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Personalized individual semantics-based approach for linguistic failure modes and effects analysis with incomplete preference information

TL;DR: This article presents the design of a PIS-based FMEA approach, in which members express their opinions over failure modes and risk factors using Linguistic Distribution Assessment Matrices (LDAMs) and also provide their opinionsover failure modes using incomplete Additive Preference Relations (APRs).
Abstract: Failure Modes and Effects Analysis (FMEA) is a very useful reliability-management instrument for detecting and mitigating risks in various fields. The linguistic assessment approach has recently be...

Summary (1 min read)

IISE Transactions -For Peer Review

  • 2 The RPN-based FMEA approach has been associated with several issues (see [1, 2, 10, 11, 23, 37, 38, 41, 46] ), being particularly relevant to the present paper that FMEA members are obliged to express accurate risk assessment information using the aforementioned 1-10 numerical points scale.
  • Indeed, in some real-world decision processes, FMEA members may prefer or feel more comfortable assessing risk using linguistic rather than numerical values (e.g., [16, 21, 40] ).
  • IISE Transactions -For Peer Review 3 (APRs) on the failure modes.
  • Section 2 includes the necessary preliminary concepts to make this paper self-contained.
  • It should be noted that the PIS-based linguistic FMEA approach is still useful with the setting of different parameter values to the above ones.

(3) Numerical scale function

  • The concept of numerical scale function was proposed to transform linguistic terms into real numbers [7] , with the aim to facilitate the computational process in the linguistic assessment approach based GDM.
  • IISE Transactions -For Peer Review linguistic GDM, and the GDM problem is referred to as a PIS-based linguistic GDM [17] [18] [19] .

5. Case study

  • This section shows the practical use of the PIS-based linguistic FMEA approach to the problem of the reliability management of blood transfusion [25, 27] .
  • For the sake of clarity and readability.

2) Comparison with random data

  • In order to obtain compelling results, Simulation methods I and II with randomly generated data are designed to compare the PIS and FNS based linguistic FMEA approaches.
  • The basic idea of Simulation methods I and II (see approach are smaller than those under the FNS-based linguistic FMEA approach in the three parameter scenarios, which is again consistent with the results obtained using the case study data.
  • These findings show that taking the PIS issue into account the PIS-based linguistic FMEA approach can improve the reliability management quality.
  • (2) Psychological behaviors, such as non-cooperative behaviors [35] and prospect theory [41] , of FMEA members play an important role in practical FMEA problems.

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1
Personalized individual semantics-based approach for
linguistic
failure modes and effects analysis with incomplete
preference information
Abstract: Failure modes and effects analysis (FMEA) is a very useful reliability-management
instrument for detecting and mitigating risks in various fields. Linguistic assessment approach has
recently been widely used in FMEA. Words mean different things to different people, so FMEA
members may present personalized individual semantics (PIS) in their linguistic assessment
information. This paper designs a PIS-based FMEA approach with members expressing their
opinions over failure modes and risk factors using linguistic distribution assessment matrices
(LDAMs) and also provide their opinions over failure modes using incomplete additive preference
relations (APRs).
A preference information preprocessing method with a two-stage optimization
model is presented to generate complete APRs with acceptable consistency levels from incomplete
APRs. Then, a deviation minimum-based optimization model is designed to personalize individual
semantics by minimizing the deviation between APR and the numerical assessment matrix derived
from the corresponding LDAM. This is followed by the developing of a ranking process to
generate the risk ordering of failure modes. A case study and a detailed comparison analysis are
presented to show the effectiveness of the PIS-based linguistic FMEA approach.
Keywords: Reliability management; failure modes and effects analysis; personalized individual
semantics; consistency; optimization
1. Introduction
Failure modes and effects analysis (FMEA) is a very powerful reliability-management
instrument, which is frequently used in product design to identify the most critical causes of a
product’s failure and to mitigate their risks [3, 9, 12, 15, 29, 32, 36]. Thus, risk assessment and
prioritization of failure modes are key issues in FMEA [4, 5, 12, 40]. Traditionally, the risk
assessment information on each failure mode with respect to the three risk factors of occurrence
(O), severity (S), and detection (D) is measured using a (1-10) numerical points scale. The product
of the (O, S, D) numerical risks values is defined as the risk priority number (RPN) of a failure
mode [39], which is subsequently used to produce a risk ordering of failure modes. Different
levels of security control measures for failure modes are implemented in order to mitigate risk,
and failure modes with high RPN values are paid more attention. Thus, the ultimate decision result
in an FMEA method/model is the risk ordering of failure modes by their RPN values. For a
comprehensive introduction of the FMEA implementation process, please refer to Refs. [22, 39].
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The RPN-based FMEA approach has been associated with several issues (see [1, 2, 10, 11, 23,
37, 38, 41, 46]), being particularly relevant to the present paper that FMEA members are obliged
to express accurate risk assessment information using the aforementioned 1-10 numerical points
scale. Indeed, in some real-world decision processes, FMEA members may prefer or feel more
comfortable assessing risk using linguistic rather than numerical values (e.g., [16, 21, 40]). To
address this issue, the following different linguistic FMEA approaches have been
developed/proposed to date: (i) interval two-tuple linguistic risk assessments and the ELECTRE
(Elimination Et Choix Traduisant la REalite) approach for ranking failure modes [24]; (ii)
triangular fuzzy linguistic risk assessments, the Choquet integral and prospect theory [41]; (iii) the
linguistic weighted geometric operator and fuzzy priority methodology [47]; (iv) linguistic
distribution of risk assessment information with an improved TODIM (Portuguese acronym for
‘interactive and multi-criteria decision making’) approach to yield the risk ordering of failure
modes [14]; (v) multi-granular linguistic distribution risk assessments to model uncertain opinions
of FMEA members [34]; (vi) consensus-based group decision-making (GDM) approaches for
FMEA with linguistic distribution risk assessments [44, 45].
These linguistic FMEA approaches represent a great progress because they provide a more
flexible framework than the previous numerical approaches. However, they still do not
accommodate all possible real scenarios because they are based on the premise that the linguistic
labels (words) implemented/used mean the same for all FMEA members, when the reality is that,
in general, words may mean different things to different individuals, a phenomenon referred to as
personalized individual semantics (PIS) that affects practical FMEA problems decision results
([17-19, 30, 31]). Indeed, when assessing the risk level of a failure mode, two FMEA members
may assess the risk level of the failure mode with the same word “high” but with distinct
semantics. As it is illustrated later in this paper in Section 3.1 (Example 1), ignoring the PIS issue
affects the reliability management quality.
To the best of our knowledge, PIS has not been considered yet in the existent linguistic FMEA
approaches, which is the goal of this paper. Thus, this paper aims at developing the mathematical
framework for managing PIS in the linguistic FMEA problem to improve the reliability
management quality. This is achieved by means of the following two main research objectives:
(1) To implement a general linguistic decision context to formulate the PIS-based FMEA
problem, which is based on the mathematical representation of the FMEA members’ preference
information using (i) the general linguistic model of linguistic distribution assessment matrices
(LDAMs) [6, 14, 20, 28, 42, 43] for the risk assessment information on the failure modes with
respect to the risk factors (O, S, D); and (ii) general incomplete additive preference relations
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(APRs) on the failure modes.
(2) To obtain the resolution procedure to deal with the PIS-based linguistic FMEA problem: (i)
First, a preference information preprocessing method based on a two-stage optimization model is
constructed to generate complete APRs with acceptable consistency levels from the incomplete
APRs; (ii) Second, inspired by the numerical scale function-based approaches for dealing with PIS
reported in [17-19], a deviation minimum-based optimization model is proposed to personalize
individual semantics in the LADMs, which seeks to minimize the deviation between the APR and
the numerical assessment matrix (NAM) derived from the LDAM using a PIS-based numerical
scale (PNS); (iii) Third, a ranking process is presented to generate the risk ordering of failure
modes from the obtained NAMs and APRs.
Finally, a validation study is reported with a detailed comparison analysis between the proposed
PIS-based linguistic FMEA approach and the fixed numerical scale (FNS) based linguistic FMEA
approach, which is complemented with the exemplification of its practical use with a case study
related to the problem of the reliability management of blood transfusion.
The remainder of this paper is arranged as follows. Section 2 includes the necessary preliminary
concepts to make this paper self-contained. Section 3 presents a motivation example and
formulates the PIS-based linguistic FMEA problem. Section 4 designs the detailed solution
procedure for the PIS-based linguistic FMEA problem. Following this, Section 5 illustrates the
practical use of the PIS-based linguistic FMEA approach with the above mentioned case study.
Subsequently, Section 6 presents a comparison analysis to show the effectiveness of the PIS-based
linguistic FMEA approach. Finally, Section 7 concludes the paper and discusses future research
directions.
In order to improve readability, all acronyms and notations used within the paper are included in
Appendix A.
2. Preliminaries
knowledge regarding APRs, the linguistic distribution assessments,
This section introduces basic
and the numerical scale function of a linguistic term set.
(1) Additive preference relations (APRs)
Let
12
{ , , ..., }
n
X x x x
be a set of objects. The concept of APR over
X
and its consistency
level are provided in the below definitions:
Definition 1 [13]. An APR on a set of objects
X
is represented by a matrix,
()
ij n n
Aa
, in
which its element
[0,1]
ij
a
represents the preference intensity of object
i
x
over object
j
x
,
subject to the following reciprocity property:
1
ij ji
aa
, {1,2,..., }i j n
.
Definition 2 [13]. The consistency level of an APR
()
ij n n
Aa
is measured with the
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following [0,1]-valued function:
. (1)
The larger the value of
()CL A
, the more consistent the APR
()
ij n n
Aa
is. In particular,
()
ij n n
Aa
is completely consistent when
( ) 1CL A
. Let
[0,1]
be a predefined threshold
value used to judge whether the consistency of
()
ij n n
Aa
is acceptable or not, i.e. when
()CL A
, then APR
()
ij n n
Aa
is of acceptable consistency; otherwise, it is not of acceptable
consistency. The determination of the parameter
usually depends on the actual
situation/problem being dealt with.
The complexity of a particular decision context may lead to a decision maker not been able to
()
ij n n
Aa
. In this case, the APR is referred to as an incomplete
provide all elements of an APR
APR. We use
()
ij n n
Aa
to denote an incomplete APR. In particular,
ij
a null
if the preference
intensity of object
i
x
over object
j
x
is not provided by the decision maker.
(2) Linguistic distribution assessments
Let
0
{ , ..., }
g
L l l
be a linguistic term set with granularity of
1g
and term
j
l
a possible
linguistic value subject to the following two conditions: (1)
L
is ordered:
ij
l l i j
, and (2)
there is an inverse function such that
()
j g j
neg l l
. The linguistic distribution assessment
approach was proposed to deal with uncertain and vague assessment information effectively [43].
The linguistic distribution assessment is formally presented below.
Definition 3 [43]. A distribution assessment of a linguistic term set
L
is represented as
{( , )| 0,1,..., }
tt
LAD l t g

, with symbolic proportions
[0,1]
t
of linguistic terms
t
l
satisfying
0
1
g
t
t
.
(3) Numerical scale function
The concept of numerical scale function was proposed to transform linguistic terms into real
numbers [7], with the aim to facilitate the computational process in the linguistic assessment
approach based GDM.
Definition 4. Let
0
{ , ..., }
g
L l l
be a linguistic term set and
RN
be the set of real numbers.
A function
:NS L RN
is called a numerical scale of
L
, and
()
i
NS l
is the numerical index of
i
l
. If the function
NS
is strictly monotone increasing, then
NS
is called an ordered numerical
scale of
L
.
In essence, the numerical scale provides numerical meaning of linguistic terms in GDM. When
all individuals in a GDM problem have the same numerical indexes of linguistic terms, then the
GDM problem is referred to as an FNS-based linguistic GDM. In many cases though, words mean
different things to different individuals, i.e. individuals have different PIS, PNSs are employed in
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linguistic GDM, and the GDM problem is referred to as a PIS-based linguistic GDM [17-19].
3. The PIS-based linguistic FMEA problem: Motivation and problem formulation
This section includes a motivation example to analyze the influence of PIS on linguistic FMEA.
Then, the PIS-based linguistic FMEA problem formulation is put forward.
3.1. Motivation example: The influence of PIS on linguistic FMEA
It was argued in the introduction section that the PIS issue may appear in the linguistic
assessments of the FMEA members and that ignoring it weakens the reliability management
quality. Here, we provide an example that provides evidence to support this argument.
Example 1: Let
0
{ very lowLl
,
1
lowl
,
2
moderately lowl
,
3
moderatel
,
4
moderate highl
,
5
highl
,
6
very high}l
be the linguistic term set used by FMEA members
1
TM
and
2
TM
to evaluate the risk level of failure modes
1
FM
and
2
FM
. The aim is to find a
risk ordering of
1
FM
and
2
FM
based on the linguistic risk assessments provided by
1
TM
and
2
TM
, who considered equally important. Let us assume that the risk assessments on
12
( , )FM FM
provided by
1
TM
and
2
TM
are (
5
l
and
4
l
) and (
3
l
and
5
l
), respectively.
The process to obtain the risk ordering of
1
FM
and
2
FM
is as follows: (1) linguistic
assessments are transformed into numerical assessments using a numerical scale function as per
Definition 4; (2) the total evaluation value (TEV) of each failure mode is obtained as the weighted
average of the numerical assessments of the two FMEA members, which in this case will be the
mean value as both members are equally important; (3) the TEV values are be used to generate the
risk ordering of
1
FM
and
2
FM
.
In the following, two cases are considered:
Case A: PIS is not considered and
1
TM
and
2
TM
use the same following numerical scale
function:
12
( ) ( ) / 6
ii
NS l NS l i
( 0,1,...,6)i
. Thus, it is
12
1 5 3
0.5( ( ) ( ))TEV NS l NS l
0.5(5/6 0.5) 0.6667
and
12
2 4 5
0.5( ( ) ( )) 0.5(2 / 3 5 / 6) 0.75TEV NS l NS l
.
Case B: PIS is considered and
1
TM
and
2
TM
use different numerical scale functions:
1,* 1,*
06
{ ( ),..., ( )}={0, 1/6, 1/3, 1/2, 0.52, 0.92, 1}NS l NS l
and
2,* 2,*
06
{ ( ),..., ( )} {0 / 6, 1/ 6, 1/ 3, 1/2,NS l NS l
2/3, 5/6, 6/6}
, respectively. Thus, it is
* 1,* 2,*
1 5 3
0.5( ( ) ( )) 0.5(0.92 0.5) 0.71TEV NS l NS l
and
* 1,*
24
0.5( ( )TEV NS l
2,*
5
( ))NS l
0.5(0.52 5/ 6) 0.6767
.
In case A, the risk level of
2
TM
is higher than
1
TM
. However, the risk level of
1
TM
is
higher than
2
TM
in case B. This example shows that ignoring the PIS issue may result in
obtaining the opposite risk ordering of failure modes. So, it is worth to design an approach to
address the PIS issue in the linguistic FMEA problem when it is present.
3.2. Problem formulation
In the following, we formulate the PIS-based FMEA problem in a general linguistic decision
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References
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Journal ArticleDOI
TL;DR: In this paper, failure mode and effect analysis: Failure Mode and Effect Analysis: FMEA From Theory to Execution Technometrics: Vol 38, No 1, pp 80-80
Abstract: (1996) Failure Mode and Effect Analysis: FMEA From Theory to Execution Technometrics: Vol 38, No 1, pp 80-80

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Q1. What contributions have the authors mentioned in the paper "Personalized individual semantics-based approach for linguistic failure modes and effects analysis with incomplete preference information" ?

This paper designs a PIS-based FMEA approach with members expressing their opinions over failure modes and risk factors using linguistic distribution assessment matrices ( LDAMs ) and also provide their opinions over failure modes using incomplete additive preference relations ( APRs ). A preference information preprocessing method with a two-stage optimization model is presented to generate complete APRs with acceptable consistency levels from incomplete APRs. This is followed by the developing of a ranking process to generate the risk ordering of failure modes. A case study and a detailed comparison analysis are presented to show the effectiveness of the PIS-based linguistic FMEA approach.