Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 4512383, 11 pages

http://dx.doi.org/10.1155/2016/4512383

## A Modified Model of Failure Mode and Effects Analysis Based on Generalized Evidence Theory

^{1}School of Electronics and Information, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, China^{2}Automotive Engineering Institute, Guangzhou Automobile Group Co., Ltd., Guangzhou, Guangdong 511434, China

Received 28 April 2016; Revised 15 June 2016; Accepted 30 June 2016

Academic Editor: Jianbing Ma

Copyright © 2016 Deyun Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Due to the incomplete knowledge, how to handle the uncertain risk factors in failure mode and effects analysis (FMEA) is still an open issue. This paper proposes a new generalized evidential FMEA (GEFMEA) model to handle the uncertain risk factor, which may not be included in the conventional FMEA model. In GEFMEA, not only the conventional risk factors, the occurrence, severity, and detectability of the failure mode, but also the other incomplete risk factors are taken into consideration. In addition, the relative importance among all these risk factors is well addressed in the proposed method. GEFMEA is based on the generalized evidence theory, which is efficient in handling incomplete information in the open world. The efficiency and some merit of the proposed method are verified by the numerical example and a real case study on aircraft turbine rotor blades.

#### 1. Introduction

Failure mode and effects analysis (FMEA) starts from aerospace industry in 1960s. It is a structural tool for analyzing the potential failure modes in a process, designing activity, service process, and so on. Based on the empirical knowledge from the FMEA team members, each failure mode will get a risk priority number to define its risk level, as well as some suggestions on how to control these failure modes to prevent them from having a bad effect on the customers. FMEA is an effective preventive approach to reduce the possibility of a failure. So far, FMEA has become a useful method in risk analysis being widely used in many real applications, like nuclear safety systems [1], software engineering [2], complex system analysis [3, 4], medical management [5–7], patient safety evaluation [8], shipping equipment [9, 10], automotive industry [11], food industry [12], and so on [13–17]. Currently, the study corresponding to FMEA mainly focuses on the following aspects.(i)Applying FMEA approach to many more particular fields for risk analysis: except for those applications mentioned above, FMEA is also used as a risk assessment tool in other particular fields like agriculture and food domain [18], environment protection [19], and so on [20, 21].(ii)Modifying the conventional risk priority number (RPN) model, which is the product of the three risks factors, occurrence (), severity (), and detection (), to make it more rational for ranking the priority of failure modes: the modified RPN value is based on many theories like the fuzzy set theory [16, 22, 23], the grey theory [24], the Monte Carlo method [25], the evidence theory [23, 26, 27], and so on [28–30]. Some of the proposed methods are hybrid methods [14, 23, 31]. A more detailed literature review on this topic is studied by Liu et al. [32].(iii)Addressing the subjective risk evaluation information of FMEA more flexibly: the evaluation information in FMEA method is effective and more flexible while it is combined with the approach of fuzzy theory [33–35], the grey theory [36, 37], the D-S evidence theory [23, 38, 39], the TOPSIS method [14, 40], the OWA operator [41], the D numbers [36], the AHP/ANP method [31, 42], the Bayesian reasoning method [28], and so on [5].These studies mentioned above all make contribution to improve the conventional FMEA method or extend it to different particular fields as an efficient risk analysis tool. But little attention has been paid to the incomplete risk factor; in other words, the other uncertain risk factor except for , , and should also be taken into consideration in real application. Other risk factors may be the period of development, the cost [30], the uncertain risk factors from many suppliers domestic and external, and so on. For example, from the commercial perspective, the cost can be the key factor in terms of a company’s financial objectives [30, 43]. And these risk factors should be taken into consideration independently like , , and . So, how to model these incomplete risk factors out of the conventional FMEA is addressed in this paper; then a modified model of FMEA is proposed based on the generalized evidence theory (GET) [44], namely, generalized evidential FMEA (GEFMEA). In addition, the relative importance among all these risk factors, not only the conventional one in RPN, but also the uncertain one, is taken into consideration in GEFMEA.

The generalized evidence theory [44], which is a more generalized situation of the Dempster-Shafer evidence theory (D-S evidence theory) [45, 46], is developed to handle the uncertain information in the open world. D-S evidence theory has been studied extensively during the past decades [47]; it is a useful mathematical theory for information fusion in real applications [26, 48–50]. Some key problems in D-S evidence theory are still worth further study, for example, the dependent evidence combination [51] and the determination of basic probability assignment [52]. The generalized evidence theory inherits the advantages of D-S evidence theory; what is more, if the frame of discernment is incomplete, the generalized basic probability assignment (GBPA) and generalized combination rule (GCR) in GET can handle the incomplete knowledge more efficiently [44]. In this paper, the incomplete risk factor which comes from the incomplete frame of discernment of FMEA in the open world is expressed by the empty set in the frame of generalized evidence theory. The GBPA is used to handle the relative importance of all these risk factors, including the incomplete one. In this way, the proposed GEFMEA model seemed as a more generalized model in the open world extended from conventional FMEA. GEFMEA can be degenerated to the conventional FMEA whenever it is necessary.

The rest of this paper is organized as follows. In Section 2, some preliminaries are briefly introduced. In Section 3, a new generalized evidential FMEA (GEFMEA) model is proposed. Two experiments based on GEFMEA are shown in Section 4. The conclusions are given in Section 5.

#### 2. Preliminaries

In this section, some preliminaries are introduced, including the failure mode and effects analysis (FMEA) model [54], D-S evidence theory [45, 46], the generalized evidence theory (GET) [44], and the pignistic probability transformation (PPT) model [55].

##### 2.1. Failure Mode and Effects Analysis

FMEA is one of the systematic techniques for risk analysis. Generally, FMEA model includes the following steps [54].

*Step 1. *Identifying the team: FMEA team members should be with the relevant experience and necessary authority.

*Step 2. *It includes defining the scope of the FMEA analysis and the customers of the FMEA process.

*Step 3. *It includes identifying the functions, requirements, and specifications relevant to the defined scope, as well as the potential failure modes, effects, causes, and controls.

*Step 4. *It includes identifying and assessing risk.

*Step 5. *It includes defining recommended actions and results.

Among all these five steps, Steps 1–3 are mainly based on empirical knowledge and qualitative analysis. In Step 4, the risk priority number (RPN) offers a useful way to assess the risk level of each failure mode. Step 5 is based on Step 4 and other more empirical knowledge. The risk evaluation in conventional FMEA is determined by the risk priorities of failure modes through the RPN value, which is defined as the product of three risk factors of a failure mode [29]:where is the probability of occurrence of a failure mode, is the severity of a failure effect, and is the probability of a failure being detected. Each risk factor has a numerical rating from 1 to 10. The suggested criterion of rating for occurrence () is shown in Table 1. Similarly, the criteria of rating for severity and detection can be found in [11, 32, 54].