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applied
sciences
Article
PAL-VMEA: A Novel Method for Enhancing
Decision-Making Consistency in
Maintenance Management
Marjorie M. Bellinello 1, Miguel A. C. Michalski 2, Arthur H. A. Melani 2,
Adherbal Caminada Netto 2, Carlos A. Murad 2and Gilberto F. M. Souza 2, *
1Department of Mechanical and Maintenance Engineering, Federal University of Technology—Paraná,
Guarapuava 85053-525, Brazil; belinelli@utfpr.edu.br
2Department of Mechatronics and Mechanical System Engineering,
Polytechnic School of the University of S
ã
o Paulo, S
ã
o Paulo 05508-030, Brazil; michalski@usp.br (M.A.C.M.);
melani@usp.br (A.H.A.M.); adherbal@usp.br (A.C.N.); carlos.murad@usp.br (C.A.M.)
*Correspondence: gfmsouza@usp.br
Received: 16 September 2020; Accepted: 16 October 2020; Published: 13 November 2020
Abstract:
Decision-making regarding maintenance planning has become increasingly critical. In view
of the need for more assertive decisions, methods, and tools based on failure analysis, performance
indicators, and risk analysis have obtained great visibility. One of these methods, the Variation and
Mode Effect Analysis (VMEA), is a statistically based method that analyses the effect of different
sources of variations on a system. One great advantage of VMEA is to facilitate the understanding of
these variations and to highlight the system areas in which improvement efforts should be directed.
However, like many knowledge-based methods, the inherent epistemic uncertainty can be propagated
to its result, influencing following decisions. To minimize this issue, this work proposes the novel
combination of VMEA with Paraconsistent Annotated Logic (PAL), a technique that withdraws
the principle of noncontradiction, allowing better decision-making when contradictory opinions
are present. To demonstrate the method applicability, a case study analyzing a hydrogenerator
components is presented. Results show how the proposed method is capable of indicating which are
the failure modes that most affect the analyzed system, as well as which variables must be monitored
so that the symptoms related to each failure mode can be observed, helping in decision-making
regarding maintenance planning.
Keywords:
Paraconsistent Annotated Logic; Best-Worst Method; Variation Mode and Effect Analysis;
maintenance management; decision-making
1. Introduction
In view of the need for assertive decisions in asset and maintenance management, methods
and tools based on failure analysis, performance indicators, and risk analysis have obtained great
visibility in industrial processes, leading to more consistent decision-making. On the other hand,
maintenance management decision-making, through a logical and structured approach, aims to ensure
high levels of productivity with costs and resources optimization, as well as personal, property and
environment safety.
Currently, the most popular reliability-based maintenance planning technique is Reliability
Centered Maintenance (RCM). That philosophy is a system-related approach that relies on the
application of Failure Mode and Effects Analysis (FMEA) to define the most critical components
regarding systems reliability. For those components, the method mainly suggests the application of
Appl. Sci. 2020,10, 8040; doi:10.3390/app10228040 www.mdpi.com/journal/applsci
Appl. Sci. 2020,10, 8040 2 of 26
preventive and predictive maintenance to avoid failure occurrence [
1
–
3
]. As an evolution of RCM,
Risk-Based Maintenance (RBM) was proposed in the 2000s and has attracted a significant attention in
the process and offshore industries, since it provides a cost-effective tool to reduce the probability of
failure in the critical components and associated consequences. The main goal of the methodology
is to define the most critical scenarios in terms of risk and to select as most critical components the
ones that are part of those critical scenarios [
4
,
5
]. Coupled to these methodologies, Decision-Making
Process (DMP) is used to improve the prioritization of pieces of equipment with regard to maintenance
planning. Besides risk and reliability factors, as prospected by the previously mentioned methods,
maintenance investment, business interruption loss, and maintenance technique feasibility can be
included as decision variables.
Accordingly, the design and implementation of maintenance plans becomes a complex problem,
involving material, economic, social, and individual aspects [
6
]. Thus, a successful implementation
requires considering the opinion of different experts in a context of uncertainty and incomplete and
inaccurate data [
7
]. For example, the uncertainty of the RCM or Risk-Based Inspection (RBI) analysis is
associated with expert judgment used to elaborate FMEA or other risk analysis techniques that use
a numerical classification system to express probability of occurrence and consequences of system
´
s
components failure modes. It is hard to reach a consensus when dealing with a great number of experts
with different backgrounds [8].
Several decision support systems have been developed to improve the determination of optimal
maintenance plans [
9
–
12
], maintenance scheduling [
13
,
14
], and maintenance workload [
15
,
16
], as well
as the determination of criticality levels of pieces of equipment [
17
–
19
]. Generally, such criticalities are
individually established, without explicitly considering potential differences between persons involved
in the analysis or areas interested in the problem [
20
]. In case of inexistence of consensus between
the experts, the opinions should be weighted through the use of weighting factors that ideally must
take into consideration the appropriateness and relevance of the expert in the field under analysis [
21
].
Percentiles can be used to combine expert opinions and arithmetic and geometric averages can be used,
although the results are dependent on the number of experts invited for the elicitation. The merits of
using performance-based weighting schemes to combine judgments of different individuals (rather
than assigning equal weights to individual experts) and the way that interaction between experts
should be handled are still ongoing research topics [
22
]. The expert opinion aggregation can become
more challenging if the information provided by experts is contradictory. A family of so-called
heterodox nonclassical logics, namely, Paraconsistent Logic (PL), whose main feature is the withdrawal
of the principle of noncontradiction can aid in decision-making when the analyst is confronted with
contradictory opinions [23].
One of the techniques that belongs to such a family and deserves special attention is the
Paraconsistent Annotated Logic (PAL) that allows a better decision-making when there are contradictory
values or opinions through the attribution of favorable and unfavorable values (the degrees of belief and
disbelief) in relation to any proposition, generating a logic that presents results in four states: true, false,
inconsistent, and indeterminate [
23
–
25
]. The method has been applied in qualitative and quantitative
approaches, such as logic programming for robotics, artificial intelligence and automation, analysis of
environmental problems, decision-making in industrial quality and logistics, logical-philosophical
reasoning, applied mathematics in decision-making in matters of medicine and law, and complexity of
computational systems (mainly assisting in inconsistent data mining). With this technique it is possible
to obtain greater consistency and reduce the epistemic uncertainties (obtained by extractors of belief
and disbelief in values) for the weights attributed by decision-makers in many decision processes.
A relatively new method proposed to improve quality and reliability of products and process is
the Variation Mode and Effect Analysis (VMEA), which has been mainly used in the areas of project
development and prototype testing in controlled environment. VMEA is a statistically based method
used to analyze the effect of different sources of variation on a specific system. One of the main
advantages of VMEA is to assist in the comprehension of these variations and to highlight the areas of
Appl. Sci. 2020,10, 8040 3 of 26
the product or process in which improvement efforts should be directed. The method systematically
assesses how Noise Factors (NF) affect the Key Product Characteristics (KPC) of a system’s components.
The VMEA result is an index, the Variation Risk Priority Number (VRPN), which indicates the transfer
of the variation of these NFs to the analyzed system, supporting the proposal of solutions that could
minimize such effects and increase the robustness of the system [
26
–
28
]. Considering the DMP
context, these characteristics make the method a strong candidate for application in the maintenance
management decision-making process.
However, despite the favorable performance of both methods in the aforementioned areas,
the lack of application of such techniques in maintenance and reliability engineering decision-making
processes, added to the difficulty in assertive decision-making in maintenance activities associated with
infrastructure systems, such as power generation and petrochemical plants, are motivating factors for
this research. In this way, the present work aims to adapt the VMEA method to analyze the sensitivity
of the KPCs of the main items of an equipment, according to the potential and functional failure
modes, which are considered as NFs. Due to the importance of the weight assignment process in the
VMEA analysis, the Paraconsistent Bi-Annotated Logic (PAL2v)—Paraconsistent Annotated Logic
with annotation of two values—is applied as a weight assignment tool for the variables involved in this
analysis, which make up the indicators that measure the impact of failure modes on the variation of the
key characteristics (main function) of the components of an equipment. As a result, the authors aim to
obtain the VRPN indicator, which can guide the development of an adequate maintenance policy for
each analyzed component, depending on its sensitivity (variation of its operation condition) to the
presence of faults, directing the attention of analysts and maintainers to areas where such variations
may be harmful.
The combined technique proposed in this work, so called PAL-VMEA, is an epistemic method, as
it transforms the tacit knowledge of decision-makers (specialists) into explicit knowledge. With logical
and mathematically structured consistency, this method brings the truth of the matter about the
critical weight relative to each variable that affects the performance of the analyzed mechanical
system, establishing validated scientific knowledge, for an assertive decision in the appropriate
maintenance policy. For the process of extracting belief and disbelief from the values attributed by
the decision-makers in the VMEA analysis, the Best-Worst Method (BWM) is also used, which made
it possible to assess and balance the degree of knowledge of each decision-maker by establishing an
index in the extraction process.
This article is structured as follows: Sections 2and 3describe the literature review on VMEA
and PAL, respectively. Section 4presents the BWM fundamentals. Sections 5and 6describe the
development steps of the LPA-VMEA method and its application in a case study considering the
components of a Kaplan turbine hydrogenerator. A comparison of the proposed approach with
indicators traditionally obtained by brainstorming is also presented in this section. Section 7presents a
discussion about the application of the proposed method and the results obtained. The conclusion of
the article is detailed in Section 8.
2. Variation Mode and Effect Analysis (VMEA)
The concept of a robust product significantly contributed to the establishment of the Robust Design
Methodology (RDM) as a methodology to improve product and process quality during the second half
of the last century [
29
]. Although the use of RDM-related methods is quite disseminated, it is clear
that only to a limited extent, some systematic techniques are used in the industry for the original
purpose, which indicates that there are lack of some elements for successful implementation [
30
–
32
].
As a response to this gap and considering that variations in the manufacturing process affect the
quality and performance characteristics of the final product in several ways and, also, that some
of that characteristics are more sensitive to that variations than others, Chakhunashvili, Johansson,
and Bergman [
32
] introduced an engineering method, VMEA, developed to systematically look for
NFs affecting KPCs in early product development phases.
Appl. Sci. 2020,10, 8040 4 of 26
Although it can be considered a derivation of Failure Mode and Effect Analysis (FMEA),
a failure-oriented approach, VMEA emphasizes the assessment of risks related to excessive variations
in the analyzed system. Originally focused on product design and analysis, in this work its objective is
to identify and prioritize NFs that contribute significantly to the variability of KPCs and could generate
undesired consequences in terms of safety, compliance with government regulations, and functional
system requirements. The resulting index of the analysis, VRPN, directs the attention of analysts and
maintainers to areas where reasonably predicted variations may be harmful. Based on the results
obtained from VMEA, a design or maintenance strategy that seeks to prioritize actions that minimize
or eliminate the causes of the observed variations can be formulated, facilitating the subsequent efforts
to obtain a more robust and reliable system.
Johansson et al. [
26
] presented a statistically based VMEA that, as the authors put it, could be
used in situations where the transfer function, i.e., the relationship between the KPCs and the factors
affecting them, is unknown. When the analytical expression of the transfer function is known, VMEA
would correspond to the well-known method of moments. The VMEA procedure would be particularly
useful to grasp information on the transfer function usually mastered by experts on the product
under study. The results of the VMEA would then serve as a basis for attaining robust designs using
traditional Design of Experiments (DoE) in the phases of parameter and tolerance design.
Carrying out a study about a jet engine components’ fatigue life in order to obtain a safety margin
that would take into consideration all identifiable causes of uncertainty, Johansson et al. [
33
] used the
probabilistic branch of VMEA implemented as a first-order, second-moment reliability method. In their
conclusions they stressed the fact that in addition to the use of both basic and enhanced VMEA in the
early design stages for the identification of critical components, whenever either scatter or uncertainty
need to be quantified, a more sophisticated probabilistic VMEA is required.
O’Brien, Clifford, and Southern [
34
] included VMEA among the most usual engineering tools
that have been used to improve and optimize processes. The authors reasoned that VMEA provided a
scientific method to discover the actual main causes of variation, as opposed to the fact that often in
process innovation engineers believe that they are instinctively aware of the main causes of variation,
while in many cases, it is one of the unsuspecting parameters which is not high on the list of offenders
that is the main cause of process problems and variation.
Pavasson et al. [
28
] stated that the possibility of predicting the reliability of hardware for both
components and systems is important in engineering design. So VMEA was used to investigate how
different sources of variation affected the reliability of a wheel loader automatic transmission clutch
shaft. The authors claimed that the upgraded probabilistic VMEA that was proposed could be used to
identify, to asses, and to manage different variations to increase the system reliability. Besides, it could
be used not only for existing products but also for new product development.
In order to investigate and compare how external parameters influence the fuel consumption of
an articulated hauler, Cronholm [
27
] used VMEA with a view to further apply an experimental design
methodology—a two-level fractional factorial test—to create a reduced test plan that focuses on the
most interesting parameters during the in service runs. It was concluded that the VMEA method may
be useful even if the available information is limited.
Luo et al. [
35
] contended that traditional FMEA is insufficient to consider detrimental variations,
which lead to soft failure. Accordingly, the authors presented a method combining the FMEA technique
with VMEA, which they named “F-VEMEA,” and applied it to the analysis of the characteristics of a
jet pipe electrohydraulic servo valve.
Since there are several methods for improving the prediction of reliability, being VMEA a relatively
new one, Pavasson and Karlberg [
36
] set out to show how VMEA differs from Fault Tree Analysis (FTA)
and FMEA in terms of requirements, limitations, and possibilities in the context of product development.
It was concluded that the results from FMEA, FTA, and VMEA are somewhat complementary and
useful during the whole product development process.
Appl. Sci. 2020,10, 8040 5 of 26
Andr
é
asson and Catalano [
37
] after having applied VMEA to a successful Six Sigma improvement
project, proposed a new development, named “Process-VMEA (P-VMEA),” providing a framework
for identifying, assessing, mitigating, and managing variations in a process. The deliveries of the
framework were mainly directed towards decision-makers and aim to strengthen fact-based decisions.
In their conclusions, however, the authors conceded that it was a statistical complex tool that required
high knowledge about variation and how to conduct the analysis of data. Besides, due to restricted
time, the P-VMEA had been applied only to one industrial case and needed further validation.
According to Sandström, Johannesson, and Sidenmar [
38
], who have applied VMEA in the
context of Ocean Harvesting Technologies (OHT) while carrying out the gear design for the rack
pinion mechanism of a gravity accumulator device, this novel methodology proved to be useful where
previous experience in designing was absent, allowing adequate safety factors to be set so the desired
reliability could be achieved.
As a result of evaluating two design criteria for the structural reliability of the double rod pretension
cylinder in a half-scale prototype Wave Energy Converter (WEC), Svensson and Johannesson [
39
]
concluded that the VMEA methodology can be a good basis for condition monitoring, where the
accumulated equivalent fatigue load can be monitored and the uncertainties may be updated based on
operational data. This gives the possibility to predict the remaining life and its uncertainty, which can
be a valuable input to maintenance planning.
As presented, despite being a method with several applications and great potential, the use of
VMEA for the area of maintenance and system reliability is still marginal.
3. Paraconsistent Annotated Logic (PAL)
Indeterminations, ambiguities, contradictions, or inconsistencies are often present in real-world
situations, where Classical Logic, being binary (two truth values: true and false), can prove ineffective
in solving problems. In contrast, PL is classified as a family of nonclassical logic, presenting a larger set
of truth values, being, therefore, a better solution to deal with problems related to nonclassical logical
systems that can present contradictions [25,40,41].
PL’s are nontrivial and nonclassical logics and their origins are traced back to the first systematic
studies that deal with the possibility of rejecting the principle of noncontradiction of classical logic [
41
].
The first studies on PL were developed in 1958, when hierarchical systems were proposed. In 1987,
the annotated logic was developed to provide a basis for PL programming, which evolved into PAL,
a more robust PL for practical application in decision-making processes [25,42–45].
An important characteristic of PL is that this nonclassical logic has found numerous applications
in philosophy, quantum mechanics, artificial intelligence, traffic control, medicine, economics, finance,
and computing, opening new directions for research in philosophy, science, and technology [
46
]. In fact,
when conducting a search in the Web of Science database (May, 2020) about application studies of PL,
the authors found 601 articles from several application areas, as presented in Figure 1. In this brief
bibliometric analysis, the authors searched for journal articles, conference proceedings, and review
articles with the following search algorithm: “Annotated Paraconsistent Logic*” OR “Paraconsistent
Logic*” OR “Paracomplete* Logic*” OR “Annotated Logic*” OR “Paracompleteness Logic*” OR
“Paraconsistency* Logic*.”
Appl. Sci. 2020,10, 8040 6 of 26
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 25
Figure 1. Number of articles found in the Web of Science database (May 2020) about Paraconsistent
Annotated Logic (PAL), by application area.
In the field of physics, Carnielli and Rodrigues [41] present a formal paraconsistent system and
a corresponding intended interpretation, according to which true contradictions are not tolerated.
Contradictions are, instead, epistemically understood as conflicting evidence, where the evidence for
proposition “A” is understood as reason for believing that “A” is true. The article defines a
paraconsistent and paracomplete natural deduction system, called Basic Evidence Logic (BEL), and
extends it to Logic of Evidence and Truth (LETJ). Da Costa and Ronde [42] presented a study on the
understanding of physical “superpositions” that exist in both classical and quantum physics. The
authors presented a paraconsistent approach to quantum superpositions, which tries to explain the
contradictory properties present in the interpretation of the meaning of quantum superpositions,
which considers the contradiction as a key element of the formal structure of the theory.
In other fields of application, studies such as Takahashi, Umeda, and Sawamura [48], developed
a basic structure of argument (means of interaction) for Extended Generalized Annotated Logical
Programs (EGAP), providing the theory of semantics and dialectical proof and proving the solidity,
integrity, and equivalence of semantics well-reasoned. Bonilla et al. [23] apply Paraconsistent Tri-
Annotated Logic (PAL3v) in the analysis of a set of emergency indicators linked to ecological and
environmental issues, aiming to assess sustainability and efficiency in minimizing the priority for the
use of nonrenewable resources. Encheva, Tumin, and Kondratenk [49] added the PAL in a support
system to select optimal decisions in transport logistics, having as the main criterion for decision the
quality of cargo delivery. Oshiyama et al. [50] used PAL to classify medical equipment based on the
ABC analysis of corrective maintenance data, developing alerts on deviations in equipment
performance, which are identified when inconsistencies and indeterminations occur in the
classification.
Summing up, PL helps to clarify the concepts of negation and contradiction, aiming to deal with
contradictory situations. Many studies, mainly practical case studies, present results that consider the
inconsistencies. For this reason, they are more propitious in framing problems caused by situations
of contradictions, ideal for applying a nonclassical logic such as PAL in the decision-making process.
Figure 1.
Number of articles found in the Web of Science database (May 2020) about Paraconsistent
Annotated Logic (PAL), by application area.
The articles related to the fields of industrial engineering, management, and operations Research
management science are primarily focused on the application of PAL in product quality decision-making,
logistics, environmental sciences, and behavioral situations, among others. Studies carried out in the
areas of electrical and electronics engineering, automation, and computer science applied, for the most
part, the PAL in the development of algorithms for automation and control of industrial systems and/or
algorithms for data mining (for analysis of distributed and often inconsistent databases). The PL’s were
also applied to examine inconsistencies from various sources in the creation and treatment of databases
and knowledge bases, i.e., application of PL in data mining to improve the veracity of information [
47
].
In the field of physics, Carnielli and Rodrigues [
41
] present a formal paraconsistent system and
a corresponding intended interpretation, according to which true contradictions are not tolerated.
Contradictions are, instead, epistemically understood as conflicting evidence, where the evidence
for proposition “A” is understood as reason for believing that “A” is true. The article defines
a paraconsistent and paracomplete natural deduction system, called Basic Evidence Logic (BEL),
and extends it to Logic of Evidence and Truth (LETJ). Da Costa and Ronde [
42
] presented a study
on the understanding of physical “superpositions” that exist in both classical and quantum physics.
The authors presented a paraconsistent approach to quantum superpositions, which tries to explain
the contradictory properties present in the interpretation of the meaning of quantum superpositions,
which considers the contradiction as a key element of the formal structure of the theory.
In other fields of application, studies such as Takahashi, Umeda, and Sawamura [
48
], developed
a basic structure of argument (means of interaction) for Extended Generalized Annotated Logical
Programs (EGAP), providing the theory of semantics and dialectical proof and proving the solidity,
integrity, and equivalence of semantics well-reasoned. Bonilla et al. [
23
] apply Paraconsistent
Tri-Annotated Logic (PAL3v) in the analysis of a set of emergency indicators linked to ecological and
environmental issues, aiming to assess sustainability and efficiency in minimizing the priority for the
use of nonrenewable resources. Encheva, Tumin, and Kondratenk [
49
] added the PAL in a support
Appl. Sci. 2020,10, 8040 7 of 26
system to select optimal decisions in transport logistics, having as the main criterion for decision the
quality of cargo delivery. Oshiyama et al. [
50
] used PAL to classify medical equipment based on the ABC
analysis of corrective maintenance data, developing alerts on deviations in equipment performance,
which are identified when inconsistencies and indeterminations occur in the classification.
Summing up, PL helps to clarify the concepts of negation and contradiction, aiming to deal with
contradictory situations. Many studies, mainly practical case studies, present results that consider the
inconsistencies. For this reason, they are more propitious in framing problems caused by situations
of contradictions, ideal for applying a nonclassical logic such as PAL in the decision-making process.
Next are presented the fundamentals of BWM, applied in conjunction with the PAL-VMEA in this work.
4. Best-Worst Method (BWM)
According to Rezaei [
51
], the Best-Worst Method (BWM) is a multicriteria decision-making
technique where the best and worst choices, among the alternatives, are defined by means of a peer
comparison between the analyzed alternatives (with a weight scale of 1–9 used for comparison).
This method also stands out for its simple application and the reduction in the time for carrying
out the peer comparison between the variables, in addition to the good performance in maintaining
consistency between the judgments [
51
,
52
]. In this work, the BWM is used as an auxiliary tool for
PAL2v, evaluating the ability (in percentage) of decision-makers (engineering experts) to assign weights
to critical variables that affect (directly and indirectly) the performance of KPCs analyzed in the
VMEA method.
In general applications, the algorithm to structure the Best-Worst Method is presented as
follows [51,53]:
•Step I: list the variables (decision criteria) involved in the decision process.
•
Step II: decision-makers must determine which criterion is the most important (BEST criterion)
and which has the least impact on the decision (WORST criterion).
•
Step III: carry out the parity comparison (using Saaty’s scale: 1–9 [
54
]) between the preference of
BEST criteria over other criteria. The result of the Best-to-Others vector is AB =(a
B1
,a
B2
,
. . .
,a
Bn
),
where aBj indicates the degree of preference of the best criterion, B, over criterion j, and 1 ≤j≤n.
•
Step IV: make the parity comparison (using Saaty’s scale: 1–9) between the preferences of the
criteria involved in the decision-making process over the determined WORST criteria. The result
of the Others-to-Worst vector is A
W
=(a
1W
,a
2W
,
. . .
,a
nW
), where a
jW
indicates the degree of
preference of the criterion jover the worst criterion, W.
•
Step V: obtain the optimal weights (percentages), (w
1
*, w
2
*,
. . .
,w
n
*), of each criterion from the
formulation of a Maximization and Minimization problem (MAX-MIN), given by Equation (1),
in order to satisfy the conditions that for each (w
B
/w
j
) and (w
j
/w
W
), (w
B
/w
j
)=a
Bj
and (w
j
/w
W
)=
a
jW
, being w
B
the importance weight of the best criterion and w
W
the importance weight of the
worst criterion.
minmax
jn
wB/wj−aBj
,
wj/wW−ajW
os.t.
n
X
j=1
wj=1; wj≥0∀j. (1)
The problem presented in Equation (1) can be simplified, as presented in Equation (2), in order to
obtain ξ*:
min(ξ)s.t.
wB/wj−aBj
≤ξ∀j;
wj/wW−ajW
≤ξ∀j;
n
P
j=1
wj=1;
wj≥0∀j.
(2)
Appl. Sci. 2020,10, 8040 8 of 26
•
Step VI: Perform the consistency verification of the assigned values (weights) by the
decision-makers for the criteria of the decision-making process. This verification can be performed
by the Consistency Ratio calculated by Equations (3) and (4):
ξ2−(1+2aBW)ξ+a2
BW −aBW=0 (3)
Consistency Ratio =ξ∗/max(ξ). (4)
Being the maximum possible
ξ
—max (
ξ
)—called Consistency Index (CI), found as function of
aBW, according to Table 1[51].
Table 1. Consistency Index.
aBW 123456789
CI 0.00 0.44 1.00 1.63 2.30 3.00 3.73 4.47 5.23
Once the consistency verification is done, the result of the percentage weight of each criterion
involved in the decision-making process is obtained. In conclusion, BWM is an easy-to-apply method
for determining the most appropriate weights for decision criteria, with guaranteed reliability of
results, as it performs a consistency check of the judgments (even comparison between the criteria)
made by the decision-makers.
5. The Proposed PAL-VMEA Method Conjugated with BWM
As previously mentioned, the present work aims to determine the appropriate maintenance policy
for an equipment, through critical maintenance indicators (VRPN) defined through the application
of the VMEA quality tool. The method based on the combination of PAL2v and BWM is used as a
weight assignment tool to VMEA inputs, considering the epistemic uncertainty, which does not occur
in decision processes where the experts’ opinions are combined based on statistical approach.
According to the flowchart of the proposed method presented in Figure 2, the VMEA tool is
initially applied to the critical analyzed components, which can be divided into subsystems. The key
point of VMEA is the assessment of how variations in the characteristics of a product affect its final
quality [
32
]. In this work, however, the use of VMEA is proposed to analyze the condition of a
system and, in this process of adapting the method to a new context related to maintenance, KPCs are
translated as the main functions of the analyzed subsystems, as Sub-KPCs are understood as the flows
(of information, matter, or energy) that integrate the components of these subsystems in the fulfillment
of their functions. In this way, these flows are basically physical measurable quantities, in which
variation outside the standards defined by the operational condition of the analyzed system is due
to faults in its components, defined as the NF in this case. To demonstrate how each NF affects the
analyzed KPC in a graphic way, an Ishikawa diagram can be used, as shown in Figure 3[32].
Appl. Sci. 2020,10, 8040 9 of 26
Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 25
Figure 2. PAL-Variation and Mode Effect Analysis (VMEA) method framework.
Figure 3. Variation transfer model—Ishikawa diagram.
From the Ishikawa diagram, it is possible to build a form for the VMEA, associating the weights
to the considered KPCs and NFs, as presented in Table 2.
Table 2. Variation and Mode Effect Analysis (VMEA) form.
System: System’s Name Subsystem: Subsystem’s Name KPC: Subsystem’s Function
Figure 2. PAL-Variation and Mode Effect Analysis (VMEA) method framework.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 25
Figure 2. PAL-Variation and Mode Effect Analysis (VMEA) method framework.
Figure 3. Variation transfer model—Ishikawa diagram.
From the Ishikawa diagram, it is possible to build a form for the VMEA, associating the weights
to the considered KPCs and NFs, as presented in Table 2.
Table 2. Variation and Mode Effect Analysis (VMEA) form.
System: System’s Name Subsystem: Subsystem’s Name KPC: Subsystem’s Function
Figure 3. Variation transfer model—Ishikawa diagram.
From the Ishikawa diagram, it is possible to build a form for the VMEA, associating the weights
to the considered KPCs and NFs, as presented in Table 2.
Appl. Sci. 2020,10, 8040 10 of 26
Table 2. Variation and Mode Effect Analysis (VMEA) form.
System: System’s Name Subsystem: Subsystem’s Name KPC: Subsystem’s Function
Sub-KPC Sub-KPC
Weight NF Variation in
NF
Sensitivity
of Sub-KPC
to NF
VRPN (NF) VRPN
(Sub-KPC)
Sub-KPC 1 w1
NF 11 v11 s11 w1×v11 ×s11
P(w1×v1m×s1m)
NF 12 v12 s12 w1×v12 ×s12
... ... ... ...
NF 1m v1ms1mw1×v1m×s1m
Sub-KPC 2 w2
NF 21 v21 s21 w2×v21 ×s21
P(w2×v2m×s2m)
NF 22 v22 s22 w2×v22 ×s22
... ... ... ...
NF 2m v2ms2mw2×v2m×s2m
... ... ... ... ... ... ...
Sub-KPC nwn
NF n1vn1sn1wn×vn1×sn1
P
(w
n×
v
nm ×
s
nm
)
NF n2vn2sn2wn×vn2×sn2
... ... ... ...
NF nm vnm snm
w
n×
v
nm ×
s
nm
The three weights considered in the VMEA form (Sub-KPC Weigh, Variation in NF, and Sensitivity
of Sub-KPC to NF) must be determined, respectively, using the following criteria: criteria for assessing
the transfer of variation from Sub-KPC to KPC, criteria for assessing the variability of noise factors,
and criteria for assessing the sensitivity of Sub-KPC to noise factors. The values associated with the
criteria for each weight are found in Tables 3–5[32].
Table 3. Criteria for assessing the transfer of variation from Sub-KPC to KPC [32].
Criteria Weight
Very low probability that the sub-KPC will transfer or
contribute with considerable amount of variation to the
selected KPC, causing significant impact on product
safety, compliance with governmental regulations,
functional requirements, or customer satisfaction
1–2
Low probability that the sub-KPC will transfer or
contribute with considerable amount of variation to the
selected KPC, causing significant impact on product
safety, compliance with governmental regulations,
functional requirements, or customer satisfaction
3–4
Moderate probability that the sub-KPC will transfer or
contribute with considerable amount of variation to the
selected KPC, causing significant impact on product
safety, compliance with governmental regulations,
functional requirements, or customer satisfaction
5–6
High probability that the sub-KPC will transfer or
contribute with considerable amount of variation to the
selected KPC, causing significant impact on product
safety, compliance with governmental regulations,
functional requirements, or customer satisfaction
7–8
Very high probability that the sub-KPC will transfer or
contribute with considerable amount of variation to the
selected KPC, causing significant impact on product
safety, compliance with governmental regulations,
functional requirements, or customer satisfaction
9–10
Appl. Sci. 2020,10, 8040 11 of 26
Table 4. Criteria for assessing the variability of noise factors [32].
Criteria Weight
Very low variability of noise factor in operating conditions,
i.e., regardless of the operating conditions, the dispersion
in noise factor remains very small
1–2
Low variability of noise factor in operating conditions, i.e.,
regardless of the operating conditions, the dispersion in
noise factor remains small
3–4
Moderate variability of noise factor in operating conditions,
i.e., regardless of the operating conditions, the dispersion
in noise factor remains fairly small
5–6
High variability of noise factor in operating conditions, i.e.,
the dispersion in the noise factor is large 7–8
Very high variability of noise factor in operating conditions,
i.e., the dispersion in the noise factor is very large 9–10
Table 5. Criteria for assessing the sensitivity of Sub-KPC to noise factors [32].
Criteria Weight
Very low sensitivity. A change of in noise factor is very
unlikely to cause a significant deviation in Sub-KPC 1–2
Low sensitivity. A change in noise factor is unlikely to
cause a significant deviation in Sub-KPC 3–4
Moderate sensitivity. A change in noise factor is quite
likely to cause a significant deviation in Sub-KPC 5–6
High sensitivity. A change in noise factor is likely to
cause a significant deviation in Sub-KPC 7–8
Very high sensitivity. A change in noise factor is very
likely to cause a significant deviation in Sub-KPC 9–10
Subsequently, the PAL2v combined with the BWM methods are applied to assign the VMEA
weights, previously presented in Tables 3–5. For such application, it is necessary to develop the
following constructs:
a.
Analyze the level of knowledge of decision-makers in relation to the skills needed for weight
allocation. List the skills necessary to assess the impact of failure modes on the functioning of
the analyzed subsystems (variation of KPCs).
b.
Conduct interviews with decision-makers to analyze the skills among each other and then
apply the BWM to obtain the distribution of the weights of the expertise of each decision-maker.
BWM is applied to assess and balance the degree of technical knowledge (%) of each decision
maker, building the base of belief (be
ij
) and disbelief extractors (de
ij
). The decision-makers’ skills
aggregated weights (W
1
and W
2
) will be used in the extraction of belief and disbelief further.
The weights W
1
and W
2
are structured, for each decision-maker, as: W
1
is the sum of weights of
knowledge concentrated on the assessment skills and W
2
is the sum of weights of knowledge
concentrated on other skills, of each KPC and NF.
c.
After defining the weights of the skills (constructive basis of extractors of belief and disbelief),
PAL
2v
is applied through a structured table containing the Sub-KPCs and NFs to be evaluated
(according to the failure modes) of each KPC. Thus, the decision-makers assign a value from 0 to
1 (0 meaning total disbelief and 1 total belief) for each value of the VMEA criteria (Tables 3–5).
This process is repeated for the evaluation of each KPC with the purpose of assigning the initial
belief weight value (a
ij
) and subsequently, the determination of belief and disbelief (b
ij
) using the
extractors developed in the presented method.
d.
The weights added to the decision-makers’ skills are used in the extraction of belief (favorable
evidence) and disbelief (unfavorable evidence) during the application of PAL
2v
. The belief and
Appl. Sci. 2020,10, 8040 12 of 26
disbelief extractors have the purpose of extracting uncertainties during the decision-making
process from the values to be attributed to the failure modes. With the belief input value (a
ij
),
the disbelief (b
ij
) is calculated, then the belief extractor (be
ij
) and disbelief extractor (de
ij
) are
applied to these values (considering a scale from 0 to 10), using Equations (5)–(7), considering
W1and W2. In the final result, a weighted average of the extractors is computed.
bij =1−aij (5)
beij =aij ·W1(6)
deij =bij ·W2. (7)
e.
To calculate the result for favorable (or belief, a
w
) and unfavorable (or disbelief, b
w
) evidences,
both values obtained by the extraction process for each Sub-KPC and NF, a weighted average of
the extractors is computed. In addition, for the estimation of the degree of certainty (H) and
uncertainty (G), a degree of requirement (for decision-making considering the most consistent
weight) must be established (generally, 0.5, i.e., a minimum of 50% of opinions must converge
with certainty so that the value is established in the Truth zone). The requirement level determines
the consistency of the analysis or the degree of caution to use the analysis, which depends on
the further use of the results (such as an indicator for decision-making) and its implications.
For a level of requirement of 50%, assessments will be carried on with at least 50% of certainty.
Thus, the weight of each Sub-KPC and NF is established by the highest degree of certainty (H
max
),
with the indicators obtained by Equations (8) and (9).
H=aw−bw(8)
G=(aw+1)−bw. (9)
f.
If the same degree of certainty (H) is obtained for different weights, i.e., there is a contradiction
of opinions establishing total indeterminacy (same level of favorable and unfavorable evidence),
decision-makers should search for more information about the particularities of the analyzed
variable for decision-making (and new weight assignment).
g.
The favorable and unfavorable evidence results determined for each Sub-KPC and NF must
be analyzed according to the zones that make up the para-analyzer algorithm plotted on the
Unitary Square on the Cartesian Plane (USCP), as presented in Figure 4and Table 6.
h.
Once the weights (with greater consistency) of the variables (Sub-KPCs and NFs) involved
in the VMEA analysis have been determined, the VRPN index is calculated. This indicator
represents the impact that the variation of the functionalities of the components can have on the
performance of the KPC of the analyzed subsystem.
Appl. Sci. 2020,10, 8040 13 of 26
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1
=⋅
ij ij
be a W (6)
2
=⋅
ij ij
de b W . (7)
e. To calculate the result for favorable (or belief, aw) and unfavorable (or disbelief, bw) evidences,
both values obtained by the extraction process for each Sub-KPC and NF, a weighted average of
the extractors is computed. In addition, for the estimation of the degree of certainty (H) and
uncertainty (G), a degree of requirement (for decision-making considering the most consistent
weight) must be established (generally, 0.5, i.e., a minimum of 50% of opinions must converge
with certainty so that the value is established in the Truth zone). The requirement level
determines the consistency of the analysis or the degree of caution to use the analysis, which
depends on the further use of the results (such as an indicator for decision-making) and its
implications. For a level of requirement of 50%, assessments will be carried on with at least 50%
of certainty. Thus, the weight of each Sub-KPC and NF is established by the highest degree of
certainty (Hmax), with the indicators obtained by Equations (8) and (9).
ww
H
ab=−
(8)
()
1
ww
Ga b=+−
. (9)
f. If the same degree of certainty (H) is obtained for different weights, i.e., there is a contradiction
of opinions establishing total indeterminacy (same level of favorable and unfavorable evidence),
decision-makers should search for more information about the particularities of the analyzed
variable for decision-making (and new weight assignment).
g. The favorable and unfavorable evidence results determined for each Sub-KPC and NF must be
analyzed according to the zones that make up the para-analyzer algorithm plotted on the
Unitary Square on the Cartesian Plane (USCP), as presented in Figure 4 and Table 6.
Figure 4. Unitary square of the Cartesian plane of the PAL2v.
Table 6. Unitary square of the Cartesian plane zones.
Extre
me
f False
T Inconsistent
Figure 4. Unitary square of the Cartesian plane of the PAL2v.
Table 6. Unitary square of the Cartesian plane zones.
Extreme Logical State
fFalse
T Inconsistent
vTrue
⊥Paracomplete
Non-Extreme
Logical State
Qf→ ⊥
Quasi-false tending to paracomplete
Q⊥ → f
Quasi-paracomplete tending to false
Qf→T Quasi-false tending to inconsistent
Q⊥ → vQuasi-paracomplete tending to true
QT →fQuasi-inconsistent tending to false
Qv→ ⊥ Quasi-true tending to paracomplete
QT →vQuasi-inconsistent tending to true
Qv→T Quasi-true tending to inconsistent
It is worth mentioning that this novel method allows to mitigate the epistemic uncertainty present
in the implementation of VMEA. The combination of PAL and VMEA aims to make the obtained
VRPN values more robust and reliable. Once the proposed method is fully applied, the main resulting
indexes of the analysis, i.e., the VRPN values, will direct the attention of analysts and maintainers to
areas where reasonably predicted variations may be harmful. From these results, therefore, a design
or maintenance strategy that seeks to prioritize actions that minimize or eliminate the causes of the
observed variations can be formulated, facilitating the subsequent efforts to obtain a more robust and
reliable system.
Appl. Sci. 2020,10, 8040 14 of 26
6. Case Study
Hydroelectric Power Plants (HPP’s) are responsible for generating more than 60% of the electric
energy that make up the Brazilian energy matrix [
55
]. The dependence on this energy source, both for
the country’s industrial development and meeting the needs of modern society, determines the
importance of ensuring the operational availability and reliability of the power generation system,
aiming at the continuity of energy supply. In this way, the maintenance management of HPP’s assets
must promptly adapt to meet the high standards of availability and reliability necessary to comply
with the energy production and dispatch schedules.
When a fault affects the main functions of a hydrogenerator, it may result in the reduction and/or
interruption of the generation capacity of the power plant. In these cases, penalties and/or high fines
established by regulatory agencies may be attributed to the power plant generating company due to
noncompliance with demand.
The weights established using the PAL-VMEA method aim to reduce the inconsistency in the
information used to obtain the VRPN indicator. As this indicator reflects the equipment
´
s operation,
maintenance, and risk to assets and employees’ safety, as well as how much the interconnected electric
system can be impacted by the failures in the analyzed mechanical systems (considering the reliability
and operational availability of the equipment), consistency is a key point in this decision process.
As a practical application of the proposed method, a case study is presented considering a Kaplan
turbine hydrogenerator. The unit belongs to a run-of-the river power plant located in the Brazilian
North region. According to its layout, a guide journal bearing is positioned near the turbine, two guide
journal bearings are placed near the generator (one above and one below) and one thrust journal
bearing is located near the shaft mid-span. The generated power output is around 150 MW. A simplified
functional tree, covering the three main mechanical systems of the hydrogenerator, as well as the
respective and most significant subsystems, is shown in Figure 5.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 25
Figure 5. Analyzed system simplified functional tree.
From the chosen subsystems, eleven KPCs were considered for the VMEA analysis:
1. Oil pressure on the air-oil accumulator
2. Response time for the Kaplan mechanism
3. Water linear momentum for the water intake
4. Transmitted torque for the turbine blades
5. Control oil flow for the Kaplan head
6. Flow rate for the lubrication system
7. Oil pressure for the lubrication system
8. Lift force for the journal bearings
9. Angular moment for the shaft and joining elements
10. Oil outlet temperature for the heat exchanger
11. Transmission force for the servo motor actuator
Seven necessary skills were listed to assess the impact of failure modes on the variation of the
eleven KPCs: reliability and risk analysis, maintenance management, product quality management
(materials and manufacturing process), failure mechanisms analysis, professional experience in
hydroelectric power plant, electrical and automation knowledge, and lubrication, hydraulics, and
pneumatics knowledge.
Four experts participated in the interviews and in the evaluation and analysis process for each
KPC. Together, these specialists have almost 100 years of experience in product design, reliability
and risk analysis, quality management, and rotating machinery monitoring and diagnosis, among
other abilities. From the application of BWM, the weight distribution of the skills of each decision-
maker was obtained. Table 7 shows the result of applying this method to define the weight of skills
for each decision-maker. Note that the sum of the knowledge weights of each evaluator is equal to 1.
It is worth mentioning that the method does not limit the number of participating experts and,
although the time consumed by the analysis increases, a greater number of participating specialists
tends to increase the accuracy of the results.
Table 7. Experts technical skills weights—Best-Worst Method (BWM) results.
Applied Technical Knowledge (K) Expert #1 Expert #2 Expert #3 Expert #4
Reliability and risk analysis (K1) 0.123 0.349 0.091 0.059
Figure 5. Analyzed system simplified functional tree.
From the chosen subsystems, eleven KPCs were considered for the VMEA analysis:
1. Oil pressure on the air-oil accumulator
2. Response time for the Kaplan mechanism
3. Water linear momentum for the water intake
4. Transmitted torque for the turbine blades
Appl. Sci. 2020,10, 8040 15 of 26
5. Control oil flow for the Kaplan head
6. Flow rate for the lubrication system
7. Oil pressure for the lubrication system
8. Lift force for the journal bearings
9. Angular moment for the shaft and joining elements
10.
Oil outlet temperature for the heat exchanger
11.
Transmission force for the servo motor actuator
Seven necessary skills were listed to assess the impact of failure modes on the variation of the
eleven KPCs: reliability and risk analysis, maintenance management, product quality management
(materials and manufacturing process), failure mechanisms analysis, professional experience in
hydroelectric power plant, electrical and automation knowledge, and lubrication, hydraulics,
and pneumatics knowledge.
Four experts participated in the interviews and in the evaluation and analysis process for each
KPC. Together, these specialists have almost 100 years of experience in product design, reliability and
risk analysis, quality management, and rotating machinery monitoring and diagnosis, among other
abilities. From the application of BWM, the weight distribution of the skills of each decision-maker
was obtained. Table 7shows the result of applying this method to define the weight of skills for each
decision-maker. Note that the sum of the knowledge weights of each evaluator is equal to 1. It is worth
mentioning that the method does not limit the number of participating experts and, although the time
consumed by the analysis increases, a greater number of participating specialists tends to increase the
accuracy of the results.
Table 7. Experts technical skills weights—Best-Worst Method (BWM) results.
Applied Technical Knowledge (K) Expert #1 Expert #2 Expert #3 Expert #4
Reliability and risk analysis (K1) 0.123 0.349 0.091 0.059
Maintenance management (K2) 0.123 0.222 0.299 0.137
Product quality management (K3) 0.379 0.148 0.299 0.027
Failure mechanisms (K4) 0.123 0.089 0.121 0.206
Professional experience in
hydroelectric power plant (K5) 0.030 0.028 0.026 0.330
Electrical and automation
(instrumentation) (K6) 0.099 0.074 0.091 0.103
Lubrication, hydraulics, and
pneumatics (K7) 0.123 0.089 0.073 0.137
For each analyzed sub-KPC, NFs were associated according to the considered failure modes.
In each case, an Ishikawa diagram was created to represent the transfer between the variations of the
NF and the KPCs analyzed. To illustrate the process, the air-oil accumulator subsystem (from the
speed governor system) will be considered, as presented in Figure 6.
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Maintenance management (K2) 0.123 0.222 0.299 0.137
Product quality management (K3) 0.379 0.148 0.299 0.027
Failure mechanisms (K4) 0.123 0.089 0.121 0.206
Professional experience in hydroelectric power plant
(K5) 0.030 0.028 0.026 0.330
Electrical and automation (instrumentation) (K6) 0.099 0.074 0.091 0.103
Lubrication, hydraulics, and pneumatics (K7) 0.123 0.089 0.073 0.137
For each analyzed sub-KPC, NFs were associated according to the considered failure modes. In
each case, an Ishikawa diagram was created to represent the transfer between the variations of the
NF and the KPCs analyzed. To illustrate the process, the air-oil accumulator subsystem (from the
speed governor system) will be considered, as presented in Figure 6.
Figure 6. Air-oil accumulator variation transfer Ishikawa diagram.
In this case, the KPC associated with the oil pressure is the capacity of the air-oil accumulator
subsystem to pressurize the control fluid. The factors (weights) to be designated by the evaluators
are: the probability of the sub-KPC’s oil volume (F1) and air pressure (F2) transferring or contributing
to a significant variation in the analyzed KPC; the variability of the NF’s oil leakage (F3), clogging of
the oil pipeline (F4) and leakage in the air pipeline (F5) with the equipment in steady state, and the
sensitivity of each sub-KPC to its NFs (F6 for oil leakage, F7 for oil pipeline clogging, and F8 for air
pipeline leakages). The necessary knowledge to attribute the beliefs of each weight are given in Table
8, while Table 9, Table 10, Table 11, and Table 12, respectively, present the degree of favorable
evidence (belief) attributed by each expert to each weight associated with the VMEA attributes (as
presented in Tables 3–5). It is worth mentioning that the results in Table 8 were obtained through
brainstorm sessions with the experts, who reached consensus on which skills would be needed to
assess each factor.
Table 8. Necessary knowledge versus VMEA weights.
K1 K2 K3 K4 K5 K6 K7
F1 X X X
F2 X X X
F3 X X X
F4 X X X X
F5 X X X
F6 X X X
Figure 6. Air-oil accumulator variation transfer Ishikawa diagram.
In this case, the KPC associated with the oil pressure is the capacity of the air-oil accumulator
subsystem to pressurize the control fluid. The factors (weights) to be designated by the evaluators are:
the probability of the sub-KPC’s oil volume (F1) and air pressure (F2) transferring or contributing to
a significant variation in the analyzed KPC; the variability of the NF’s oil leakage (F3), clogging of
the oil pipeline (F4) and leakage in the air pipeline (F5) with the equipment in steady state, and the
sensitivity of each sub-KPC to its NFs (F6 for oil leakage, F7 for oil pipeline clogging, and F8 for air
pipeline leakages). The necessary knowledge to attribute the beliefs of each weight are given in Table 8,
while Table 9, Table 10, Table 11, and Table 12, respectively, present the degree of favorable evidence
(belief) attributed by each expert to each weight associated with the VMEA attributes (as presented
in Tables 3–5). It is worth mentioning that the results in Table 8were obtained through brainstorm
sessions with the experts, who reached consensus on which skills would be needed to assess each factor.
Table 8. Necessary knowledge versus VMEA weights.
K1 K2 K3 K4 K5 K6 K7
F1 X X X
F2 X X X
F3 X X X
F4 X X X X
F5 X X X
F6 X X X
F7 X X X X
F8 X X X
Table 9. Expert #1 favorable evidence degree versus VMEA weights.
1 2 3 4 5 6 7 8 9 10
F1 0.00 0.00 0.00 0.00 0.00 0.00 0.90 0.90 1.00 1.00
F2 0.00 0.00 0.00 0.00 0.00 0.00 0.90 0.90 1.00 1.00
F3 0.30 0.30 0.50 0.50 1.00 1.00 0.50 0.50 0.30 0.30
F4 0.30 0.30 0.50 0.50 1.00 1.00 0.50 0.50 0.30 0.30
F5 0.30 0.30 0.50 0.50 1.00 1.00 0.70 0.70 0.50 0.50
F6 0.00 0.00 0.00 0.00 0.30 0.30 0.90 0.90 1.00 1.00
F7 0.00 0.00 0.00 0.00 0.10 0.10 0.90 0.90 1.00 1.00
F8 0.00 0.00 0.00 0.00 0.00 0.00 0.90 0.90 1.00 1.00
Appl. Sci. 2020,10, 8040 17 of 26
Table 10. Expert #2 favorable evidence degree versus VMEA weights.
1 2 3 4 5 6 7 8 9 10
F1 0.00 0.00 0.00 0.00 0.30 0.50 0.50 0.30 0.00 0.00
F2 0.00 0.00 0.00 0.00 0.00 0.00 0.10 0.30 0.70 0.20
F3 0.30 0.30 0.30 0.30 0.00 0.00 0.00 0.00 0.00 0.00
F4 0.30 0.30 0.30 0.30 0.00 0.00 0.00 0.00 0.00 0.00
F5 0.30 0.30 0.30 0.30 0.00 0.00 0.00 0.00 0.00 0.00
F6 0.00 0.00 0.00 0.30 0.30 0.30 0.30 0.00 0.00 0.00
F7 0.00 0.00 0.00 0.00 0.30 0.30 0.30 0.30 0.00 0.00
F8 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.60 0.60 0.60
Table 11. Expert #3 favorable evidence degree versus VMEA weights.
1 2 3 4 5 6 7 8 9 10
F1 0.10 0.10 0.10 0.10 0.50 0.50 0.80 0.80 0.90 0.90
F2 0.10 0.10 0.10 0.10 0.50 0.50 0.80 0.80 0.90 0.90
F3 0.10 0.10 0.10 0.10 0.40 0.40 0.80 0.80 1.00 1.00
F4 0.00 0.00 0.00 0.00 0.10 0.10 0.20 0.20 0.20 0.20
F5 0.10 0.10 0.10 0.10 0.60 0.60 0.80 0.80 0.90 0.90
F6 0.00 0.00 0.00 0.00 0.50 0.50 0.60 0.60 1.00 1.00
F7 0.00 0.00 0.00 0.00 0.10 0.10 0.20 0.20 0.20 0.20
F8 0.10 0.10 0.10 0.10 0.60 0.60 0.80 0.80 0.90 0.90
Table 12. Expert #4 favorable evidence degree versus VMEA weights.
1 2 3 4 5 6 7 8 9 10
F1 0.00 0.00 0.00 0.00 0.00 0.00 0.30 0.70 0.90 0.50
F2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.30 0.70 1.00
F3 0.70 0.90 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00
F4 0.50 0.90 0.80 0.20 0.00 0.00 0.00 0.00 0.00 0.00
F5 0.90 0.70 0.20 0.00 0.00 0.00 0.00 0.00 0.00 0.00
F6 0.00 0.00 0.00 0.00 0.00 0.00 0.20 0.50 1.00 0.70
F7 0.00 0.00 0.00 0.00 0.00 0.20 0.50 1.00 0.80 0.50
F8 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.50 1.00
Applying the evidence values associated with each weight (Tables 9–12), as well as the weights
related to each knowledge necessary for the evaluation of each weight (Tables 7and 8), the results
presented in Table 13 are achieved for each VMEA weight.
Table 13. VMEA weights results.
Value awbwH G
F1 9.00 0.7146 0.3113 0.4033 0.0260
F2 9.00 0.8201 0.1712 0.6489 −0.0086
F3 2.00 0.4089 0.6069 −0.1980 0.0158
F4 3.00 0.3640 0.5334 −0.1694 −0.1026
F5 1.00 0.4089 0.6069 −0.1980 0.0158
F6 9.00 0.7705 0.2658 0.5047 0.0363
F7 8.00 0.5795 0.3620 0.2175 −0.0586
F8 10.00 0.8799 0.1288 0.7511 0.0087
The favorable and unfavorable evidence results of each evaluated factor, for the given example,
plotted in the USCP are shown in Figure 7.
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Table 13. VMEA weights results.
Value aw bw H G
F1 9.00 0.7146 0.3113 0.4033 0.0260
F2 9.00 0.8201 0.1712 0.6489 −0.0086
F3 2.00 0.4089 0.6069 −0.1980 0.0158
F4 3.00 0.3640 0.5334 −0.1694 −0.1026
F5 1.00 0.4089 0.6069 −0.1980 0.0158
F6 9.00 0.7705 0.2658 0.5047 0.0363
F7 8.00 0.5795 0.3620 0.2175 −0.0586
F8 10.00 0.8799 0.1288 0.7511 0.0087
The favorable and unfavorable evidence results of each evaluated factor, for the given example,
plotted in the USCP are shown in Figure 7.
Figure 7. Air-oil accumulator example Unitary Square on the Cartesian Plane (USCP).
Considering the obtained results for the sub-KPC’s oil volume (F1 = 9) and air pressure (F2 = 9);
the variability of the NF’s oil leakage (F3 = 2), clogging of the oil pipeline (F4 = 3) and leakage in the
air pipeline (F5 = 1); and the sensitivity of each sub-KPC to its NFs (F6 = 9, for oil leakage, F7 = 8, for
oil pipeline clogging, and F8 = 10, for air pipeline leakages), presented in Table 13, the VMEA form
completed for this case study is shown in Table 14.
Table 14. VMEA form—air-oil accumulator example.
System:
Speed Governor
Subsystem:
Air-Oil Accumulator
KPC:
Pressurize the Control Fluid
Sub-KPC Weighting of
Sub-KPC NF
Size of
variation in
NF
Sensitivity of
Sub-KPC to NF
VRPN
(NF)
VRPN
(Sub-KPC)
Oil
Volume 9 Leakage 2 9 162 378
Clogging 3 8 216
Air
Pressure 9 Leakage 1 10 90 90
Figure 7. Air-oil accumulator example Unitary Square on the Cartesian Plane (USCP).
Considering the obtained results for the sub-KPC’s oil volume (F1 =9) and air pressure (F2 =9);
the variability of the NF’s oil leakage (F3 =2), clogging of the oil pipeline (F4 =3) and leakage in the
air pipeline (F5 =1); and the sensitivity of each sub-KPC to its NFs (F6 =9, for oil leakage, F7 =8,
for oil pipeline clogging, and F8 =10, for air pipeline leakages), presented in Table 13, the VMEA form
completed for this case study is shown in Table 14.
Table 14. VMEA form—air-oil accumulator example.
System:
Speed Governor
Subsystem:
Air-Oil Accumulator
KPC:
Pressurize the Control Fluid
Sub-KPC Weighting
of Sub-KPC NF Size of
variation in NF
Sensitivity
of Sub-KPC
to NF
VRPN
(NF)
VRPN
(Sub-KPC)
Oil Volume 9 Leakage 2 9 162 378
Clogging 3 8 216
Air Pressure 9 Leakage 1 10 90 90
Table 14 presents the expected result of the proposed method, i.e., the VMEA form filled with
values where epistemic uncertainty was properly worked out in order to increase the robustness of
the results.
The interpretation of this table is relatively simple, since the VRPN values (both for the NF and
for the Sub-KPC) clearly indicate which disturbance (failure) the analyzed system is more sensitive,
in the case of VRPN (NF), as well as which physical quantity (Sub-KPC) should be monitored in order
to predict the occurrence of the failure in question, in the case of VRPN (Sub-KPC). These two pieces
of information are essential for proper maintenance planning, especially in the Reliability-Centered
Maintenance (RCM) case.
In order to create a reference for the obtained results, the same experts who participated in the
PAL-VMEA process evaluated the VMEA weights and, through meetings and the classic brainstorming
process, arrived at the results presented in Table 15.
Appl. Sci. 2020,10, 8040 19 of 26
Table 15. VMEA form—air-oil accumulator example (brainstorming).
System:
Speed Governor
Subsystem:
Air-Oil Accumulator
KPC:
Pressurize the Control Fluid
Sub-KPC Weighting
of Sub-KPC NF Size of
variation in NF
Sensitivity
of Sub-KPC
to NF
VRPN
(NF)
VRPN
(Sub-KPC)
Oil Volume 8 Leakage 2 6 96 176
Clogging 2 5 80
Air Pressure 8 Leakage 2 6 96 96
Seeking to determine a comparison between the results obtained with the PAL-VMEA method
and the brainstorming process, the 66 NFs and 24 KPCs of the entire analyzed system were evaluated
and the result are shown in Figure 8a,b, respectively.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 18 of 25
Table 14 presents the expected result of the proposed method, i.e., the VMEA form filled with
values where epistemic uncertainty was properly worked out in order to increase the robustness of
the results.
The interpretation of this table is relatively simple, since the VRPN values (both for the NF and
for the Sub-KPC) clearly indicate which disturbance (failure) the analyzed system is more sensitive,
in the case of VRPN (NF), as well as which physical quantity (Sub-KPC) should be monitored in order
to predict the occurrence of the failure in question, in the case of VRPN (Sub-KPC). These two pieces
of information are essential for proper maintenance planning, especially in the Reliability-Centered
Maintenance (RCM) case.
In order to create a reference for the obtained results, the same experts who participated in the
PAL-VMEA process evaluated the VMEA weights and, through meetings and the classic
brainstorming process, arrived at the results presented in Table 15.
Table 15. VMEA form—air-oil accumulator example (brainstorming).
System:
Speed Governor
Subsystem:
Air-Oil Accumulator
KPC:
Pressurize the Control Fluid
Sub-KPC Weighting of
Sub-KPC NF
Size of
variation in
NF
Sensitivity of
Sub-KPC to NF
VRPN
(NF)
VRPN
(Sub-KPC)
Oil
Volume 8 Leakage 2 6 96 176
Clogging 2 5 80
Air
Pressure 8 Leakage 2 6 96 96
Seeking to determine a comparison between the results obtained with the PAL-VMEA method
and the brainstorming process, the 66 NFs and 24 KPCs of the entire analyzed system were evaluated
and the result are shown in Figure 8a,b, respectively.
Figure 8. Comparison between the PAL-VMEA method and the brainstorming process results for (a)
Noise Factors and (b) Key Product Characteristics .
In this case, each point represents an ordered pair formed by the result of the two processes
(PAL-VMEA and brainstorming) for the same NF or KPC. The diagonal line represents the total
correspondence between the results of the two methods, i.e., NF
brainstorm
= NF
PAL-VMEA
and KPC
brainstorm
= KPC
PAL-VMEA
. The colors intensity in the graphs represents the distance between the results, with the
yellow zone representing the region of equivalence between results, the red zone representing the
region in which the results found via brainstorm are greater than PAL-VMEA results, and the green
zone representing the opposite.
Figure 8.
Comparison between the PAL-VMEA method and the brainstorming process results for
(a) Noise Factors and (b) Key Product Characteristics.
In this case, each point represents an ordered pair formed by the result of the two processes
(PAL-VMEA and brainstorming) for the same NF or KPC. The diagonal line represents the total
correspondence between the results of the two methods, i.e., NF
brainstorm
=NF
PAL-VMEA
and
KPCbrainstorm =KPCPAL-VMEA. The colors intensity in the graphs represents the distance between the
results, with the yellow zone representing the region of equivalence between results, the red zone
representing the region in which the results found via brainstorm are greater than PAL-VMEA results,
and the green zone representing the opposite.
It is noted that the results of the two methods have some correlation, which is equal to 0.757 in
the case of NFs and 0.840 in the case of KPCs, but the variation between results for the same criterion
is significant. In most cases, the values found with the PAL-VMEA method are greater than those
obtained via the brainstorming process (which would mean a more conservative result for the former),
especially in the case of KPCs. It is also interesting to bear in mind that in the brainstorming process,
a consensus must be reached among evaluators, even though not always in a truly democratic way,
especially if there are different hierarchical levels involved. On the other hand, in the proposed method,
the weighting is done individually, therefore emphasizing the experience of each expert. In this way,
the result would not derive from the “average” of the appraisers’ experiences, but from their “sum.”
The results obtained can be analyzed more deeply, being of great interest, e.g., to investigate and
translate the position of each factor evaluated in the USCP from a physical point of view, considering
the failure mechanism involved.
Appl. Sci. 2020,10, 8040 20 of 26
7. Results and Discussion
The PAL-VMEA method culminates in the presentation and analysis of the VMEA form for each
system and subsystem analyzed. This form, when correctly interpreted, provides the maintainer and
maintenance planner with information of great value for assertive decisions regarding maintenance
management, as previously presented. However, it can be said that the application of the PAL-VMEA
is an example that the journey can be as important as the arrival.
When interpreting the positioning of the favorable and unfavorable evidences of each factor
(weight) evaluated in relation to the quadrants of the USCP, e.g., it is possible to verify, and understand,
some fundamentals related to failure modes, and their observability, that can affect the analyzed system.
Analyzing these positions, considering this first example, the following conclusions are reached:
•
For the F1 factor, the value found for assessing the transfer of variation from Sub-KPC to KPC
criteria is equal to 9, which translates into a very high sensitivity, i.e., a change in noise factor is
very likely to cause a significant deviation in Sub-KPC. Being the result in the Quasi-true tending
to paracomplete zone, it is understood, in this case, that if there is a small loss of oil, it may
not affect the pressurization of the air-oil accumulator as the air pressure would compensate
(with the filling of the bladder). However, this compensation has a limit, once it is exceeded,
the oil pressurization drops, so the variation of the oil volume starts to affect the accumulator
pressurization capacity, being able to interrupt the hydrogenerator operation.
•
The weight value F2, which also refers to the transfer of variation from the Sub-KPC to KPC criteria,
is equal to 9, translating into a very high sensitivity, which points out that the decision falls in the
zone of Truth probably because the decision-makers have full knowledge of the failure mechanism.
Without air pressure, it is not possible to pressurize the air-oil accumulator, which may interrupt
the operation of the entire generator.
•
The third weight, F3, is associated with the criteria for assessing the variability of NFs. Being equal
to 2, it indicates a very low variability of NF in operating conditions. In this case, it is understood
that, for being in the Quasi-false tending to inconsistent zone, practically bordering on quasi-false
tending to paracomplete zone, the following assumptions were taken into account: as the origin of
oil leaks in the air-oil accumulator can be due to cracks in the pressure vessel and/or failures in the
joints and connections, it is impossible to make a consistent measurement over time. So, measuring
the derivative of such a measurement (indicator of variability) is an almost impossible task and
the decision-makers do not have accurate data for an assessment with complete certainty.
•
The fourth factor, F4, also related to the variability of the NFs, has a value equal to 3, indicating a
low variability of NF in operating conditions. Being in the Quasi-false tending to paracomplete
zone, it is understood that measuring clogging in the intake or exit pipeline of the accumulator
is a complex task, requiring specific equipment and techniques, such as ultrasonic testing.
Therefore, it is difficult to make a consistent measurement of the variability of the clogging over
time. So, decision-makers do not have accurate data for an assessment with complete certainty.
•
The F5 factor, also related to the variability of the NFs, is equal to 1. This value indicates a very
low variability of NF in operating conditions. Being in the Quasi-false tending to inconsistent
zone, overlapping the F3 factor, this result is related to the fact that measuring the leakage in the
air pipeline could be a complex task. Since the maintainer does not have easy access to the entire
length of the pipeline to inspect it, specific techniques and instruments are needed to solve the
problem. If there was information about the leak over time, the decision-makers’ opinions would
likely converge on the truth zone (due to the more consistent monitoring data).
•
The F6 factor, associated with the sensitivity of Sub-KPC to NF, is equal to 9, demonstrating a very
high sensitivity, i.e., a change in the NF is very likely to cause a significant deviation in Sub-KPC.
Being practically on the edge of the Truth zone, the result is an indication that the existence of
leaks directly affects the volume of oil, regardless of the variability of the leak. As the variation
in volume is directly proportional to the variation in leakage, the opinions of decision-makers
Appl. Sci. 2020,10, 8040 21 of 26
converged with full certainty to identify that the volume of oil is affected by any occurrence
of leakage.
•
The seventh factor, F7, is also associated with the sensitivity of Sub-KPC to NF. Its value is equal to
8, indicating a high sensitivity, i.e., a change in noise factor is likely to cause a significant deviation
in Sub-KPC, and it is located at the Quasi-true tending to paracomplete zone. Despite the lack of
consistent data regarding the variability of the clogging, characterizing the lack of information for
decision-making, the opinions of decision-makers converge. This agreement occurs because if
there is any indication of clogging, there will be a great influence on the oil volume, as the failure
mechanism is known.
•
The last and eighth factor in this analysis, F8, is also associated with the sensitivity of Sub-KPC
to NF. With a value equal to 10, result is found in the zone of Truth. The analysis was based
on the concept of functional failure. A very small leak could be compensated by the action of
the compressor, not leading to the loss of function of the air-oil accumulator. However, when
there is an impact on the function of the equipment, any variation in leaks affects the air pressure.
Thus, the opinions of the decision-makers converged with full certainty to identify that the air
pressure has a high sensitivity due to the variability of leaks.
The method was applied to all other considered subsystems, totaling 10 subsystems. The number
of KPCs, Sub-KPCs, and NFs varies significantly from case to case, totaling more than 140 analyzed
factors. From all of these analyzes, the conclusions regarding the positioning of the weights in the
USCP were reached as presented in Table 16.
Table 16. Results discussion regarding Unitary Square on the Cartesian Plane (USCP) zones.
USCP Zones Results Discussions
Zone of Truth
The evaluators understand (believe) and agree with
the proposed failure mode cause and effect
mechanism, having sufficient information
(well-defined physical principles or measurement
data) to analyze the mechanism during the system
operation and have a converging opinion
Falsehood Zone
The evaluators have doubts, disbelief, do not
understand or do not agree with the proposed failure
mode cause and effect mechanism, although they
have sufficient information for the analysis
(measurement data) and their opinions are
convergent
Inconsistency zone
The evaluators’ opinion is divergent, regardless of
their agreement or belief in the proposed failure
mode cause and effect mechanism and the level of
information available
Paracomplete zone
The information available for the analysis of the
failure mode during the system operation is
insufficient, regardless of the evaluators agreement or
belief in the proposed cause and effect mechanism
and the convergence of their opinion
Appl. Sci. 2020,10, 8040 22 of 26
Table 16. Cont.
USCP Zones Results Discussions
Quasi-true tending to paracomplete and
Quasi-paracomplete tending to true zones
The evaluators understand and agree with the
proposed failure mode cause and effect mechanism
and their opinion about it is convergent. However,
they do not have enough information to analyze the
mechanism during the system operation. The
relationship between the level of understanding and
the level of information available determines whether
the answer will be in the Quasi-true tending to
paracomplete zone or Quasi-paracomplete tending to
true zone
Quasi-true tending to inconsistent and
Quasi-inconsistent tending to true zones
Evaluators understand and agree with the proposed
failure mode cause and effect mechanism and have
enough information to analyze it during the system
operation. However, their opinions about it are
divergent. The relationship between the level of
divergence and understanding of the evaluators
defines whether the answer will be in the Quasi-true
tending to inconsistent zone or Quasi-inconsistent
tending to true zone
Quasi-false tending to paracomplete and
Quasi-paracomplete tending to false zones
The evaluators have doubts, do not understand, or do
not agree with the proposed failure mode cause and
effect mechanism and do not have enough
information to analyze the mechanism during the
system operation. The relationship between the level
of information and the understanding of the
mechanism determines whether the answer will be in
the Quasi-false tending to paracomplete zone or
Quasi-paracomplete tending to false zone
Quasi-false tending to inconsistent and
Quasi-inconsistent tending to false zones
The evaluators have doubts, do not understand, or do
not agree with the proposed failure mode cause and
effect mechanism and their opinions are divergent.
The relationship between the level of understanding
and divergence determines whether the answer will
be in the Quasi-false tending to inconsistent zone or
Quasi-inconsistent tending to false zone
Center Undefined analysis. No conclusion can be reached
Regarding the VMEA form, the results obtained for the different VRPNs can be considered
individually for each subsystem or jointly, considering each system or even the hydrogenerator in its
entirety. The largest VRPNs demonstrate which NFs and Sub-KPCs need more attention.
8. Conclusions
The PAL-VMEA method combined with the BWM method, presented in this work, is a variation of
the VMEA method with the inclusion of a mechanism for assessing the epistemic uncertainty inherent
in knowledge-based methods, such as the FMEA itself and its offspring.
The VMEA method, originally created to fill a gap in the RDM area, is a technique that assesses
how NFs (disturbances) can affect the quality of a product’s KPCs. When taken to the maintenance
area, NFs can be translated as failure modes and KPCs as the main functions of a system. In this
way, the Sub-KPCs translate into the way of observing the effect of the NFs, being basically physical
quantities that quantify the flows between the components of the evaluated system.
In this way, the result obtained with the VMEA, the VRPN index, points to the failure modes,
considering the VRPN (NF), that most affect the analyzed system, as well as which quantities must be
Appl. Sci. 2020,10, 8040 23 of 26
monitored, considering the VRPN (Sub-KPC), so that the symptoms related to each failure mode can
be observed, helping in decision-making regarding maintenance planning and management.
The PAL method, since it belongs to a family of nonclassical methods, rejects the principle
of noncontradiction, therefore being a very robust tool for the evaluation of epistemic uncertainty.
Epistemic uncertainty can be considered an issue in several processes, and this is no different regarding
decision-making, planning, and maintenance management.
By combining the PAL with the VMEA, the authors seek to make the valuation of the weights
associated with the VMEA more robust and thereby allow more accurate decisions for the maintainers
who apply the method in their systems. However, seeking to consider the individual experience of
each evaluator in the final result, BWM was also combined with PAL-VMEA, making the proposed
method even more robust.
To demonstrate the application of the method, a Kaplan hydrogenerator was considered as an
example case, being subdivided into three large systems that, in turn, were subdivided in subsystems,
totaling 10 subsystems. One of these subsystems (the speed governor air-oil accumulator, which can be
considered the heart of a hydrogenerator) was chosen to demonstrate the development of the method,
reaching the final result, the VMEA form. In this example, clogging in the oil pipeline was considered
the failure mode for which the equipment shows greater sensitivity, as well as the volume of oil in the
accumulator as the most relevant quantity to be monitored.
The favorable and unfavorable evidence results determined for each Sub-KPC and NF were
also analyzed according to the zones that make up the para-analyzer algorithm plotted on the USCP.
This analysis demonstrated the coherence of the method, also serving as a guide for other applications
due to the logic of the results.
In addition to the advantages already demonstrated, a factor that makes the application of
PAL-VMEA even more interesting is the way that specialists evaluate and value weights. As the
evaluation by the proposed method is individual, the consensus between the different opinions,
which is usually obtained via brainstorming with debates and discussions, is found in this case from a
logical and mathematical process.
The method ends up requiring the action of a mediator, who will be responsible for the calculations,
being an additional element to the team of experts. Besides that, the method proves to be quite laborious
for the mediator when applied to a large system, and its automation can be advantageous. Standardized
forms can assist in interviews and information collection. Moreover, as a future work and natural
continuation of this article, based on its results, it is possible to seek the development of a framework
aiming at adequate maintenance policy for the components of a hydrogenerator systems and promoting
greater reliability and operational availability to the power generation process.
Author Contributions:
Conceptualization, M.M.B., M.A.C.M., A.H.A.M., A.C.N., C.A.M., and G.F.M.S.;
methodology, M.M.B., M.A.C.M., A.H.A.M., A.C.N., C.A.M., and G.F.M.S.; validation, M.M.B., M.A.C.M.,
A.H.A.M., A.C.N., C.A.M., and G.F.M.S.; formal analysis, M.M.B., M.A.C.M., A.H.A.M., A.C.N., C.A.M.,
and G.F.M.S.; investigation, M.M.B., M.A.C.M., A.H.A.M., A.C.N., C.A.M., and G.F.M.S.; resources, M.M.B.,
M.A.C.M., A.H.A.M., A.C.N., C.A.M., and G.F.M.S.; data curation, M.M.B., M.A.C.M., A.H.A.M., A.C.N., C.A.M.,
and G.F.M.S.; writing—original draft preparation, M.M.B., M.A.C.M., A.H.A.M., A.C.N., C.A.M., and G.F.M.S.;
writing—review and editing, M.M.B., M.A.C.M., A.H.A.M., A.C.N., C.A.M., and G.F.M.S.; visualization, M.M.B.,
M.A.C.M., A.H.A.M., A.C.N., C.A.M., and G.F.M.S.; supervision, G.F.M.S.; project administration, G.F.M.S.;
funding acquisition, G.F.M.S. All authors have read and agreed to the published version of the manuscript.
Funding:
This study was financed in part by the Coordenaç
ã
o de Aperfeiçoamento de Pessoal de N
í
vel
Superior—Brasil (CAPES)—Finance Code 001. The authors thank the financial support of FDTE (Fundaç
ã
o para o
Desenvolvimento Tecnol
ó
gico da Engenharia), CAPES, CNPq (Conselho Nacional de Desenvolvimento Cient
í
fico
e Tecnológico), and EDP Brasil for the development of the present research as part of an ANEEL P&D Project.
Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the
study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to
publish the results.
Appl. Sci. 2020,10, 8040 24 of 26
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