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A Modified Method for Risk Evaluation in Failure

Mode and Effects Analysis

Jun-Li Shi 1,2*, Ya-Jun Wang1, Hai-Hua Jin1, Shuang-Jiao Fan1,Qin-Yi Ma1 and Mao-Jun Zhou1

1School of Mechanical Engineering and Automation, Dalian Polytechnic University,

Dalian 116034, P.R. China2Institute of Sustainable Design and Manufacturing, Dalian University of Technology,

Dalian 116024, P.R. China

Abstract

This study proposes a modified failure mode and effects analysis (FMEA) method based on

fuzzy set theory and fuzzy analytic hierarchy process (FAHP) by analyzing the limitations of the

traditional FMEA. First, the fuzzy language set of severity, occurrence, and detection is set up in this

method. Second, the failure mode is evaluated by a triangular fuzzy number based on the fuzzy

language set. Then, the weights of severity, occurrence, and detection are determined by the FAHP.

Finally, the risk priority of the failure modes is determined by the modified risk priority number (RPN).

The efficiency and feasibility of the modified FMEA method are verified by using it to deal with risk

evaluation of the failure modes for a compressor crankshaft.

Key Words: Failure Mode and Effects Analysis, Fuzzy Language Set, Triangular Fuzzy Number,

Fuzzy Analytical Hierarchy Process, Risk Priority Number

1. Introduction

The failure mode and effects analysis (FMEA), which

was first developed as a formal design methodology in

the 1960s, is an extensively used risk assessment tool to

define and identify potential failures in products, pro-

cesses, designs, and services [1]. The FMEA technique

has been extensively used in a wide range of industries,

such as in the aerospace, automotive, electronics, me-

dical and mechanical technology industries [2�5]. In

FMEA, prioritization of the failure modes is generally

determined through the risk priority number (RPN),

which provides an effective method of ranking the fai-

lure modes. The traditional RPN is obtained by multiply-

ing the occurrence (O), severity (S), and detection (D) of

a failure mode, as expressed in Eq. (1):

RPN = S � O � D (1)

where, S is the severity of the failure mode, O is the oc-

currence of the failure mode, and D is the probability of

not detecting the failure mode. The higher the RPN value

of a failure mode, the greater the risk for the product/

system. Three risk factors are evaluated by a numeric

scale (rating) from 1 to 10 to obtain the RPN of a poten-

tial failure mode. Table 1 shows the proposed criteria of

the rating for S of a failure mode in the FMEA. The nu-

meric scales for O and D follow the same criteria, be-

cause of the length limitation no more tautology here.

However, the RPN is criticized in most cases as a

crisp value because S, O, and D are crisp numbers [6].

The three main reasons for this are the following: First,

experts encounter difficulties in giving a precise number

for the three risk parameters in the crisp model because

FMEA experts’ opinions are mainly subjective and qual-

Journal of Applied Science and Engineering, Vol. 19, No. 2, pp. 177�186 (2016) DOI: 10.6180/jase.2016.19.2.08

*Corresponding author. E-mail: [email protected]

itative descriptions [7,8]. Second, the three risk factors

are considered to be of equal importance, and the relative

importance of the risk parameters is not considered while

calculating the RPN value [9]. Third, different combina-

tions of O, S, and D may result in exactly the same RPN

value, which in reality may be a different risk implica-

tion altogether [10].

The fuzzy concepts of the FMEA have been applied

in many attempts to reduce the aforementioned draw-

backs. Liu et al. [11] proposed a intuitionistic fuzzy hy-

brid technique for order preference by similarity to an

ideal solution (TOPSIS), which is a new modified me-

thod to determine the risk priorities of the identified fai-

lure modes. Mandal and Maiti [12] introduced fuzzy nu-

merical technique to remove the drawbacks of the crisp

FMEA. This technique integrated the concepts of the si-

milarity value measure of fuzzy numbers and possibility

theory. The methodology is more robust because it does

not require arbitrary precise operations (e.g., defuzzifi-

cation) to prioritize the failure modes. Wang et al. [13]

dealt with the problem of the crisp RPN not realistically

determining the risk priority of the failure modes by pro-

posing fuzzy RPNs (FRPNs). The FRPNs in their me-

thod were defined as the fuzzy weighted geometric means

of the fuzzy grades for O, S, and D. These means were

computed using alpha-level sets and linear programming

models. Hu et al. [14] applied the fuzzy analytic hierar-

chy process (FAHP) to determine the relative weights of

four factors when analyzing the risks of green compo-

nents in the incoming quality control stage in Taiwan. A

green component RPN is used to calculate each of the

components in this method. Xu et al. [15] presented a

fuzzy logic-based FMEA method to address the issue of

uncertain failure modes. They also showed a platform

for a fuzzy expert assessment, which was integrated with

the proposed method.

The aforementioned literature review shows signifi-

cant achievements in fuzzy FMEA research. This study

proposes a new risk assessment model by incorporating

the traditional FMEA and FAHP theory. The new model

could not only evaluate expert knowledge and experi-

ences more reasonably but could also consider the rela-

tive importance of the risk parameters (i.e., S, O, and D)

while calculating the RPN value.

2. Modified FMEA Method Based on Fuzzy

Theory and the FAHP

Figure 1 shows the broad framework of this me-

thod. This approach is developed to determine the func-

tional process and possible failure modes of the products,

analyze the causes and effects, and establish the fuzzy

language set and triangular fuzzy number (TFN) for S, O,

and D. Then, a clear number is calculated using defuzzi-

fication mathematical operations. Subsequently, a paired

comparison matrix is built using FAHP theory to deter-

178 Jun-Li Shi et al.

Table 1. Suggested rating criteria of failure severity in FMEA

Rating Effect Severity of effect

1 None No effect

2 Very minor System performance and satisfaction with slight effect

3 Minor System performance and satisfaction with minor effect

4 Low System performance is small affected, maintenance may not be needed

5 Moderate Performance of system or product is affected seriously, maintenance is needed

6 Significant Operation of system or product is continued and performance is degraded

7 Major Operation of system or product may be continued but performance is affected

8 Extreme Operation of system or product is broken down without compromising safe

9 Hazardous with warning Higher severity ranking of a failure mode, occurring with warning,consequence is hazardous

10 Hazardous without warning Highest severity ranking of a failure mode, occurring without warning andconsequence is hazardous

mine the weights of S, O, and D. Finally, the modified

RPN of each failure mode is calculated and correspond-

ing improvement measures are implemented accordingly.

2.1 Fuzzy Language Set of S, O and D

In traditional FMEA, since the assessment informa-

tion for risk factors mainly based on experts’ subjective

judgments, there is a high level of uncertainty involved.

In this paper, we choose linguistic terms for the assess-

ment of risk factors and the individual evaluation grade

set is defined as a language fuzzy set, as: S/O/D = {very

low (VL), low (L), medium (M), high (H), very high

(VH)}, the meaning of the fuzzy language set is shown in

Table 2.

2.2 Defuzzification Algorithm of the TFN

Quantification of the fuzzy language set can be

achieved using TFN. TFN is one of the major compo-

nents of fuzzy set theory, which is designed to deal with

the extraction of the primary possible outcome from a

multiplicity of information vaguely and imprecisely [16].

According to Laarhoven and Pedrycz [17], a TFN should

possess the following features:

Assuming that the TFN is~A = (l, m, u), the member-

ship function is defined in Eq. (2):

(2)

where l and u represent the lower and upper bounds of

the TFN, and m is the median value. TFN can be deter-

mined on the basis of the experts’ knowledge and expe-

riences.

Assuming the presence of n experts, if the weight of

the ith expert is �i, then the fuzzy evaluation variable of

a failure model for this expert is xi, xi � (1, 10) and xi =

(li, mi, ui). Then, the weighted average TFN of this vari-

able is obtained using Eqs. (3) to (6):

A Modified Method for Risk Evaluation in Failure Mode and Effects Analysis 179

Figure 1. Broad framework of modified FMEA.

Table 2. Meaning of fuzzy language set for S, O, D

Meaning of the fuzzy language setEvaluationdegree Severity (S) Occurrence (O) Detection (D)

Very low(VL)

System can basically or even cannot meet therequirements, but few customers could find defective

Failure is unlikelyoccurs

Probability of failure bedetected out is very high

Low(L)

System can run, but the performance of comfort orconvenience decreased, customer feel not satisfied

Failure rarelyoccurs

Probability of failure bedetected out is high

Medium(M)

System can run, but the components of comfort orconvenience cannot work, customers feel not satisfied

Failuressometimes occur

Failure cannot be detectedout occasionally

High(H)

System can run, but the performance drops, thecustomer feel not satisfied

Failures oftenoccur

Probability of failure bedetected out is relatively low

Very high(VH)

System cannot run, the basic functions are lost Failures occur Probability of failure bedetected out is very low

(3)

(4)

(5)

�i can be expressed as follows:

(6)

The operational laws of the two TFNs (i.e.,~A1 (l1,

m1, u1) and~A2 (l2, m2, u2)) comply with the following

rules [18] shown in Eqs. (7) to (10):

Addition of the fuzzy number:

(7)

Multiplication of the fuzzy number:

(8)

Division of the fuzzy number:

(9)

Reciprocal of the fuzzy number:

(10)

With regard to the defuzzification algorithm of the

TFN, this study selects the non-fuzzy method presented

by Xiao and Lee [19]. The calculation is presented in Eq.

(11):

(11)

where �(x) is the clear number of xi. M and N are deter-

mined by the degree of the deviation of l, m, and u,

which indicates that the possibility of m may be M times

of u and N times of l.

2.3 Weight Determination of S, O and D Based on

the FAHP

The AHP process, which was first introduced by

Saaty [20], is one of the extensively used multi-criteria

decision-making methods. However, the AHP is fre-

quently criticized because of its inability to overcome

fuzziness deficiency during decision making [21]. There-

fore, the FAHP, which is a fuzzy extension of the AHP,

is developed to solve vague problems. Laarhoven and

Pedrycz [17] incorporated Saaty’s AHP into fuzzy theory.

The FAHP procedure of determining the weights of S,

O, and D is described as follows:

Step 1: Construction of a hierarchical structure.

The goal of the desired problem is placed on the top

layer of the hierarchical structure, the evaluation criteria

and the alternatives are placed on the second and bottom

layer.

Step 2: Construction of the fuzzy judgment matrix~C .

The fuzzy judgment matrix~C is a pair wise compari-

son matrix of each alternative and evaluation criterion,

which is expressed in Eqs. (12) and (13), as follows:

(12)

(13)

Linguistic terms are assigned to the pair wise com-

parisons by investigating which of the two criteria is

more important [22]. Table 3 is the membership function

of linguistic scale


Step 3: Calculation of the TFN weights of each crite-

rion.

The calculation rules of the TFN weights are taken

from Buckley [23]. The computations are shown in Eq.

(14):

(14)

where ~cij is the fuzzy comparison value of criteria i to j,~r is the geometric mean of the fuzzy comparison value

of criterion i to each criterion, and ~�i is the fuzzy weight

of the ith criterion (i.e., i is S, O, and D).

Step 4: Calculation of the normalized clear weights of

each criterion.

The TFN weight ~�i of each criterion can be trans-

formed to the clear weight �' t using Eq. (11). The clear

weight would be transformed to a normalized clear

weight, as expressed in Eq. (15):

(15)

where ��S, ��O, and ��D are the clear weights of S, O,

and D, respectively, and �i is the normalized clear

weight of S, O, and D.

2.4 RPN Calculation

This calculation process aims to obtain the value of

the modified RPN based on the clear numbers and

weights of the three risk factors determined by Eqs. (11)

and (15). The modified RPN is calculated, as shown in

Eq. (16), for each failure mode:

(16)

3. Case Study

Compressor is the core component of air condition-

ing systems and refrigeration products. Its quality per-

formance directly affects the quality of these refrigera-

tion products. A compressor company plans to develop a

new type of scroll compressor and set up an FMEA pro-

ject team. The first task for this team is to identify and

predict the potential failure modes for six large parts of

the compressor. The “crankshaft” plays an important role

in the compressor and is usually used in power transmis-

sion, which demands higher quality and reliability. The

process using the modified FMEA method to identify

and evaluate the potential failure modes for this compo-

nent is discussed in the subsequent sections.

3.1 Potential Failure Mode Analysis of the

Compressor Crankshaft

Five cross-functional members in the FMEA team

decide to evaluate the modes using linguistic terms. The

five members are assigned the relative weights of 0.2,

0.3, 0.1, 0.2 and 0.2. Table 4 defines the fuzzy language

sets for five main potential failure modes.

3.2 Determining the TFN and Clear Number

The assessment information of the TFNs for the five

failure modes is presented in Table 5. The average TFN

of xi is calculated using Eqs. (3) to (6). The correspond-

ing clear number is obtained through Eq. (11).

When taking the calculation process “VL” of “bad

hardness” as an example, the average weight TFN be-

comes (l, m, u) = (1.3, 2.3, 2.7).

Accordingly, M = m/u = 0.85, N = m/l = 1.77.

Therefore, the clear number is obtained as follows:

(17)

The clear numbers of L, M, H, and VH for all the


failure modes identified in the FMEA are obtained using

the same method. Table 6 shows the results.

3.3 Determining the Weights of S, O and D

The fuzzy judgment matrix of S, O, and D that corre-


Table 5. Triangular fuzzy number of compressor crankshaft

Triangular fuzzy number (TFN)Potential failuremode Expert No � VL L M H VH

Bad hardness 1 0.2 (1.0, 2.1, 2.6) (2.2, 3.0, 4.2) (3.3, 4.6, 6.5) (5.3, 7.6, 8.6) (8.3, 9.6, 10)2 0.3 (1.4, 2.3, 2.9) (2.4, 3.5, 4.6) (3.9, 4.7, 6.3) (5.9, 7.4, 8.8) (7.9, 9.8, 10)3 0.1 (1.2, 2.4, 2.7) (2.6, 3.2, 4.5) (3.4, 4.3, 6.4) (5.8, 7.8, 8.5) (8.2, 9.5, 10)4 0.2 (1.6, 2.2, 2.8) (2.0, 3.3, 4.8) (3.5, 4.5, 6.2) (5.7, 7.5, 8.7) (7.8, 9.7, 10)5 0.2 (1.3, 2.3, 2.6) (2.4, 3.4, 4.7) (3.6, 4.4, 6.0) (5.5, 7.6, 8.4) (8.5, 9.4, 10)

Weighted average (1.3, 2.3, 2.7) (2.3, 3.3, 4.6) (3.6, 4.5, 6.3) (5.7, 7.5, 8.6) (8.1, 9.6, 10)

1 0.2 (1.0, 2.4, 3.1) (2.6, 3.5, 4.5) (4.7, 5.8, 6.4) (6.8, 7.3, 7.9) (8.6, 9.5, 10)2 0.3 (1.3, 2.1, 3.3) (2.7, 3.6, 4.4) (4.7, 5.7, 6.5) (6.7, 7.4, 8.3) (7.9, 9.1, 10)3 0.1 (1.4, 2.3, 3.5) (2.5, 3.4, 4.3) (4.6, 5.8, 6.4) (6.9, 7.8, 8.5) (8.8, 9.4, 10)4 0.2 (1.3, 2.2, 3.4) (2.6, 3.3, 4.2) (4.8, 5.6, 6.2) (6.7, 7.5, 8.3) (8.7, 9.6, 10)

Coaxiality tolerance

5 0.2 (1.2, 2.5, 3.2) (2.9, 3.6, 5.1) (5.1, 5.8, 6.3) (6.6, 7.6, 8.4) (7.8, 9.3, 10)Weighted average (1.2, 2.3, 3.3) (2.7, 3.5, 4.5) (4.7, 5.7, 6.4) (6.7, 7.5, 8.3) (8.3, 9.3, 10)

1 0.2 (1.1, 2.4, 3.1) (3.1, 4.1, 4.9) (4.7, 5.8, 6.4) (6.6, 7.1, 7.8) (8.7, 9.7, 10)2 0.3 (1.3, 2.6, 3.8) (3.2, 4.2, 5.1) (4.7, 5.7, 6.1) (6.9, 7.4, 8.4) (8.8, 9.6, 10)3 0.1 (1.4, 2.8, 3.8) (2.9, 4.3, 5.3) (4.6, 5.7, 6.3) (6.6, 7.2, 7.7) (7.9, 9.5, 10)4 0.2 (1.3, 2.5, 3.9) (3.1, 4.1, 4.8) (4.8, 5.6, 6.2) (6.7, 7.4, 8.2) (7.7, 9.2, 10)

Interleaving burr


1 0.2 (1.4, 2.4, 3.4) (2.9, 4.2, 5.4) (4.8, 5.8, 6.8) (6.8, 7.8, 8.8) (8.7, 9.7, 10)2 0.3 (1.3, 2.1, 2.8) (3.4, 4.5, 5.3) (4.7, 5.7, 6.7) (6.7, 7.6, 8.5) (7.8, 8.8, 10)3 0.1 (1.8, 2.8, 3.7) (2.8, 3.9, 4.9) (5.0, 5.8, 6.7) (5.9, 6.9, 7.6) (8.6, 9.5, 10)4 0.2 (1.5, 2.5, 2.9) (3.3, 4.3, 4.8) (4.6, 5.6, 6.6) (6.7, 7.7, 8.3) (7.8, 8.9, 10)

Supersize difference


1 0.2 (1.1, 2.4, 3.1) (3.6, 4.1, 4.6) (4.7, 5.8, 6.4) (6.8, 7.6, 8.4) (8.6, 9.5, 10)2 0.3 (1.3, 2.6, 2.8) (3.7, 4.2, 5.1) (4.7, 5.7, 6.5) (6.7, 7.4, 8.3) (7.9, 9.1, 10)3 0.1 (1.4, 2.8, 2.8) (3.5, 4.4, 5.3) (4.6, 5.8, 6.4) (6.6, 7.5, 8.5) (7.8, 9.4, 10)4 0.2 (1.3, 2.5, 2.9) (3.6, 4.3, 5.2) (4.8, 5.6, 6.2) (6.7, 7.5, 8.3) (8.7, 9.6, 10)

Cylindricity error


The TFN here is the measurement of failure mode getting from experts’ experiences and knowledge, for example, (1.0,2.1, 2.6) is the TFN of ‘VL’ for ‘Bad hardness’ getting from NO. 1 expert, in his opinion, the smallest value is 1.0, thebiggest value is 2.6, and the median value is 2.1. The other TFNs are obtained as the same way.

Table 4. Linguistic terms and fuzzy language sets of five failure modes for compressor crankshaft

Potential failure mode analysis

Potential failure mode Consequences of failures Causes of failures S O D

Bad hardness Unstable working performance Serious abrasion of Jigs and fixtures H M LCoaxiality tolerance Unable to install and connect Bad clamping and positioning L VL MInterleaving burr Unstable working performance Worker’s weak quality awareness M L VLSuper size difference Unable to install the connection Error compensation value of tools VH H MCylindricity error Cause the device to the cutter Top Seriously wear VH L M

sponds to the relative importance of the RPN is deter-

mined using Eq. (12) (Table 7). The weights of S, O, and

D are calculated using the method proposed in section

2.3. Table 8 shows the results. The weights of �S, �O, and

�D for “bad hardness” are calculated as follows:

(18)

The clear weight numbers of ��S, ��O, and ��D and

the normalized clear weights of �S, �O, and �D are ob-

tained using Eqs. (11) and (15), respectively (Table 8).

3.4 Calculating the Modified RPN Value and

Determining the Risk Ranking

Finally, the modified RPN value is calculated using

Eq. (16). The first failure mode “bad hardness” is taken

as an example, as follows:

Modified RPN = s�C � o�o � d�D =7.4 � 0.54 � 4.8

� 0.28 � 3.5 � 0.18 = 3.38

The modified RPN value for all the failure modes is

calculated using the same method (Table 9). The clear

numbers of the modified S, O, and D are obtained from

Tables 4 and 6. The weights are obtained from Table 8.

As is shown in Table 9, the RPN values of “super size

difference” and “bad hardness” are ranked as first and

second, respectively. Therefore, they have the highest risk

and should be well controlled.

3.5 Traditional RPN Value and Risk Ranking

Table 10 shows the risk ranking of the failure modes

according to the traditional FMEA method. The tradi-

tional values of S, O, and D are obtained from the previ-

ous FMEA team of this compressor company. The value

selection criteria are obtained from Table 1, and the RPN

value is calculated using Eq. (1). Table 10 shows that

“super size difference” and “cylindricity error” are the

first and second risk potential failure modes to be con-

trolled.

3.6 Comparison and Discussion

Figure 2 shows the percentage comparison of the two

RPN alternatives for five failure modes. It is clearly that


Table 6. Clear number of failure modes

Clear numberPotential failure mode

VL L M H VH

Bad hardness 2.2 3.5 4.8 7.4 9.4Coaxiality tolerance 2.4 3.6 5.7 7.5 9.2Interleaving burr 2.7 4.2 5.7 7.4 9.3Super size difference 2.4 4.4 5.8 7.5 9.2Cylindricity error 2.4 4.3 5.7 7.5 9.2

the two RPN results are similar with each other. The

most serious failure mode in the two methods is “super

size difference,” which is 53.14% and 47.47% in the

modified and traditional RPNs, respectively. The two

least serious failure modes are “interleaving burr” and

“coaxiality tolerance” in both methods and the percent-

age results are similar also. The “interleaving burr” of all

the failure modes is only 2.06% and 3.30% in the modi-

fied and traditional RPNs, whereas the “coaxiality toler-

ance” is 7.87% and 7.91%, respectively.

However, the severity and detection of the failure

mode “cylindricity error” are very high in the traditional

FMEA, the RPN value is therefore also higher than the

others and ranks second in the modes to be controlled.

By contrast, the occurrence of “bad hardness” is higher

than “cylindricity error” in the modified FMEA, the RPN

value is also higher, which takes this mode to the second


Table 9. Modified RPN risk ranking

Clear number of S, O, D and RPN risk rankingPotential failure mode

s o d RPN Percent (%) Risk ranking

Bad hardness 7.4 4.8 3.5 3.38 25.84 2Coaxiality tolerance 3.6 2.4 5.7 1.03 07.87 4Interleaving burr 5.7 4.2 2.7 0.27 02.06 5Super size difference 9.2 7.5 5.8 6.95 53.14 1Cylindricity error 9.2 2.4 5.7 1.45 11.09 3

Figure 2. Modified and traditional RPN percentage of fivefailure modes.

Table 10. Traditional RPN risk ranking

Traditional number of S, O, D and RPN risk rankingPotential failure mode

s o d RPN Percent (%) Risk ranking

Bad hardness 8 5 4 160 17.58 3Coaxiality tolerance 4 3 6 072 07.91 4Interleaving burr 5 3 2 030 03.30 5Super size difference 9 8 6 432 47.47 1Cylindricity error 9 4 6 216 23.74 2

place, as a result, the risk priority is changed. This is

because that the clear numbers of S, O, and D for the

failure mode are obtained by the TFN operation, and the

weight is fully considered. Furthermore, expert know-

ledge and experience are more reasonably processed,

which could enable the compressor FMEA team to con-

trol the measures for the failure modes more objectively.

Consequently, the modified FMEA method could

make more comprehensive and accurate judgments on

the risk priority for the failure modes, which overcome

the limitation of crisp RPN, and can be practically used

in industrial production.

4. Conclusions

The FMEA, which has been extensively used in in-

dustries, plays an important role in analyzing safety and

reliability. This study develops and applies a modified

FMEA method to determine the risk priority of the fail-

ure modes considering the difficulty in acquiring precise

assessment information on failure modes. Accordingly,

expert knowledge and experiences are fully considered.

This method could provide a qualitative evaluation of

the failure modes by establishing a fuzzy language set

and TFNs. The weights of severity, occurrence, and

detection can also be determined through the FAHP by

comprehensively considering the importance of each va-

riable and the decision maker’s risk preference. In this

way, the limitations associated with the traditional crisp

RPN-based FMEA in risk and failure analysis can be

overcome to a significant extent.

The potential failure modes of the “compressor crank-

shaft” are evaluated to test and verify the feasibility and

validity of the proposed method. This evaluation is con-

ducted by calculating and comparing the modified and

traditional RPNs and determining the risk priority rank-

ing of each failure mode.

Notably, the TFNs determining for each potential

failure mode is based on expert investigation when using

this modified FMEA method. Therefore, the experts se-

lected must be familiar with product design and produc-

tion. The TFN algorithm employed to derive the clear

number is not limited to the case presented in this study.

This method could certainly be used for other products or

systems to determine potentially high-risk failure modes.

Acknowledge

The authors gratefully acknowledge the support of

Liaoning Province Natural Science Foundation (20140

26006) and Dalian Sanyo Co., LTD.

The authors would like to thank the editor and re-

viewers for their constructive suggestions of the paper.

References

[1] Bowles, J. B. and Peláez, C. E., “Fuzzy Logic Priori-

tization of Failures in a System Failure Mode, Effects

and Criticality Analysis,” Reliability Engineering and

System Safety, Vol. 50, No. 2, pp. 203�213 (1995). doi:

10.1016/0951-8320(95)00068-D.

[2] Su, X. Y., Deng, Y., Mahadevan, S. and Bao, Q. L.,

“An Improved Method for Risk Evaluation in Failure

Modes and Effects Analysis of Aircraft Engine Rotor

Blades,” Engineering Failure Analysis, Vol. 26, pp.

164�174 (2012). doi: 10.1016/j.engfailanal.2012.07.

009

[3] Chang, K. H. and Cheng, C. H., “Evaluating the Risk

of Failure Using the Fuzzy OWA and DEMATEL

Method,” Journal of Intelligent Manufacturing, Vol.

22, pp. 113�129 (2011). doi: 10.1007/s10845-009-

0266-x

[4] Arabian-Hoseynabadi, H., Oraee, H. and Tavner, P. J.,

“Failure Modes and Effects Analysis (FMEA) for Wind

Turbines,” Electrical Power and Energy Systems, Vol.

32, No. 7, pp. 817�824 (2010). doi: 10.1016/j.ijepes.

2010.01.019

[5] Silveira, E., Atxaga, G. and Irisarri, A. M., “Failure

Analysis of Two Sets of Aircraft Blades,” Engineering

Failure Analysis, Vol. 17, No. 3, pp. 641�647 (2010).

doi: 10.1016/j.engfailanal.2008.10.015

[6] Liu, H. C., Liu, L., Liu, N. and Mao, L. X., “Risk Eval-

uation in Failure Mode and Effects Analysis with Ex-

tended VIKOR Method under Fuzzy Environment,”


Expert Systems with Applications, Vol. 39, No. 7, pp.

12926�12934 (2012). doi: 10.1016/j.eswa.2012.05.031.

[7] Zhang, Z. F. and Chu, X. N., “Risk Prioritization in

Failure Mode and Effects Analysis under Uncertainty,”


206�214 (2011). doi: 10.1016/j.eswa.2010.06.046

[8] Zammori, F. and Gabbrielli, R., “ANP/RPN: A Multi

Criteria Evaluation of the Risk Priority Number,” Qua-

lity and Reliability Engineering International, Vol. 28,

No. 1, pp. 85�104 (2012). doi: 10.1002/qre.1217

[9] Kutlu, A. C. and Ekmekçio�lu, M., “Fuzzy Failure

Modes and Effects Analysis by Using Fuzzy TOPSIS-

based Fuzzy AHP,” Expert Systems with Applications,

Vol. 39, No. 1, pp. 61�67 (2012). doi: 10.1016/j.eswa.

2011.06.044

[10] Keskin, G. A. and Özkan, C., “An Alternative Evalua-

tion of FMEA: Fuzzy ART Algorithm,” Quality and

Reliability Engineering International, Vol. 25, No. 6,

pp. 647�661 (2009). doi: 10.1002/qre.984

[11] Liu, H. C., You, J. X., Shan, M. M. and Shao, L. N.,

“Failure Mode and Effects Analysis Using Intuition-

istic Fuzzy Hybrid TOPSIS Approach,” Soft Comput-

ing, Vol. 19, No. 4, pp. 1085�1098 (2015). doi: 10.

1007/s00500-014-1321-x

[12] Mandal, S. and Maiti, J., “Risk Analysis Using FMEA:

Fuzzy Similarity Value and Possibility Theory Based

Approach,” Expert Systems with Applications, Vol. 41,

No. 7, pp. 3527�3537 (2014). doi: 10.1016/j.eswa.2013.

10.058

[13] Wang, Y. M., Chin, K. S., KaKwaiPoon, G. and Yang,

J. B., “Risk Evaluation in Failure Mode and Effects

Analysis Using Fuzzy Weighted Geometric Mean,”


1195�1207 (2009). doi: 10.1016/j.eswa.2007.11.028

[14] Hu, A. H., Hsu, C. W., Kuo, T. C. and Wu, W. C., “Risk

Evaluation of Green Components to Hazardous Sub-

stance Using FMEA and FAHP,” Expert Systems with

Applications, Vol. 36, No. 3, pp. 7142�7147 (2009).

doi: 10.1016/j.eswa.2008.08.031

[15] Xu, K., Tang, L. C., Xie, M., Ho, S. L. and Zhu, M. L.,

“Fuzzy Assessment of FMEA for Engine Systems,”

Reliability Engineering and System Safety, Vol. 75,

No. 1, pp. 17�29 (2002). doi: 10.1016/S0951-8320

(01)00101-6

[16] Zadeh, L. A., “Fuzzy Sets,” Information and Control,

Vol. 8, No. 3, pp. 338�353 (1965). doi: 10.1016/

S0019-9958(65)90241-X

[17] Laarhoven, P. J. M. and Pedrycz, W., “A Fuzzy Exten-

sion of Saaty’s Priority Theory,” Fuzzy Sets and

Systems, Vol. 11, pp. 229�241 (1983). doi: 10.1016/

S0165-0114(83)80082-7

[18] Kaufmann, A. and Gupta, M. M., “Fuzzy Mathemati-

cal Models in Engineering and Management Science,”

Amsterdam: North Holland, pp. 121�122 (1988).

[19] Xiao, Y. and Lee, H., “Improvement on Judgment Ma-

trix Based on Triangle Fuzzy Number,” Fuzzy Systems

and Mathematics, Vol. 17, pp. 59�64 (2003).

[20] Saaty, T. L., The Analytic Hierarchy Process, McGraw-

Hill, New York (1980).

[21] Abdullah, L. and Zulkifli, N., “Integration of Fuzzy

AHP and Interval Type-2 Fuzzy DEMATEL: an Appli-

cation to Human Resource Management,” Expert Sys-

tems with Applications, Vol. 42, No. 9, pp. 4397�4409

(2015). doi: 10.1016/j.eswa.2015.01.021

[22] Hosseini Ezzabadi, J., Saryazdi, M. D. and Mostafa-

eipour, A., “Implementing Fuzzy Logic and AHP into

the EFQM Model for Performance Improvement: a

Case Study,” Applied Soft Computing, Vol. 36, pp.

165�176 (2015). doi: 10.1016/j.asoc.2015.06.051

[23] Buckley, J. J., “Fuzzy Hierarchical Analysis,” Fuzzy

Sets and Systems, Vol. 17, No. 3, pp. 233�247 (1985).

doi: 10.1016/0165-0114(85)90090-9

Manuscript Received: Nov. 27, 2015

Accepted: Apr. 21, 2016


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