Failure mode and effects analysis (FMEA) for risk assessment based on interval type-2 fuzzy evidential reasoning method

Highlights

• An interval type-2 fuzzy evidential reasoning method for FMEA is proposed.

• Various assessments of team members are expressed by predefined linguistic terms.

• A linear programming model to generate belief structure is developed.

• An interval RPN is produced by fusing the information of three risk factors.

• Demonstrate advantages of the proposed risk model with a steam valve system case.

Abstract

Failure mode and effect analysis (FMEA) has been widely adopted to define, identity, and remove potential and recognized hazards. As an indicator in traditional FMEA, the risk priority number (RPN) is an effective tool for measuring risk and the calculation of RPN is also very simple. Nevertheless, there are many drawbacks in the conventional FMEA method. It is necessary to seek approaches that can make up for the deficiency of traditional FMEA method and strengthen assessment capability of ranking failure modes according to three relevant risk factors. This paper presents a way to combine interval type-2 fuzzy sets (IT2FSs) with evidential reasoning (ER) method, which is able to overcome some disadvantages of the conventional FMEA approach and deal with uncertainties more efficiently. First, we give a more precise expression of the risk factors in the form of IT2FSs and gain the relative weight of three risk factors. Second, one can judge the failure modes in relation to each risk factors with belief structures. Finally, the ER method is used to combine the belief structures under the weight of the three risk factors. To verify the feasibility of the method, an application for steam valve system is performed and the obtained results show the effectiveness of the method.

Introduction

Failure mode and effects analysis (FMEA) used in systems, designs, and product has drawn much attention [1]. Unlike other risk assessment tools that look for solutions after failure occurred, the main functions of FMEA include identifying various potential failures and assessing their risk. Then precautions may be taken to decrease the likelihood and severity of failure or avoid dangerous accidents. FMEA was proposed by aeronautical engineering in the 1960s to inform risk management decisions [2]. When used in critical analysis, it is also known as the failure mode, effects and criticality analysis (FMECA) [3], [4]. In general, a team of experts who have a good command of expertise in some certain fields are required to examine and quantify failure modes, impacts, reasons and come up with present countermeasures comprehensively in FMEA.

A classic FMEA is made up of five implementing procedures: preparation, identification, prioritization, risk reduction, and re-evaluation [5]. Among them, prioritization between each failure mode by suitable way is the main task of this paper. The RPN is a useful tool for measure risk, which takes the occurrence of failure modes ($O$), the severity of failures effect ($S$) and the probability of not detecting the failure ($D$) into account [6]. Normally, analysts or experts rate the three risk factors from 1 to 10, then RPN is obtained as the product of three risk factors. A failure mode with a higher RPN is regarded more dangerous and worth giving greater attention [7].

The FMEA method has been widely applied to automotive [8], medical and health [9], [10], [11], electronics [1], aerospace [12] and other fields. However, various deficiencies of the original RPN formula have also attracted attention, for instance, there is the difficulty in dealing with the complex uncertainty in risk assessment [4]. The uncertainties may present in many ways, for instance, limited professional knowledge and background leading to inaccurate and incomplete evaluation of FMEA team members [13]. Up to now, uncertainty has been studied widely with the use of various uncertainty theories, such as fuzzy set theory [14], [15], evidence reasoning theory [13], [16], grey theory [17], D-numbers approach [18] and others.

Fuzzy sets theory provides a means to express the uncertainty, which can well deal with fuzzy concepts. Considerable research efforts have been devoted to fuzzy sets theory in FMEA approach [5], [19], [20], [21]. Meanwhile, various methods under fuzzy environment applied to handle FMEA problem have widely received attention. For example, Liu et al. [20] developed a fuzzy VIKOR approach for prioritizing failure modes. Comparing with type-1 fuzzy sets (T1FSs), that IT2FSs are capable of coping with the intra-uncertainty and inter-uncertainty in risk assessment problems [5] also makes it widely used in numerous models, while few studies have concentrated on FMEA problem.

In other way, evidential reasoning (ER) method is a kind of decision-making method firstly proposed on the basis of Dempster–Shafer (D–S) evidence theory and decision theory. The ER method makes up for the traditional MCDM method by establishing a unified confidence framework to describe all kinds of uncertainties in the problem. In general, the D–S theory can well handle many synthesis problems with fuzzy and uncertain information, and has certain advantages when aggregating different experts’ opinions. But it is often necessary to consider the impact of multiple risk factors on the failure mode. Hence, it is reasonable to apply ER method which uses weights to correct the evidence and improves D–S evidence theory in FMEA. The ER method integrated with other theories have also had intensive applications in FMEA. For instance, Liu et al. [22] used fuzzy evidential reasoning (FER) method and grey theory to modify the traditional risk assessment model. Du et al. [23] developed a fuzzy FMEA method adopting ER and TOPSIS, in which ER is to present the evaluation information of FMEA team members and TOPSIS is taken to rank the risk priority of failure mode. Li and Chen [24] came up with an evidential method combining fuzzy BPAs and grey relational projection method

The main motivation of this study is as follows: For one thing, there are a large quantity of uncertainties in FMEA. ER in dealing with uncertain or incomplete decision information has a unique advantage. For another, combination rule of ER can effectively integrate the consistent part of evidence and strengthen the result of the consistent part. Using such formula one can fuse the individual risk information of $O$, $S$ and $D$ and have a comprehensive understanding of risk level. This paper attempts to come up with a FMEA approach on the basis of interval type-2 fuzzy evidential reasoning method, which combines the IT2FSs and evidence theory and measures risk more precisely.

Aiming at the uncertainty and fuzziness in the course of risk assessment, this paper uses the linguistic variable that being expressed as IT2FSs to appraise the fuzzy related importance about risk factors and the fuzzy rating of failure mode. According to the risk factors in failure mode analysis, the ER method is used to synthesize interval risk evidence and a new failure mode priority ranking method is found. The major contributions of this paper are summarized up as follows: (1) Risk factors reflect the source or influence of risk from three different perspectives. The relative importance given by experts as the weight of each attributes is effective to deal with extremely conflicting evidence [25] because D–S evidence theory may draw a counter-intuitive conclusion. (2) As an extension of the T1FSs, the extra one-dimensional membership of IT2FSs makes it more flexible than the T1FSs in expressing the fuzziness. So IT2FSs can express the fuzzy language evaluation information more efficiently. By synthesizing each expert’s opinion in the form of IT2FSs and assigning the collective IT2FSs to its two adjacent levels, the belief structure becomes an interval that includes all possible belief degree value, which makes it more flexible in expressing the fuzziness than a certain belief degree value. (3) By integrating the risk information of $O$, $S$ and $D$, the value of final RPN in the shape of interval could be gained. The interval RPN scales are continuous and most of them are unique, which can improve the weakness of traditional methods and correctly reflect the subtle differences in evaluation.

The paper is organized as follows. In the following section, the previous studies concerned with FMEA, ER method and IT2FSs are reviewed. In Section 3, A brief description of some basic concepts related to IT2FSs and ER method are introduced. Section 4 presents the proposed FMEA method in detail, which combines IT2FSs and ER for prioritization. A specific example with the application of presented FMEA method is put into use in Section 5 to demonstrate the feasibility of the method. Finally, Section 6 covers conclusions of this paper and points out future research directions.