent relationships between the failure modes on the risk priority of failure modes. For instance, [PERSON] et al. [39] developed a risk assessment method of FMEA based on a fuzzy-logic-based approach and an expert system to explore the direct and indirect relationships among various failure modes. Subsequently, the decision-making trial and evaluation laboratory (DEMATEL), which possesses the capacity to identify and analyse the interdependencies between the failure modes, was used by [PERSON] et al. [40] to rank the risk priority of failure modes. Motivated by the advantages of the TOPSIS method, [PERSON] et al. [41] presented a new method that integrates TOPSIS and DEMATEL to determine the risk priority of failure modes. [PERSON] et al. [35] developed a hybrid MCDM method, which integrates VIKOR, DEMATEL, and an analytic hierarchy process method, to rank the risk of the failure modes identified in FMEA. [PERSON] et al. [42] proposed a novel risk assessment method of failure modes that combines fuzzy weighted averaging with the DEMATEL approach. The Multi-attributive border approximation area comparison (MABAC) approach is a novel MCDM technique originally developed by [PERSON] andCirovic [43] that is a useful and reliable tool to solve MCDM problems. The main advantages of this method are summarized as follows [44]: (1) The MABAC method has a simple calculation process and can obtain a stable result; (2) This method considers the potential values of gains and losses; and (3) It can be incorporated with other methods. Accordingly, this approach has been applied to various fields, including material selection [45], hospital management [44], the location of wind farms [46], and strategic project portfolio selection [47]. Hence, based on its primary characteristic, the MABAC method is modified and applied to obtain the ranking of failure modes.