**1. Introduction**

Failure mode, effects and criticality analysis (FMECA), also known as failure mode and effects analysis (FMEA) when without referring to criticality analysis, is a risk and reliability analysis tool based on multidisciplinary team cooperation [1]. The FMEA method originates from the formal design methodology by NASA and first proposed in 1960s for solving their obvious reliability and safety requirements [2]. In many fields, it can be used to enhance the reliability and safety for a system by recognizing the various failure modes and analyzing their reasons and effects in the system and process during product design and manufacturing processes. The main task of FMEA is to evaluate the likelihood of the potential failure modes and their impact and severity to identify weaknesses and key projects in the system and then provide a basis for developing improved control measures. Differing from some other reliability managemen<sup>t</sup> approaches, FMEA emphasizes taking

**Citation:** Wang, Z.; Wang, R.; Deng, W.; Zhao, Y. An Integrated Approach-Based FMECA for Risk Assessment: Application to Offshore Wind Turbine Pitch System. *Energies* **2022**, *15*, 1858. https://doi.org/ 10.3390/en15051858

Academic Editor: Eugen Rusu

Received: 3 December 2021 Accepted: 30 December 2021 Published: 3 March 2022

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precautions against failures rather than finding a solution after the failures happen [3], which can greatly reduce the frequency of occurrence of failure modes and avoid serious accidents. As a widely used methodology in safety and reliability analysis, FMEA has gained a widespread attention due to its visibility and simplicity, and up to now it has been extensively used in various industries [4–11].

In traditional FMECA, each failure mode identified in a system is evaluated by three risk factors of severity (*S*), occurrence ( *O*) and detectability ( *D*), and their risk priorities are determined by sorting their risk priority numbers (RPNs) [12], which is obtained by multiplying the values of *S*, *O* and *D*. Generally, *S*, *O* and *D* of failure modes are scored by experts and a number ranged from 1 to 10 is given for each of the three risk factors, usually the large the number, the worse the case is. Based on the values of RPNs, the risk priorities of failure modes are determined, which can help the analyst to pinpoint system inherent vulnerabilities. A failure mode with higher RPN is regarded as more important [13], which means it has greater harm to the system and will be given a higher risk priority. Thus for guaranteeing safety and reliability, some measures of prevention and improvement should be taken preferentially to the failure modes with high risk priority to avoid their occurrence. However, the crisp value of RPN has been highly criticized for various reasons [14–19], most of which are listed as follows:


In order to conquer the shortcomings mentioned above and enhance the applicability of traditional FMECA to real cases [3], much attention have been paid to its improvements and a variety of theories and methods have been introduced to FMECA. For example, fuzzy set has been introduced to FMECA for transforming the vagueness of experts' evaluation into a mathematical formula; information fusion method like Dempster–Shafer Theory and rough number, etc., are introduced to FMECA for aggregating different evaluations; multicriteria decision making methods like the VIsekriterijumska optimizacija i KOmpromisno Resenje (VIKOR) method and Technique for Ordering Preference by Similarity to Ideal Solution (TOPSIS) method, etc., are introduced to FMECA for ranking failure modes. Some of the main theories and methods are presented in Table 1.

In studies of FMECA in wind turbines, some experts take the structures of different wind turbines, economic factors, costs and climatic regions into consideration. For example,

Mahmood et al. [21] developed a mathematical tool for risk and failure mode analysis of wind turbine systems (both onshore and offshore) by integrating the aspects of traditional FMEA and some economic considerations such as power production losses, and the costs of logistics and transportation. Samet et al. [22] proposed a FMECA methodology with considering different weather conditions or climatic regions and different wind turbine design types such as direct-drive model and geared-drive model. Nacef et al. [23] developed a hybrid cost-FMEA by integrating cost factors to assess the criticality, these costs vary from replacement costs to expected failure costs.


**Table 1.** Some of the theories and methods used in FMECA.

Although many theories and methods have been introduced to FMECA to eliminate the defects of the traditional FMECA, the representation of expert's judgments on the

evaluation of failure modes, the aggregation of experts' diversified evaluation information, and the determination of risk priorities of failure modes are still open issues, especially in terms of the defect of without considering the dependencies among different failure modes. In this paper, an integrated approach-based risk assessment model for FMECA was proposed to the existing defects, which integrates the strong expressive ability of *Z*-numbers to vagueness and uncertainty information, the strong point of the DEMATEL method in studying dependence among failure modes, the advantage of rough numbers in aggregating experts' diversity evaluation information, and the merit of VIKOR evaluation structure in flexibly modeling multi-criteria decision-making. Based on the integrated approach, the proposed risk assessment model can well capture and aggregate FMECA team members' diversity evaluations and prioritize failure modes under different types of uncertainties with considering the failure propagation. The rest of this paper is organized as follows. Some existing improvement methods to traditional FMECA are introduced in Section 2. Section 3 introduces the proposed new risk assessment model for FMECA using *Z*-number, rough number, DEMATEL method and VIKOR method. An illustrative case and the comparison and discussion for the proposed FMECA approach are respectively provided in Sections 4 and 5. Section 6 concludes the paper with a summary.

#### **2. Literature Review**

In the recent decades, scholars and researchers have done a lot of significant work to the improvements of FMECA. Among these improvement methods we can find they are mainly focusing on the following four aspects.

In term of the defect of traditional FMECA without considering the weights of risk factors, Hua et al. [33] introduced fuzzy analytic hierarchy process (FAHP) approach to FMECA for determining the weights of risk factors. Liu et al. [13] introduced a subjective weight and objective weight for risk factors by integrating fuzzy analytic hierarchy process (FAHP) and entropy method. Bozdag et al. [34] proposed a new fuzzy FMECA approach based on IT2 fuzzy sets for obtaining the uncertainty both in intrapersonal and interpersonal, which considers the optimal weights of risk factors and synthetizes them by using an ordered weighted averaging operator based on-cut. Liu et al. [35] introduced fuzzy digraph and matrix approach to FMECA for developing a new FMECA model with considering the relative weights of risk factors expressed by linguistic terms and transformed to fuzzy numbers, which determines the risk priorities of failure mode using their risk priority indexes that computed based on the formed corresponding fuzzy risk matrixes for failure modes. Zhou et al. [36] proposed a new generalized evidential FMECA (GEFMECA) model to handle the uncertain risk factors comprised of not only the conventional risk factors, but also the other incomplete risk factors. Based on the generalized evidence theory, the relative weights among all risk factors are well addressed. Liu et al. [37] proposed an integrated FMECA approach for the improvement of its performance based on the interval-valued intuitionistic fuzzy sets (IVIFSs) and multi-attributive border approximation area comparison (MABAC) method, in which the linear programming model is developed for obtaining the optimal weights of risk factors even if the weight information among risk factors is incompletely known.

In view of the defect that the evaluations obtained from FMECA team members are expressed in a linguistic way which are difficult to be converted directly and correctly into numerical value. To handle this case, fuzzy set theory and its improvement methods were introduced to FMECA by many researchers, which can be well used to transform the linguistic item into a mathematical formula and improve the decision making ability for FMECA in real application. Bowles and Peláez [2] first introduced fuzzy set theory into FMECA and proposed a technique based on fuzzy logic to prioritize failure modes in a system FMECA, which enables analysts to evaluate the failure modes using the linguistic terms directly and provides a more flexible structure to combine the parameters of risk factors. For dealing with the drawbacks of traditional fuzzy logic (i.e., rule-based) methods used in FMECA, Yang et al. [38] proposed a fuzzy rule-based Bayesian reasoning approach

for the prioritization of failure modes. Jee et al. [39] presented a new fuzzy inference system (FIS)-based risk assessment model for FMECA to prioritizing failure modes, in which a new two-stage method is introduced for reducing the number of fuzzy rules which need to be gathered. By integrating FMECA and fuzzy linguistic scale method, Gajanand et al. [40] proposed a new strategy for the reliability-centered maintenance, in which the failure modes are prioritized by using the weighted Euclidean distance and centroid defuzzification based on fuzzy logic. Tooranloo et al. [41] proposed a new model for FMECA based on intuitionistic fuzzy approach, which evaluates failure modes under vague concepts and insufficient data. Jian et al. [42] proposed a new risk evaluation approach for failure mode analysis in FMECA by integrating intuitionistic fuzzy sets (IFSs) and evidence theory. In their method, linguistic items and intuitionistic fuzzy numbers are used to evaluate the risk factors of failure modes and then the evaluations are transformed into basic probability assignment functions based on evidence theory. Jiang et al. [43] assessed the risk factors of failure modes using fuzzy membership degree in their proposed fuzzy evidential method for FMECA, and ranked the failure modes by fusing the feature information of risk factors with D–S theory of evidence.

Aiming at the controversial mathematical formula for RPN calculation and the ranking problem of failure modes, many researchers have viewed the risk ranking problem of failure modes as a multiple criteria decision-making (MCDM) issue [16], and a lot of MCDM methods such as Analytical Hierarchy Process (AHP), technique for ordering preference by similarity to ideal solution (TOPSIS), Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE), grey theory, and VIsekriterijumska optimizacija i KOmpromisno Resenje (VIKOR) are introduced to FMECA. For example, Aydogan [44] introduced an integrated approach by using the rough AHP and fuzzy TOPSIS method for the performance analysis of organizations under fuzzy environment. Song et al. [20], taking advantage of the merit of rough set theory in manipulating uncertainty and the strength of the TOPSIS method in modeling multi-criteria decision making, proposed a new risk assessment model for FMECA. Liu et al. [45] introduced an intuitionistic fuzzy hybrid TOP-SIS method to FMECA for determining the risk priorities of failure modes. Silvia et al. [46] proposed an maintenance approach based on by combining reliability analysis and MCDM method to optimize maintenance activities of complex systems, in which the AHP is used for weight evaluation of criteria and fuzzy TOPSIS method is responsible for risk ranking of failure modes identified in the system. Vahdani et al. [47] integrated fuzzy belief structure and TOPSIS method in FMECA to describe expert knowledge and rank failure modes in risk analysis. Zhou et al. [48] introduced grey theory and fuzzy theory into FMECA for the failure prediction of tanker equipment, in which the risk priorities of failure modes are determined by two criteria of the fuzzy risk priority numbers (FRPNs) obtained by fuzzy set theory and the grey relational coefficient obtained by grey theory. Liu et al. [28] introduced a new FMECA approach based on grey relational projection method (GRP) and D numbers for determining the risk priority orders of failure modes. Liu et al. [49] developed a framework for FMECA by integrating cloud model and PROMETHEE method for handling the representation of diversified risk evaluations of FMECA team members and the determination of the risk priorities of failure modes. Mandal et al. [50] presented a methodology utilizing VIKOR approach for ranking the human errors. Baloch et al. [51] integrated fuzzy VIKOR method and data envelopment analysis method into FMECA for determining the rankings of potential manners and selecting the most important impairment manner.

For better capturing and aggregating different experts' diversity evaluations which are difficult to be handled by traditional FMECA, evidential reasoning and Dempster–Shafer (D–S) Theory are introduced to FMECA in many literatures. Chin et al. [25] proposed an FMECA approach based on group-based evidential reasoning (ER) for capturing experts' diversity evaluations and prioritizing failure modes in the situation of various uncertainty. Liu et al. [52] proposed an improvement approach for FMECA based on fuzzy evidential reasoning (FER) and grey theory to solve the two shortcomings of traditional FMECA with respect to the acquirement and aggregation of different experts' evaluations and the

determination of the risk priorities of failure modes. Liu et al. [53] proposed a new risk assessment model for the prioritization of failure modes in FMECA based on FER and belief rule-based (BRB) method. In their method, FER method is utilized to capture and aggregate the diversified, uncertain evaluations provided by experts and the relationships of nonlinear and uncertainty between risk factors and corresponding risk level are modeled by BRB method. Du et al. [54] proposed a new method in fuzzy FMECA based on evidential reasoning (ER) and TOPSIS method for precisely determining and aggregating the risk factors. Li et al. [55] proposed a new method by integrating D–S Theory, DEMATEL, and IFS method to prioritize alternatives and make risk assessment for system FMECA. Yang et al. [27] introduced D–S Theory to FMECA for analyzing different failure modes in the rotor blades of an aircraft engine under multiple evaluation sources with uncertainty. Su et al. [56] aiming at the method of Yang et al. proposed a modification for dealing with the combination of conflicting evidence by using the Gaussian distribution-based uncertain reasoning method to reconstruct the basic belief assignments (BBAs) with considering the weight of each expert. Shi et al. [57] proposed a aggregation method for aggregating hybrid preference information based on IFS and D–S Theory, which determines the weight of each expert based on the conflict degree that is obtained by computing the conflict coefficient with Jousselme distance [58]. Jiang et al. [59] proposed a modified method for improving the performance of evidence theory used in FMECA, which reassigns the basic belief assignments by considering the reliability coefficients obtained based on evidence distance to reduce the conflicts among expert's opinion [60].

#### **3. Proposed FMECA Approach**
