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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
180 Jun-Li Shi et al.
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
A Modified Method for Risk Evaluation in Failure Mode and Effects Analysis 181
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-
182 Jun-Li Shi et al.
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
5 0.2 (1.2, 2.6, 3.2) (3.2, 4.2, 5.1) (5.0, 5.8, 6.3) (6.7, 7.6, 8.3) (8.6, 9.5, 10)Weighted average (1.3, 2.6, 3.6) (3.2, 4.2, 5.0) (4.7, 5.7, 6.4) (6.7, 7.4, 8.2) (8.3, 9.5, 10)
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
5 0.2 (1.4, 2.2, 3.3) (3.8, 4.6, 5.5) (4.9, 5.9, 6.6) (6.6, 7.6, 8.6) (8.7, 9.7, 10)Weighted average (1.4, 2.3, 3.1) (3.3, 4.4, 5.2) (4.8, 5.7, 6.7) (6.7, 7.4, 8.5) (8.2, 9.3, 10)
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
5 0.2 (1.2, 2.6, 3.2) (3.9, 4.6, 5.1) (5.0, 5.8, 6.3) (6.6, 7.6, 8.4) (8.1, 9.1, 10)Weighted average (1.3, 2.6, 3.0) (3.7, 4.3, 5.0) (4.8, 5.7, 6.4) (6.7, 7.5, 8.4) (8.2, 9.3, 10)
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
A Modified Method for Risk Evaluation in Failure Mode and Effects Analysis 183
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
184 Jun-Li Shi et al.
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.
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Manuscript Received: Nov. 27, 2015
Accepted: Apr. 21, 2016
186 Jun-Li Shi et al.