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Quality Engineering
ISSN: 0898-2112 (Print) 1532-4222 (Online) Journal homepage: http://www.tandfonline.com/loi/lqen20
An improved approach for failure mode and effect
analysis involving large group of experts: An
application to the healthcare field
Hu-Chen Liu, Xiao-Yue You, Fugee Tsung & Ping Ji
To cite this article: Hu-Chen Liu, Xiao-Yue You, Fugee Tsung & Ping Ji (2018): An improved
approach for failure mode and effect analysis involving large group of experts: An application to the
healthcare field, Quality Engineering, DOI: 10.1080/08982112.2018.1448089
To link to this article: https://doi.org/10.1080/08982112.2018.1448089
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QUALITY ENGINEERING
, VOL. , NO. , –
https://doi.org/./..
An improved approach for failure mode and effect analysis involving large
group of experts: An application to the healthcare field
Hu-Chen Liua,b,Xiao-YueYou
b, Fugee Tsungc, and Ping Jid
aSchool of Management, Shanghai University, Shanghai, China; bSchool of Economics and Management, Tongji University, Shanghai, PR China;
cDepartment of Industrial Engineering and Logistics Management, Hong Kong University of Science and Technology, Kowloon, Hong Kong;
dDepartment of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong
KEYWORDS
Cluster analysis; failure mode
and effect analysis (FMEA);
healthcare risk assessment;
prospect theory; reliability
management
ABSTRACT
Failure mode and eect analysis (FMEA) is a team-based technique for prospectively identifying and
prioritizing failure modes of products, processes, and services. Given its simplicity and visibility, FMEA
has been widely used in dierent industries for quality and reliability planning. However, various
shortcomings are inherent to the traditional FMEA method, particularly in assessing failure modes,
weighting risk factors, and ranking failure modes, which greatly reduce the accuracy of FMEA. Addi-
tionally, the classical FMEA focuses on the risk analysis problems in which a small number of experts
participate. Nowadays, with the increasing complexity of products and processes, an FMEA may
require the participation of larger number of experts from distributed departments or organizations.
Therefore, in this article, we present a novel risk priority approach using cluster analysis and prospect
theory for FMEA when involving a large group of experts. Furthermore, an entropy-based method is
proposed to derive the weights of risk factors objectively by utilizing the risk-evaluation information.
Finally, we take an empirical healthcare risk analysis case to illustrate the proposed large group FMEA
(LGFMEA) approach, and conduct a comparative study to evaluate its validity and practicability.
Introduction
Failure mode and eect analysis (FMEA) is a system-
atic reliability analytical technique to identify, analyze
and reduce the failures of products, processes, and
services (Stamatis 2003). It provides a group-oriented,
structured, and stepwise tool to quantify the eects
of potential failure modes, allowing a company to
set priorities for risk-management activities. Since its
development in the 1960s in the aerospace industry,
the FMEA technique has been rapidly adopted by
the automotive industry and many other industries
(Kim and Zuo 2018;Liu2016). Compared with other
reliability management tools, FMEA can prospectively
examine a high-risk process and identify vulnerabil-
itiestogeneratecorrectivemeasurestohelpimprove
reliability (Liu et al. 2016b; Peeters, Basten, and Tinga,
2018). Hence, a great deal of expenses, resources, and
time can be saved by analyzing fault scenarios before
they have occurred and preventing the occurrence of
causes or mechanisms of failures. Nowadays, FMEA
CONTACT Xiao-Yue You huchenliu@shu.edu.cn;youxiaoyue@gmail.com School of Economics and Management, Tongji University, Siping Road,
Shanghai , PR China.
Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lqen.
has become an important tool in Lean/Six Sigma
and concurrent engineering, and has been used not
only in manufacturing systems (Certa et al. 2017a;
Zhou et al. 2016), but also in healthcare risk assess-
ment (Faiella et al. 2018;Liuetal.2017a), maritime
transport(Akyuzetal.2016), food processing (Selim,
Yunusoglu, and Yılmaz Balaman, 2016), photovoltaic
systems maintenance (Villarini et al. 2017), etc.
In the traditional FMEA, importance of each fail-
uremodeisrankedbasedontheriskprioritynum-
ber(RPN),whichisderivedbytheproductofthree
risk factors: occurrence (O), severity (S), and detec-
tion (D). Based on pre-established criteria, a 10-scale
measurement is often employed to evaluate each of
the three risk factors, 10 being the number indicat-
ing the most severe, most frequent, and least detectable
failure mode, respectively. After computing RPNs, the
failuremodesareanalyzedusingaParetodistribu-
tion. The failure modes with higher RPNs could be
viewed as more important and should be given the top
© Taylor & Francis
2H.-C. LIU ET AL.
priority for risk mitigation. All the identied failure
modes are collected on a standard table of FMEA, and
recommended actions are suggested for the anoma-
lous situations exhibiting the highest RPN values. The
results of the risk analysis can be updated after under-
taking mitigating measures and preventive actions,
until a satisfying value of RPN is achieved for all the
listed failure modes. However, the traditional RPN
method, when used in real situations, shows some
important drawbacks as cited in (Certa et al. 2017b;
Chemweno et al. 2017;Chinetal.2009;Jee,Tay,and
Lim, 2015;Liuetal.2017c;Liuetal.2016a;Pillay
and Wang 2003;Songetal.2014). In many cases,
FMEA team members’ judgments and assessments
are ambiguous, vague, and cannot be estimated with
numeric values, so the exact values from 1 to 10 are
not suitable to model practical risk analysis situations.
Second,theweightsgiventothethreeriskfactorsare
equal. However, in the real-life application, the weights
for quantitative and qualitative risk factors may be dif-
ferent. Third, the multiplication of risk factors to obtain
theRPNisafundamentalawinthetraditionalFMEA.
TheriskfactorsO,S,andDareevaluatedbasedon
ordinal scales, but their multiplication is not a mean-
ingful measure in terms of the measurement theory.
Therefore, in the past decade, many researchers have
developed a lot of modied FMEA models to deter-
mine the ranking orders of failure modes, taking care
of the limitations discussed above. For an excellent
review of the drawbacks related to the conventional
RPN method and the alternative risk priority models
that have appeared in the literature, see Liu, Liu, and Liu
(2013b).
Some scholars indicated that FMEA is a decision
function performed by a cross-functional and mul-
tidisciplinary team (Carpitella et al. 2018;Liuetal.
2017b;Liuetal.2017c). Guerrero and Bradley (2013)
proved that groups outperform individuals in the pri-
oritization of failure modes via an experimental study.
However, current FMEA practices are dominated by
critically analysis problems featuring few experts (ve
or less). Along with more complicacy of products and
processes, FMEAs are often implemented under dis-
tributed settings, such as oshore outsourcing. That is,
FMEAmightbeusedtocoordinateanexpertgroup
that is dispersed across organizations and countries
such that the incidence of failures can be reduced.
In such situations, it is often the case that the risk anal-
ysis results by a small FMEA team are either hard or
impossible to reect the actual situation of a distributed
organization. This causes a serious dilemma for FMEA
practice: The FMEA has been broadly used in vari-
ous areas but it is working worse than many people
expected. To ensure the eectiveness of FMEA, large
numbers of experts from distributed departments or
institutions should be involved especially for complex
products and services. Guerrero and Bradley (2013)
made an important statement in their research that a
super group can lead to the reduction of bias and errors
for individual risk experts (i.e., “wisdom of crowds”).
However, the experts participating in a large group
FMEA (LGFMEA) (the FMEA team involves more
than 20 experts) may have many dierences in their
attitudes, knowledge, and self-interests. Thus, it is reg-
ularly very dicult to reach a unanimous agreement
among large FMEA team members. Consequently, it
is of great theoretical signicance and practical value
to develop new risk priority models that can eec-
tively handle challenges posed by the explosion of risk-
assessment data in LGFMEA.
Based on the above discussions, we develop a novel
risk priority approach for solving the LGFMEA prob-
lems characterized by unknown risk factor weights and
linguistic assessment information. For the proposed
approach,werstclusterfailuremodeassessments
of large FMEA group using a clustering method and
each produced cluster is considered as a decision unit.
Then we aggregate the risk assessments of various clus-
ters fully considering conict assessments and majority
opinions of experts. Next, we propose an entropy-based
method to derive the weights of risk factors objec-
tively by utilizing the risk evaluation information. After
that, prospect theory is used to generate the risk rank-
ing of the failure modes that have been recognized.
For doing so, the remainder of this article is struc-
tured as follows. Section “Related literature” reviews
the literature related to this study briey. Section “The
proposed LGFMEA model” develops the risk-ranking
model for FMEA within the large group context. Sec-
tion “Case study” investigates the feasibility and valid-
ity of the proposed LGFMEA approach through a prac-
ticalhealthcareriskanalysisexample.Finally,section
“Conclusions” summarizes the major research ndings
and outline future research directions.
QUALITY ENGINEERING 3
Related literature
This article is mainly related to two streams of litera-
ture. The rst one is the literature on FMEA improve-
ment. Currently, plenty of attentions have been paid
to the limitations of the traditional FMEA and many
useful risk-ranking methods have been brought up, for
example, by using mathematical programming (Chin
et al. 2009), articial intelligence (Jee, Tay, and Lim,
2015;Liu,LiuandLin,2013a), and other methods (Kim
and Zuo 2018;vonAhsen2008). This article is particu-
larly related to previous researches on the application of
multiple criteria decision-making (MCDM) methods
to enhance the performance of FMEA. In this aspect,
Chang, Wei, and Lee (1999) used the fuzzy gray rela-
tional analysis (GRA) approach for nding the risk pri-
ority of product and process failures, Braglia, Frosolini,
and Montanari (2003) adopted the fuzzy technique for
order preference by similarity to ideal solution (TOP-
SIS) method to prioritize the potential risks of fail-
ure modes in criticality analysis, and Seyed-Hosseini,
Safaei, and Asgharpour (2006) applied the decision-
making trial and evaluation laboratory (DEMATEL)
technique for the priority ranking of failures in the sys-
tem with many subsystems or components. Liu et al.
(2014) evaluated the risk of failure modes with an
extended MULTIMOORA (multi-objective optimiza-
tion by ratio analysis plus the full multiplicative form)
method under fuzzy environment, Adhikary et al.
(2014) estimated the criticalities of failure modes by
employing the gray-complex proportional assessment
(COPRAS-G) tool, and Liu et al. (2016a) determined
theriskpriorityoffailuremodesusinganELECTRE
(ELimination Et Choix Traduisant la REalité) approach
within interval 2-tuple linguistic setting. Besides, a sys-
tematic introduction of the modied FMEA models
based on uncertainty theories and MCDM methods
can be found in (Liu 2016). In this study, we con-
tribute to the literature by applying a prospect theory-
based method for the reprioritization of failure modes
in FMEA. The new method overcomes the critical weak
points of the traditional FMEA and provides more
reasonable and credible solutions for facilitating risk-
management decision making.
The second related stream of research is the one
on group decision making, which is one of the central
topics in decision science. Given that many decisions
within organizations are made in a group setting,
group decision-making problems have been studied
extensively for making better decisions. For example,
Yu (1973) presented a class of solutions for group
decision problems of which each individual’s utility
function over a decision space is assumed to be known.
Keeney (1975) suggested a group decision-making
method to address the complexities that there is
uncertainty concerning the impact of alternatives and
individuals have dierent preference attitudes toward
risks. In Bodily (1979), the authors proposed a dele-
gation process to set the weights of decision makers
in a surrogate utility function for group decision mak-
ing under uncertainty. Boje and Murnighan (1982)
investigated the eect of two group decision-making
techniques on a set of problems in dierent group sizes,
and found that pooled individual estimates are more
accurate than those obtained from face-to-face verbal
feedback and received written feedback. Hochbaum
and Levin (2006) put forward an optimization frame-
work for group-ranking decisions, which allows for
exibility in decision protocols and considers imprecise
beliefs and dierentiation between reviewers accord-
ing to their expertise. Altuzarra, Moreno-Jiménez,
and Salvador (2010) employed a Bayesian-based
framework for establishing consensus in the analytic
hierarchy process (AHP) group decision making,
which permits automatic identication of “agreement”
and “disagreement” zones among the involved decision
makers.However,fewexistingstudiesfocusonthe
large group decision-making problems (Cai et al. 2017,
Liu et al. 2015), especially in FMEA. Our contribution
to the group decision-making literature is providing
an algorithm to cope with the group decision making
characterized by large numbers of participators in
distributedgroupsandbasedonconictassessments
and majority opinions. This method is helpful to get
representative collective assessments that are easily
accepted by decision makers, and can relieve the inu-
ence of biased opinions and assessment dierences on
the nal decision results.
The proposed LGFMEA model
ALGFMEAproblemcanbedenedasasituation
wherealargenumberofexpertsfrommultiplegroups
are involved to make a high-quality risk analysis by
identifying the most serious failure modes among a
set of potential ones for corrective actions. Generally,
when the number of experts in an FMEA exceeds 20
4H.-C. LIU ET AL.
Figure . LGFMEA with experts from distributed groups.
(Liu et al. 2015;Zhouetal.2017), the risk analysis
process in which they participate can be considered
as LGFMEA (as displayed in Figure 1). In this sec-
tion, we develop a novel risk priority framework for
LGFMEA, which is comprised of four parts: (1) clus-
ter experts into small-groups according to their evalua-
tions on failure modes; (2) aggregate dierent opinions
of experts into group risk assessments; (3) determine
the relative weights of risk factors; and (4) determine
theriskpriorityordersoffailuremodes.Adetaileddia-
grammatic representation of the proposed LGFMEA
mode is shown in Figure 2.
In a LGFMEA, without loss of generality, we
assume that mfailure modes FMi(i=1,2,...,m)are
Figure . Flowchart of the proposed LGFMEA mode.
identied and needed to be evaluated by lexperts or
team members TMk(k=1,2,...,l)according to n
risk factors RF j(j=1,2,...,n).Sinceriskfactors
are dicult to be precisely estimated in the actual
risk-assessment process, it is assumed that the experts
provide their judgments on the failure modes using
ambiguous linguistic terms. According to the approach
illustrated in Figure 2, the detailed explanations of the
proposed LGFMEA approach in prioritizing failure
modesaregivenasfollows.
Risk experts clustering
For the LGFMEA problem, a consensus process is
required to deal with the enormous amount of risk-
assessment information obtained from experts. In the
consensus process, participants seek to reach a mutual
agreement with the expectation of gaining an accept-
able whole group assessment. Because of the complex-
ity of large groups and the dierence among group
members, clustering method is usually applied to
derive the subgroups or so-called clusters in which
experts have similar assessments. Then the subse-
quentanalysisismucheasiertomanagebasedon
the obtained clusters. Therefore, cluster analysis is an
essential part of the proposed risk priority approach.
Several clustering methods such as the k-mean algo-
rithm (Wu and Xu 2018), the hierarchical clustering
method (Zhu et al. 2016), and the preference clustering
method (Xu et al. 2015) have been utilized in the
large group decision-making literature. The similarity
QUALITY ENGINEERING 5
degree is a simple and popular used algorithm because
its ease of implementation, eciency, and empirical
success (Cai et al. 2017). However, this clustering
method has not yet been developed for LGFMEA.
Therefore, in this part, a similarity degree-based
clustering method is proposed to deal with the classi-
cation of risk assessments in large group environment.
Step 1. Acquire individual hesitant linguistic assess-
ment matrices Hk
In practical situations, FMEA team members prefer
to utilize linguistic labels to state their assessments on
the risk of failure modes (Liu et al. 2016a;Zhouetal.
2016). Moreover, due to information insuciency or
limited expertise, experts may hesitate among dierent
linguistic terms or require complex linguistic expres-
sions to represent their opinions accurately (Huang,
Li and Liu, 2017;Liuetal.2016b). Therefore, hesi-
tant linguistic term sets (HLTSs) (Rodríguez, Martínez,
and Herrera, 2012)areusedinthisstudytodealwith
theuncertainlinguisticassessmentsprovidedbyteam
members in LGFMEA.
For computing with words with the HLTSs,
various linguistic assessments of experts need
to be transformed into hesitant linguistic ele-
ments (HLEs) rst. Let dk
ij be the linguistic
assessment values that team member TMkpro-
videsforfailuremodeFM
iagainst risk factor
RFj(i=1,2,...,m;j=1,2,...,n;k=1,2,...,l).
Then, the risk assessments over all failure modes versus
each risk factor made by the kth expert form a hesitant
linguistic assessment matrix Hk.Thatis,
Hk=⎡
⎢
⎢
⎢
⎣
hk
11 hk
12 ··· hk
1n
hk
21 hk
22 ··· hk
2n
.
.
..
.
.··· .
.
.
hk
m1hk
m2···hk
mn
⎤
⎥
⎥
⎥
⎦
,(1)
where hk
ij is an HLE converted from the linguistic
assessment dk
ij. For example, if an expert evaluates the
risk of failure modes using the following linguistic term
set:
S=s0=Ve r y lo w ,s1=Low,s2=Medium low ,
s3=Medium,s4=Medium high,
s5=High,s6=Ve r y h i gh .
Then dierent types of linguistic assessments given
by the expert can be represented by HLEs as follows:
rA deterministic linguistic rating such as Low can
be denoted by {s1}; and
rA hesitant linguistic rating such as Medium high
and High can be expressed as {s4,s5}.
Step 2. Cluster hesitant linguistic assessment matrices
into subgroups
Determining an appropriate clustering threshold is
critical to cluster the hesitant linguistic matrices of
all risk experts Hk(k=1,2,...,l).Motivatedbythe
method of (Cai et al. 2017), we determine a clustering
threshold based on the similarities between individual
hesitant linguistic assessments as
λ=min
p,q=1,2,...,l,p=qSD Hp,Hq
+2
3max
p,q=1,2,...,l,p=qSD Hp,Hq
−min
p,q=1,2,...,l,p=qSD Hp,Hq,(2)
where SD(Hp,Hq)is the similarity degree between the
hesitant linguistic assessment matrices Hpand Hq,and
can be computed by
SD Hp,Hq=1
mn
m
i=1
n
j=1
×
Ehp
ijEhq
ij
Ehp
ij2
+Ehq
ij2
−Ehp
ijEhq
ij.(3)
It is easy to know that 0 ≤λ≤1. If SD(Hp,Hq)
≥λ,thenHpand Hqare placed into the same
cluster (or subgroup). As a result, the khesitant
linguistic assessment matrices Hk(k=1,2,...,l)
can be divided into Lsmall-scale clusters
GK(K=1,2,...,L)by means of the proposed clus-
tering method. The number of experts in cluster GKis
dened as lKand L
K=1lK=l.Notethatthenumber
of clusters should be no less than three in the LGFMEA
so as to avoid the extreme situation in which only two
clusters exist and their opinions are absolutely opposite
in the risk analysis. In addition, the clustering results
areassumedtobereasonableifeachoftheLclusters
has more than one expert (L≥2).Otherwise,ifonly
one expert in a single cluster, then the expert is advised
to exit the LGFMEA process since the consensus levels
with the other experts are low (Xu et al. 2015).
Risk-assessment aggregation
After clustering the hesitant linguistic assessment
matrices into subgroups, this stage is to aggregate the
6H.-C. LIU ET AL.
risk assessment of each cluster to attain a cluster risk-
assessment matrix, and aggregate the risk assessments
of all clusters to establish a group risk-assessment
matrix.
Step 3. Construct the cluster risk-assessment matrix RK
InthesameclusterGK, the similarity degree between
experts is suciently high, which means that the risk
assessments of failure modes in each cluster are basi-
cally coherent. Therefore, we suppose that the risk
expertsinaclusterhaveequalweightsinthehesitant
linguistic assessment aggregation. Therefore, the clus-
ter risk-assessment matrix RK=[rk
ij]m×ncorrespond-
ing to cluster GKcan be obtained by
rK
ij =1
lK
lK
k∈lK
Ehk
ij,(4)
where E(hk
ij)is an expected value for the HLE hk
ij.
Step 4. Construct the group risk-assessment matrix R
Once obtaining the cluster risk-assessment matri-
ces RK(K=1,2,...,L),thisstepistodeterminethe
group risk assessment matrix R=[rij]m×nby
rij =
L
K=1
vKrK
ij,(5)
where vKsignies the weight of the Kth expert cluster.
From Eq. (5), it is known that the weight of each
expert cluster should be computed rst prior to aggre-
gating the cluster risk assessments. In this study, the
clusters’ respective weights are yielded in terms of the
following two methods. First, because of the com-
plexity and uncertainty of LGFMEA problems, the
team members with dierent experiences, knowledge,
and backgrounds cannot achieve absolute consistent
regarding failure modes’ assessment. Therefore, risk-
assessment conicts among clusters should be taken
into account to aggregate the cluster risk-assessment
information. The cluster weight vector can be derived
based on the conict degree between the cluster risk-
assessment matrix RKand the ideal risk-assessment
matrix R∗,whichisdenedas
εK=1
mn dRK,R∗,(6)
where d(RK,R∗)=m
i=1n
j=1(rK
ij −r∗
ij)2is the
Euclidean distance between RKand R∗.Inspired
by the relevant literature (Yue 2011), the average matrix
of the Lcluster risk assessments is considered as the
ideal risk-assessment matrix R∗.
AlargervalueofεKindicates that a higher assess-
ment conict between the cluster GKand the ideal risk
assessments. In general, the less conict level of the
cluster GK, the more weight should be placed on it.
Hence, we use Eq. (7) for determining the rst-type
weights of clusters v(1)
K(K=1,2,...,L).
v(1)
K=1−εK
L
K(1−εK).(7)
Based on the majority principle, another method can
be used here for specifying the cluster weights. The
larger the cluster is, the greater impact the group risk
assessments would have. In other words, if the number
of experts in a cluster is larger than other clusters, then
itcanbeseenthattheclusterplaysamoreimportant
role in the LGFMEA and should be assigned a higher
weight.Onthecontrary,ifaclustercomestobesmaller
than other clusters, then this cluster should be assigned
a lower weight. Accordingly, the second-type weights
of clusters GK(K=1,2,...,L)are computed through
the following formula:
v(2)
K=(lK)2
L
K(lK)2.(8)
In real-life situations, both the risk-assessment
conict and the majority principle should be taken
into consideration. Therefore, the above two types of
weights can be combined to determine cluster weights
comprehensively. For example, the ultimate weighting
vector of clusters v=(v1,v2,...,vL)is derived by
vK=αv(1)
K+(1−α)v(2)
K,(9)
where αis a parameter representing the relative impor-
tance between the two types of weights, 0 ≤α≤1.
Risk factor weighting
SolvingriskfactorweightsisacriticalstepinFMEA
because the variation of weight values may lead to
dierent risk-ranking orders of the identied failure
modes. Vast majority of FMEA methods in the lit-
erature assumed that the weights of risk factors are
given beforehand or determined subjectively. In the
QUALITY ENGINEERING 7
real world, however, it may be hard or even impos-
sible to dene the important weight of each risk fac-
tor, because of the complexity of practical risk-analysis
problems and the inherent subjective nature of human
thinking. The entropy theory (Shannon and Weaver
1947) is a measurement index used to measure the
amount of information implied in data. It is well suited
for measuring the relative contrast intensities of crite-
ria to represent the intrinsic information transmitted
to the decision maker. Therefore, the entropy method
hasbeenwidelyusedinmanyeldsforestimating
the relative weights of evaluation criteria (Gitinavard,
Mousavi, and Vahdani 2017;Liuetal.2017d). For
the LGFMEA problem, we propose an entropy-based
method to objectively compute the weights of risk fac-
tors by utilizing the evaluation information of experts.
The calculation process of risk factor weights based on
the entropy method is shown as below.
Step 5. Compute the normalized risk-assessment
matrix P
The group risk-assessment matrix R=[rij]m×nis
normalized to get the normalized risk-assessment
matrix P=[pij]m×nby
pij =rij
m
i=1rij
,(10)
where pij is the normalized value of rij,representingthe
projected outcome of risk factor RFjconcerning failure
mode FMi.
Step 6. Compute the entropy values of risk factors
The entropy with respect to each risk factor is calcu-
lated via
Ej=−1
ln mm
i=1
pij ln pij,j=1,2,...,n,
(11)
where mis the number of failure modes and guarantees
that the value of Ejlies between 0 and 1.
Step 7. Obtain the relative weigh of each risk factor
According to the entropy theory (Shannon and
Weaver 1947), Ejindicates the discrimination degree of
the overall risk-assessment information contained by
RFj. The smaller the entropy value Ej,thebiggerthedif-
ference across failure modes under the risk factor (i.e.,
it provides decision makers with more eective infor-
mation), and then a higher weight should be assigned
to the risk factor RFj. Therefore, the entropy weight of
RFjis dened as (Liu et al. 2017):
wj=1−Ej
n
j=11−Ej,j=1,2,...,n.(12)
Asaresult,wecanobtaintheweightvector
w=(w1,w2,...,wn)of all the risk factors RFj
(j=1,2,...,n)with wj∈[0,1] and n
j=1wj=1.
Failure mode ranking
The prospect theory was rst proposed by Kahneman
and Tversky (1979) for behavioral decision making
under uncertainty, which considers decision maker’s
personality, psychological attitude, and risk prefer-
ence,aswellasenvironmentalandotherfactorsin
the decision-making process. Due to its characteris-
tics of simple computation and clear logic, the prospect
theory has been broadly used as behavioral model of
decision-making in dierent areas (Ren, Xu, and Hao,
2017;Wangetal.2017). In this study, the prospect the-
oryisadoptedtodeterminetherisk-rankingoffailure
modes, and the specic steps are described as follows.
Step 8. Dene the risk reference point r0
The risk reference point is normally assigned based
on previous risk analysis experience or directly inferred
according to the risk assessments of experts. With the
group risk-assessment matrix R=[rij]m×ndetermined
in the second stage, the preference point r0can be com-
puted by
r0=1
mn
m
i=1
n
j=1
rij.(13)
Step 9. Calculate the prospect risk-assessment matrix
V
The prospect values of failure modes against each
risk factor vij (i=1, 2,…, m, j =1,2, …, n)are
determined by the value function v(rij)to construct
the prospect risk-assessment matrix V=[vij]m×n.The
value function is expressed in the following equation:
vrij=rij −r0α,rij ≥r0,
−λrij −r0βrij <r0,(14)
8H.-C. LIU ET AL.
where α∈[0,1] and β∈[0,1] are diminishing sen-
sitivity coecients specifying the concavity and con-
vexity of the value function, respectively. The decision
maker is more prone to risk if the values of αand βare
higher. The parameter λis the loss aversion coecient
indicatingthedegreeofseverefeelingstowardloss,and
when λ>1, the decision maker exhibits a greater sen-
sitivity to losses.
Step 10. Compute the overall prospect value of each
failure mode
Finally, the overall prospect values of the mfailure
modes can be determined by
Vi=
n
j=1
wjvij,i=1,2,...,m.(15)
The larger the value of Vi,thehigherriskthefailure
mode FMi. Therefore, all the identied failure modes
can be ranked in accordance with the descending order
of their overall prospect values and the most important
failures can be selected.
Note that the parameters α,β,andλare involved
in the value function dened in Eq. (14). The determi-
nation of them plays a crucial role in the risk-ranking
process. Some researches have been carried out to
dene the three parameter values appropriately (Abdel-
laoui, Bleichrodt, and Paraschiv, 2007;Tverskyand
Kahneman 1992). Through experiments, Tversky and
Kahneman (1992) suggested that the diminishing sen-
sitivity coecients α=β=0.88 and the loss aver-
sion coecient λ=2.25, which are more suitable to
describe the behavior of most decision makers. If nec-
essary, these parameters can be adjusted based on the
specic problems we are dealing with.
Case study
In this section, we consider the risk analysis of blood
transfusion as an example to illustrate the applicability
and performance of our proposed LGFMEA approach
and particularly the potentials of prioritizing failure
modes within the larger group context.
Background description
Blood transfusion is a procedure routinely performed
in healthcare organizations, which saves lives and
reduces morbidities in many clinical diseases and con-
ditions. But blood transfusion is a costly and complex
procedure associating with certain risks such as trans-
mission of infectious disease, clerical error, hemolytic
reactions and transfusion-related lung injury. This
has led to a trend towards safer transfusion practices,
minimizing the risk of errors in the blood transfusion.
Identication and prevention of blood transfusion
failures is of great importance to the transfusion safety.
In this study, we applied the proposed LGFMEA model
to analyze the risks in blood transfusion to improve
patient care and safety. Through brainstorming, a
total of nineteen potential failure modes were rec-
ognized within the whole blood transfusion process
(Lu et al. 2013). Among them, eight failure modes FMi
(i=1,2, …, 8) with their RPN values bigger than 100
are considered for further discussions. These failure
modes, the causes for them and their eects are sum-
marized in Table 1. To determine the risk-ranking of
the failure modes, a total of 28 eligible subjects in a
university teaching hospital were invited and asked to
conduct the risk evaluation based on a web-based ques-
tionnaire system. As a consequence, 20 usable surveys
were collected from the hospital. In the following, the
risk-assessment data of the 20 respondents, denoted
as TMk(k=1,2,...,20),areusedtodemonstrate
the proposed LGFMEA approach. These experts
from dierent departments include managers of blood
transfusion department, doctors, nurses, and sta from
quality-control department. Moreover, they possess
professional knowledge of healthcare risk assessment
andhaveworkedinrelatedeldsformorethan3years.
All the experts rated the risk of each failure mode with
respect to the risk factors, O, S, and D, and express
their judgments by using the linguistic term set ˙
S,
˙
S=
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎩
s0=Almost None(AN),
s1=Extremely Low(EL), s2=Ver y Lo w (VL),
s3=Low (L), s4=Medium Low (ML),
s5=Medium (M), s6=Medium High (MH),
s7=High (H), s8=Ve r y Hi g h (VH),
s9=Extremely High (EH)
⎫
⎪
⎪
⎪
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎪
⎪
⎪
⎭
.
Note that a ten-point linguistic term set is used here
in order to make a comparison of the ranking result
of the proposed approach with the one derived by the
traditional FMEA. In actual applications, the linguistic
term set ˙
Scan be determined according to the specic
problem considered and the opinions of FMEA team
members. In this case study, the linguistic assessments
of the eight failure modes under each risk factor pro-
vided by the 20 experts are presented in Tab le 2.
QUALITY ENGINEERING 9
Tab le . FMEA of the blood transfusion process.
No. Failure modes Failure causes Failure effects
Insufficient and/or incorrect clinical
information on request form
Request form filled out incorrectly/incompletely;
patient provided incorrect blood group
Normal process is interrupted; transfusion
cannot be performed within appropriate time
frame
Blood plasma abuse Blood plasma still used in volume expansion, as
nutritional supplement and to improve
immunoglobulin levels
Blood resources wasted, risk of
transfusion-related reaction and infection
increased
Insufficient preoperative assessment of
the blood product requirement
Improper evaluation of the disease or potential
blood loss
Adverse event if compatible blood cannot be
prepared in time after emergency
cross-matching procedure
Blood group verification incomplete Importance of performing blood group testing on two
separate occasions not recognized; use of another
sample collected separately or historical records
ABO-incompatible transfusion reaction if no
historical blood type or another sample for
verification
Preparation time before infusion > min Delivery of blood products to clinic department takes
too long; Infusion is not started in time
Blood components not transfused within min,
resulting in reduced quality and associated
potential risks to the patient
Transfusion cannot be completed within
the appropriate time
Transfusion not started when blood products are sent
to clinic area; inappropriate transfusion time
Transfusion is delayed and patients receive
uncertain quality blood products
Blood transfusion reaction occurs during
the transfusion process
Patient not monitored during the transfusion process Emergency treatment is delayed, putting the
patient’s life in danger
Bags of blood products are improperly
disposed of
Staff unfamiliar with procedures for waste bags Contamination of environment, traceability
cannot be guaranteed if required later
Results
To solve the healthcare risk analysis problem and iden-
tify the most serious failures for corrective actions, the
LGFMEA approach proposed in this article is imple-
mented as follows.
Based on the data of Table 2,wersttransform
the linguistic assessments of each expert into HLEs
to obtain the hesitant linguistic assessment matrices
Hk(k=1,2,...,20).TakingtheexpertTM
9as an
example, the hesitant linguistic assessment matrix H9
obtained is shown in Table 3 .Then,byEqs.(2)and
(3), the clustering threshold is computed as λ=0.801,
and the large group can be divided into three smaller
clusters according to the introduced clustering method,
Tab le . Linguistic assessments for the failure modes.
Failure modes
Risk experts Risk factors FMFMFMFMFMFMFMFM
TMOMLVLLLVLMLL
S MHLLEHMMVHL
D MLLLMLLMLL
TMO LHHANMMELEL
S H MH MH EH M M M L
D VH MHMHEL VL VL VL VL
TMOMLELANHHANL
SHMHHEHLVLEHH
D ELVLVLANL ANMLM
··· ··· ··· ··· ··· ··· ··· ··· ··· ···
TM OHMMHMHMMMHH
SMHMHMHMHMHMHMH
D MHHHMHL MHML
TM OLMHMMHMMMHML
S ML H MH H H MH M VL
D MLMLMLMLM MLMHEL
Tab le . Hesitant fuzzy linguistic assessment matrix H9.
Risk factors
Failure modes O S D
FM{s}{s}{s}
FM{s}{s}{s}
FM{s}{s}{s}
FM{s}{s,s}{s}
FM{s}{s}{s}
FM{s}{s}{s}
FM{s}{s,s}{s}
FM{s}{s}{s}
i.e.,
G1={H2,H4,H6,H7,H8,H10,H12 ,H13,H14},
G2={H15,H16 ,H17,H18,H19,H20},G3={H1,H5}.
Note that the hesitant linguistic assessment matrices
H3,H9,andH11 are excluded from the risk analysis
because their similarity degrees with the other experts’
hesitant linguistic assessments are low than the cluster-
ing threshold.
In the second stage, the cluster risk assessment
matrices RK(K=1,2,3)with respect to the three risk
assessment clusters GK(K=1,2,3)are determined by
using Eq. (4), and presented in Table 4.Basedonthe
clustering results and via Eqs. (6)–(9), the two types
of cluster weights and the ultimate cluster weights are
yielded as shown in Tab l e 5. By applying Eq. (16), we
obtain the group risk-assessment matrix R=[rij]8×3as
reported in Tabl e 6 .
Subsequently the entropy method is applied to
computetheobjectiveweightsofriskfactors.We
rst calculate the normalized risk assessment matrix
10 H.-C. LIU ET AL.
Tab le . Cluster risk-assessment matrices for the failure modes.
Failure modes
Clusters Risk factors FMFMFMFMFMFMFMFM
GO . . . . . . . .
S . . . . . . . .
D . . . . . . . .
GO . . . . . . . .
S . . . . . . . .
D . . . . . . . .
GO . . . . . . . .
S . . . . . . . .
D . . . . . . . .
Tab le . Two types of cluster weights and ultimate cluster weights.
GGG
v(1)
K. . .
v(2)
K. . .
vK. . .
Tab le . Group risk-assessment matrix of failure modes.
Failure modes O S D
FM. . .
FM. . .
FM. . .
FM. . .
FM. . .
FM. . .
FM. . .
FM. . .
P=[pij]8×3according to Eq. (10), then acquire the
entropy value of every risk factor through Eq. (11),
and the relative weighs of risk factors are derived with
Eq. (12). The above computation results are provided
in Table 7 .
Finally, we adopt the prospect theory to deter-
mine the risk-ranking of the considered failure modes.
Using Eq. (13), the reference point for the healthcare
risk analysis is acquired as 5.872. The prospect risk
assessment matrix V=[vij]8×3is calculated based on
Eq. (14), and the overall prospect values of the fail-
ure modes Vi(i=1,2,...,8)are determined using
Tab le . Normalized risk-assessment matrix and objective weights
of risk factors.
Failure modes O S D
FM. . .
FM. . .
FM. . .
FM. . .
FM. . .
FM. . .
FM. . .
FM. . .
Ej. . .
wj. . .
Tab le . Results of the prospect theory and risk priority ranking.
Failure modes O S D ViRanking
FM. . −. .
FM. . −. .
FM−. . . −.
FM−. . −. −.
FM. . −. .
FM. . −. .
FM−. . −. −.
FM−. . −. −.
Tab le . Ranking comparisons.
Traditional FMEA
Fail ure Proposed
modes O S D RPN Ranking Average Median method
FM
FM
FM
FM
FM
FM
FM
FM
Eq. (15). Tab l e 8 shows the calculation results in detail.
Therefore, the risk priority of the eight failure modes is
FM6FM1FM4FM3FM7FM8FM2
FM5, and FM6 is the most severe failure mode. Accord-
ingly, preventive measures can be arranged to enhance
the reliability and safety of the blood transfusion
process.
Discussions
This part compares our proposed LGFMEA model
with some related risk ranking methods to investigate
its eectiveness and advantages. First, as the proposed
approach aims to enhance the risk evaluation capa-
bility of the traditional FMEA, a comparison with the
RPN method is performed. Besides, Guerrero and
Bradley (2013) found that synthesized group ranking
methods,i.e.,averageandmedianofindividualscores,
performaswellasorbetterthanthegroupconsensus
method, and the median is preferred in the super
group risk assessment. Therefore, the average and the
median methods are also selected for the comparative
experiments. Table 9 summarizes the risk ranking
results of the eight failure modes determined by using
these methods.
First of all, the top two failures obtained by the pro-
posed FMEA are FM5and FM6and the last two fail-
ures are FM7and FM8,whichareinagreementwith
the ones determined by the RPN method. This demon-
strates the validity of the suggested risk priority model
QUALITY ENGINEERING 11
for prioritizing failure modes. However, the ranking
orders of four of the eight failure modes derived by
the proposed approach and the RPN method are dif-
ferent. Particularly, the priority orders of FM1,FM
3,
and FM5cannot be discriminated in terms of the tra-
ditional FMEA. The possible reasons mainly lie in the
shortcomings of the conventional RPN method. First,
the failures FM1and FM3, where O, S, and D are rated
as 6, 6, 5 and 5, 6, 6, respectively, have exactly the
same RPN value of 180. Thus, they are assumed as hav-
ing the same priority in terms of the RPN method. In
the reality, the two failure modes should have dierent
risk levels because their O and D values are dierent.
Accordingly, FM1is ranked higher than FM3when the
proposed approach is leveraged. Second, based on the
numericscalefrom1to10,theO,S,andDscoresfor
FM1and FM5areconsistentandthetwofailurescannot
be dierentiated according to the RPN method. This
ranking could be unreasonable especially when FMEA
team members’ assessment data are vague and uncer-
tainty and exact values cannot reect their judgments
suciently. According to the proposed FMEA, FM5is
given a higher priority compared to FM1. Third, the
inuence of risk factor weights used in the proposed
FMEAapproachcanbeseenintherankingsforfail-
ure modes FM2and FM3,whereO,S,andDare5,7,5
and5,6,6,respectively.UsingtheRPNmethod,FM
3is
ranked higher than FM2. However, by applying the pre-
sented approach, FM2has a higher priority in compari-
son with FM3since the weightof S is bigger than that of
D(cf.Table 7). Finally, only ve experts are involved in
the RPN-based risk analysis, which may lead to a lack
of precision in the nal ranking result.
According to the comparative experiments above,
the proposed FMEA approach based on cluster analy-
sis and prospect theory provides a useful and practical
way for risk evaluation when involving large group of
experts. In summary, the prominent advantages of the
proposed LGFMEA model are as follows:
rBy the use of HLTSs, FMEA team members
can use exible and richer expressions to eval-
uatethefailuremodesoneachriskfactor
more accurately. Thus, the linguistic ratings of
failure modes can be appropriately represented to
directly account for the uncertainties in complex
or ill-dened situations.
rBased on the cluster analysis method, the pro-
posed FMEA is able to obtain a relatively satis-
factoryfailuremoderankingwithinthecontext
of larger group. Therefore, it useful for model-
ing LGFMEA problems where the scale of FMEA
groups is larger and the type of FMEA groups is
complex due to the complexity and insucient
information of failure modes.
rImportance weights of risk factors are taken into
account in determining the risk priority of fail-
ure modes. Particularly, an entropy-based is pro-
posedtoobjectivelydetermineriskfactorweights
by comprehensively utilizing the risk assessment
information in FMEA.
rThe proposed method can compensate the weak-
nesses of the conventional RPN method and get
a more accurate and credible risk priorities of
failure modes by using the prospect theory, thus
providing useful and practical information for
risk-management decision making.
Conclusions and future directions
In this article, we developed a novel risk priority
approach for the LGFMEA with unknown risk fac-
tor weights and linguistic assessment information. The
proposed FMEA model is initiated by clustering the
large group experts from dierent sectors and pro-
fessional elds via a similarity measure-based clus-
tering method. Then, a group risk-assessment matrix
was constructed by taking conict degree and major-
ity principle into account simultaneously to improve
the consistency of group opinions. Next, an entropy-
based objective weighting method was suggested to
derive the weights of risk factors with the collective
risk-evaluation information. In addition, the prospect
theory was modied to derive the risk-ranking of the
failure modes identied in FMEA. After designing the
proposed risk priority approach, we tested and eval-
uated it via an empirical healthcare risk analysis case
study. The example analysis revealed that the proposed
model is feasible and eective, which is conducive to
improve the rationality and accuracy of large-group
risk analysis in distributed settings. In particular, the
importance of our LGFMEA approach stems from the
increasing dispersal of product design and produce
activities in terms of geography and dierent organi-
zations.
In the future, we will further extend our research in
the following directions. First, the work presented in
this article does not consider noncooperative behav-
iors and minority opinions of experts, which may be
12 H.-C. LIU ET AL.
happening in real world settings, particularly among
large and diversied group members. Thus, our pro-
posed FMEA could be enhanced in the future, mak-
ing it more applicable to distributed large group-based
FMEA problems. Second, dierent attitudes of FMEA
team members have a direct impact on the risk-ranking
results, but they are not reected in the introduced
LGFMEA model. In the future, we can consider expert
attitude as an important inuencing factor in the large
group risk analysis. Third, it will be interesting to fur-
ther extend our approach to manage the large group
risk analysis problems with incomplete assessment
information, because experts may not able to evaluate
all failure modes due to their limitations in knowledge,
experience, and interests. In addition, future research
should be conducted in developing a web-based
risk-management system that is helpful and convenient
for domain experts located in dierent places to per-
form LGFMEA via a web interface.
About the authors
Hu-Chen Liu is a professor at the School of Management,
Shanghai University. His main research interests include qual-
ity management, articial intelligence, Petri net theory and
applications, and healthcare operation management. He has
published more than 100 papers in these areas in leading jour-
nals,suchasIIETransactions,IEEETransactionsonReliability,
IEEE Transactions on Cybernetics, IEEE Transactions on Fuzzy
Systems, International Journal of Production Economics, Inter-
national Journal of Production Research, Quality Engineering,
and Computers & Industrial Engineering. Dr. Liu is a member
of the IEEE Reliability Society, the IEEE Systems, Man, and
Cybernetics Society, the INFORMS, the Institute of Industrial
& Systems Engineers (IISE), and the China Association for
Quality.
Xiao-Yue You received the B.S. degree in mechanical engineer-
ing from Tongji University, China, in 2009, and the M.S. degree
in mechanical engineering from Tongji University, China in
2015. She is working toward the Ph.D. degree in Management
Science and Engineering at the School of Economics and Man-
agement, Tongji University. Her research interests include data
mining, strategy management, and quality management.
Fugee Tsung is a Professor with the Department of Industrial
Engineering and Logistics Management and the Director of the
Quality and Data Analytics Laboratory with The Hong Kong
University of Science and Technology, Hong Kong. He has
authored over 100 refereed journal publications. His current
research interests include quality engineering and management
to manufacturing and service industries, statistical process
control, monitoring, and diagnosis. Prof. Tsung is a fellow of
the Institute of Industrial Engineers, the American Society for
Quality, and the Hong Kong Institution of Engineers, and an
Academician of the International Academy for Quality. He was
a recipient of the best paper award for the IIE Transactions in
2003 and 2009. He is Editor-in-Chief of the Journal of Quality
Technology.
Ping Ji is a professor at the Department of Industrial and
Systems Engineering, Hong Kong Polytechnic University. His
research interests include industrial engineering including sup-
ply chain management and operations management. He has
published more than 100 papers in various journals including
IIE Transactions, IEEE Transactions on Robotics and Automa-
tion, the European Journal of Operational Research, and
Bioinformatics.
Acknowledgments
The authors are very grateful to the respected editor and the
anonymous referees for their insightful and constructive com-
ments, which helped to improve the overall quality of the article.
Funding
This work was partially supported by the National Natural
Science Foundation of China (Nos. 61773250, 71671125, and
71402090), a grant from the Research Committee of The Hong
Kong Polytechnic University (No. G-YBLR), and the Shanghai
Youth Top-Notch Talent Development Program.
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