As stated in the previous section, the FMECA analysis relies on the expert knowledge of analysis team members. These team members evaluate failure modes qualitatively, introducing uncertainty and vagueness into the process. The literature contains several approaches proposed to deal with uncertainties related to risk and safety analysis, especially in FMECA analysis.

In [14], the authors present an in-depth analysis of uncertainty sources in process safety analysis (PSA). The study identified three sources of uncertainty: completeness uncertainty refers to including all significant aspects within the analysis; modeling uncertainty, related to deficiencies in the accident scenario probabilities and consequences modeling; parameter uncertainty, related to incomplete available data. The paper includes an exhaustive identification of uncertainties associated with the different methods used in the following four PSA stages: hazard analysis, consequence assessment, frequency estimation, and risk estimation. The authors propose a hybrid approach consisting of the traditional qualitative hazard identification process and a quantitative model based on a fuzzy logic system (FLS) used to quantify the frequency, severity of consequences, and risk index. Authors propose a fuzzy logic-based “bow-tie” model to compute frequency; the consequence analysis is conducted by individual fuzzy logic models to deal with the consequence analysis complexity, showing an application for the boiling liquid expanding vapor explosion (BLEVE) calculation on a 600 m³ tank with LPG. The risk index assessment model considers fuzzy frequency and severity input variables. Finally, to compute the risk correction index (RCI), which represents the effect of PSA quality on the overall risk index, the authors proposed an FLS approach consisting of three categories for complexity, three categories for experience, and nine fuzzy rules. The authors’ main conclusion states that FLS is a promising approach to dealing with uncertainty in the PSA process.

Reference [15], the same authors present another innovative and recent fuzzy logic application to deal with uncertainty in the representative accident scenarios (RAS) identification as part of Hazard and Operability (HAZOP) analysis conducted by a team of experts. The study identified two main sources of uncertainty: uncertainties related to team member’s knowledge and experience; uncertainties related to the effect of safety barriers [15]. To take into account the effects of the safety barriers, the authors propose a risk correction index (RCI); RCI is represented as a function of the quality index (QI), represented by the complexity of the system under analysis and the experience of the analysis team, and as a function of the efficacy index (EI) that represents the performance of the safety barriers qualitatively. The proposed approach for the RAS identification considers the following four stages: (1) The HAZOP analysis to identify the accident scenarios; (2) a traditional initial risk ranking and a fuzzy-based initial risk ranking that includes categories for classical and fuzzy frequency, and classical and fuzzy consequences; (3) a final risk ranking assessment, based on the traditional and fuzzy RCI, traditional and fuzzy QI and traditional and fuzzy EI; a final RAS selection between the traditional RAS or the fuzzy RAS. When applied to RAS identification in liquefied natural gas (LNG) storage tanks in a typical regasification terminal, the results show that the fuzzy initial risk and fuzzy final risk indices for each accident scenario were determined with more accuracy when compared to the traditional approach [15].

Several approaches have been applied in the last two decades to overcome the shortcomings mentioned above in classical FMECA. In [16], the author shows extensive bibliographic research on methods to improve the FMECA prioritization process from 1998 to 2018. The researchers used the following two-level keyword structure to conduct the bibliographic research: "FMEA” or “FMECA”. Between the subordinate keywords, they propose “risk priority number”, “risk evaluation”, “risk assessment”, “risk prioritization”, “risk ranking”, “risk factor weight”, “reliability analysis”, “criticality analysis”, all these being determined based on published papers and experts’ advice. Years from 2014 to 2018 account for 60% of the published papers, representing a significant growth in FMECA-oriented research in the last 25% of the analyzed period. China is the major contributor to the FMECA improvement. The methods of “gray theory” and “fuzzy inference systems” appear to be the most used in the last decade to improve the FMECA analysis, mainly in mechanical systems, aircraft systems, electronics, the automobile industry, and healthcare risk management [16]. The main issues were using weights for a certain quality judgment of each FMECA team member and the internal relationships among failure modes and associated correction actions.

In [17], the authors compared the classical FMECA with two modified FMECA based on Grey relational theory (GRT) and fuzzy rule base (FRB). Five risk categories and triangular membership functions represent the linguistic terms related to risk factors. A 125-rule base was formulated, and the Mamdani FRB was used to assess the risk priority in the fuzzy rule base. The GRT is used to include experts’ diverse opinions and to assign a relative weight to each assessment factor. The proposed approach assessed the risk of 27 failure modes in pipeline systems. When comparing the three methods in two failure modes having the same risk factors values, the classical and rule-based FMECA provided the same ranking. However, the GRT method pointed to a different ranking for both failure modes, thus not in agreement with the first two. The main advantages of using the rule-based and GRT-based FMECA are that both allow the expert’s weighted experience to be better incorporated into FMECA when there is limited operational data.

In [18], the authors propose an FMECA method combining fuzzy set theory, analytical hierarchy process (AHP), and data envelopment analysis (DEA) to handle the uncertainty in risk analysis of aircraft landing systems. The fuzzy stage considers the risk factors of five categories, triangular and trapezoidal membership functions. The AHP assigns a weight for each FMECA risk factor associated with four experts. The DEA determines the optimum corrective actions for the riskiest failure modes. The authors applied their methodology to assess risk in a simple aircraft landing system, comparing it with the fuzzy-developed FMEA (FDFMEA). Authors conclude that their approach can provide much more information to make a better decision decreasing the risk level. However, the failure modes prioritization based on risk continued to remain subjective. A sensitivity analysis could provide more information about the proposed model’s relationship between risk and cost.

Reference [19] shows an approach based on a combination of a modified fuzzy AHP method to obtain the weights attributed to each risk factor plus a modified fuzzy weighted multi-objective optimization on the basis of a ratio analysis plus the full MULTIplicative form (MULTIMOORA) methodology to determine priority weights for the decision-makers. The proposed approach includes the following three new risk factors: time T, cost C, and profit P. Each risk factor fuzzification considered seven risk categories formalized with triangular membership functions. The model was applied for risk assessment in a steel factory and compared with the traditional fuzzy-FMECA and weighted fuzzy-FMECA methods. The authors highlight some advantages of their proposed model, such as a more precise risk evaluation due to the simultaneous use of risk factors weighting and establishing a set of priority weights for the decision-maker’s criteria and experience.

In [20], a type-II fuzzy system is applied to identify hazardous conditions in marine power systems applications. The method applied was a general type-II fuzzy system (GT2FS) decomposed into several interval type-II fuzzy systems (IT2FS) to reduce the computational complexity. The GT2FS considers five risk categories, type-II triangular membership functions, and thus 125 fuzzy rules. Compared with the type-I fuzzy-based FMECA and the classical FMECA, the authors state that their approach highlights the differences between different failure modes’ rankings, becoming more robust and efficient for the RPN calculation and the prioritization process.

Reference [21] contains another application of improved FMECA in the marine context. The authors proposed a combined methodology based on fuzzy logic and the decision-making trial and evaluation laboratory (DEMATEL) for correlation between failure modes and their causes. The fuzzy system considered ten categories, trapezoidal membership functions for the risk factors S, O, and D, and five categories with triangular membership functions to represent risk factors weights. Before performing the risk assessment, an expert’s total credibility weight also ponders the risk factor and its associated weights. The fuzzy RPN is then computed using the weighted geometric mean between risk factors, with the final RPN value obtained using the Centroid of Area COA. The DEMATEL method is applied in the next step to correlate the failure modes with their occurrence, computing a causal degree to rank the failure modes. When applied to the risk assessment in shipboard-integrated electric propulsion systems, the authors conclude that their approach is consistent with the practical engineering failure cases, and their approach considers the correlation effects between failure modes and causes, giving higher risk priority to common cause failure modes. In other words, a higher risk priority is achieved if the same cause induces multiple failure modes.

In [22], the authors proposed a new technique for fuzzy risk assessment in an FMECA analysis based on D numbers and multi-sensor information. The fuzzy stage considers seven risk categories with triangular and trapezoidal membership functions for risk factors. The weights for risk factors are computed, with them transformed into D numbers. Finally, the risk factors are ranked. When applying their approach to a case study that assesses the risk of the general anesthesia process, the proposed method overcomes the shortcomings of the traditional RPN approach to some degree, obtaining comparable performances relative to other MCDM technologies used in FMEA as the Vise Kriterijumska Optimizacija I Kompromisno Resenje VIKOR method. The proposed approach is especially suitable for the case that contains non-exclusive fuzzy evaluations.

Reference [23] introduces the notion of fuzzy relative importance for the FMECA risk factors. These were modeled by triangular membership functions, with authors including the failure modes priority through three trapezoidal-based linguistic terms (low, moderate, and high priority). In addition, two sets of fuzzy weights for the risk factors are computed. The authors apply the proposed approach to the manufacturing process. Their approach allows for establishing the relative importance of the risk factors by introducing a specific fuzzy variable. Using fuzzy weights allows representation of the perception of the experts from the FMECA team regarding each risk factor. The main limitation of this methodology is, however, the assignment of the parameters for the membership functions related to the importance and priority indices since they must be the result of consensus among the members of the FMECA team.

In [24], the authors use the FMECA method in the logistic environment facing the COVID-19 outbreak. The proposed approach considers a fuzzy-based FMECA to represent twelve process failures identified and an Analytic Hierarchy Process (AHP) method to obtain the weights for the three FMECA risk factors. The authors classified the failures into the following three main groups: business risks, safety risks, and special issues. Results show that failure mode, denoted by the Exposure of employees to high-risk groups with fever, is the riskiest, showing the influence of the COVID-19 pandemic on the logistical systems. The main advantage of the proposed approach combining the fuzzy-FMECA and AHP is the accuracy of the degree of risk computation. The limitation of this work is the dependence on the experts’ knowledge because the results may vary for different groups of experts.

In [25], the authors present an approach combining the fuzzy-FMECA analysis and Fault Tree Analysis (FTA) to assess the riskiest failure modes quantitatively. The fuzzy-FMECA considers five risk categories, triangular membership functions, and a fuzzy inference system (FIS) to compute the risk priority number. When applied to a system with four failure modes, the authors concluded that their approach proves efficient because as the FTA only considers the riskiest failure modes, this allowed for reducing the tree size, concentrating on the most severe failures that affect the system.

Reference [26] introduces the application of fuzzy-based FMECA analysis for risk evaluation in power transformers. The proposed approach combines aggregation tools based on hesitant fuzzy systems (HFS) and the Criteria Importance Through Inter-criteria Correlation (CRITIC) technique. In the first step, an FMEA group, including three experts, is asked to offer their opinions on the risk evaluations for seven failure modes using the HFS. The second step considers the assignment of weights for each expert using the CRITIC weighting method. The global risk for each failure mode is computed using a novel hesitant fuzzy weighted geometric average (HFWGA), and finally, the failure modes are ranked. In addition, the authors conduct a comparison between their approach, the Hesitant Fuzzy Vise Kriterijumska Optimizacija I Kompromisno Resenje (HF-VIKOR), the Hesitant Fuzzy Technique for Order Preference by Similarity to the Ideal Solution (HF-TOPSIS), and extended generalized TOmada de Decisao Interativa Multicriterio (TODIM). The authors’ results state that their rankings are consistent with the classical FMECA and the generalized TODIM, concluding that the proposed FMEA framework is valid for evaluating and ranking failure modes’ risk prioritization. The proposed FMECA approach is flexible in handling risk assessment teams with multiple experts and includes a relative weighting among them. The three risk factors and the inherent relation between risk factors should be investigated to improve the method.

In [27], it is introduced the application of the fuzzy-FMECA analysis for the safety risk assessment in a water diversion infrastructure. Failure modes were classified into the following four main groups: social impact, operation management, engineering technology, and environmental impact. The fuzzy structure considers fives risk categories, triangular membership functions and Mamdani fuzzy inference system. The approach is applied to a strategic infrastructure in China, the Huixian section of the Middle Route Project of the South-to-North Water Diversion Project (MRP-SNWDP). To collect the data for the analysis, the authors asked twenty-four experts to fill out a questionary to determine the scores for occurrence and detectability, and the data for severity obtained from the inspection reports. In addition, a weight was associated with the experts’ experience. Compared with the classical FMECA, the proposed approach can make a systematic risk prioritization, with the prioritization results obtained from both FMECA methods being very similar. This approach’s main limitation is related to the subjectivity of the questionnaire survey and the use of qualitative indicators for the three risk factors.

A different application of fuzzy-based FMECA is found in [28], where the authors show its application in a quantifier prototype of methane gas (CH₄) and carbon dioxide (CO₂) specifically developed to measure the emissions generated by cattle. A group of specialists identified 30 failure modes through the classical FMECA analysis. The proposed fuzzy-FMECA architecture comprises five risk categories, trapezoidal membership functions for the three risk factors, seven categories and triangular membership functions for the RPN, and a Mamdani fuzzy inference system with 125 rules. From the results, the authors conclude that fuzzy logic is adequate for risk assessment, especially in the project or porotypes development stages, when no operational information is available to support the decisions. Although the fuzzy-based FMECA deals with the uncertainty associated with the expert’s criteria, using classical ratings to assess the risk factors can disadvantage this methodology.

A recent application of adaptive neuro-fuzzy inference systems (ANFIS) and support vector machines (SVM) to improve the FMECA process is shown in [29]. FMECA analysis is a proactive diagnosis technique for this work’s edible oil purification process. The authors propose an approach consisting of the following steps: (1) A process description where the authors define the system’s main functions and the failure modes’ causes, effects, and consequences; (2) A knowledge-based approach, where authors determine the risk parameters, defined the ANFIS and SVM structures; (3) A final step that includes the RPN computing and sensitive analysis. Four experts identified 67 failure modes from 14 components. The ANFIS approach considered 3 fuzzy categories with 27 rules, 5 fuzzy categories with 125 rules, and 10 categories with 1000 rules; in addition, the analysis considered a combination of eight membership functions for the risk factors triangular, trapezoidal, pi, gauss, gauss2, g-bell, p-sigmoid and d-sigmoid). The application of SVM considered the following two algorithms: Sequential Minimal Optimization (SMO) and Iterative Single Data Algorithm (ISDA), which classify the 67 failure modes into 67 risk clusters. The ANFIS network using hybrid training, specifically the 3-categories (27-rule) and the 5-categories (125-rule), showed high potential to create maximum risk number cluster failure modes.

In [5], the authors show one of the first approaches that apply type-I Mamdani fuzzy systems for the FMECA analysis in the smart grid environment. The fuzzy-FMECA analysis was performed in the following two stages: first, an intermediate fuzzy variable called “impact” is computed using the fuzzy inference system between risk factor Severity and Occurrence. The fuzzy RPN is computed by applying the fuzzy inference system between the impact and the Detection. Risk factors were represented by triangular and Gaussian membership functions corresponding to five risk categories. The proposed approach was applied for risk assessment on eight smart grid components, showing that the fuzzy-based FMECA adequately prioritizes the failure modes. However, one must point out that this analysis does not consider any interdependency between the different components.

Reference [30] also shows the application of type-I fuzzy inference systems for improving the FMEA analysis in a smart grid distribution system. The fuzzy system considers 125 fuzzy rules, triangular membership functions for the risk factors O, S, and D, and Gaussian membership functions for the RPN. The Mamdani inference system and COA were used in the defuzzification process. When applied to a power grid test system shown in [12] consisting of 24 failure modes, authors conclude that their approach deal with the uncertainty in predicting failure modes where there is insufficient data or even knowledge to make accurate decisions, providing a way for dealing with multiple experts with conflicting opinions. The results proved that the method is more robust and accurate than classical FMECA. Moreover, the method developed can be improved by considering economic constraints.