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Citation: Stanic, N.; Gomilanovic, M.;
Markovic, P.; Krzanovic, D.;
Doderovic, A.; Stepanovic, S. A Model
for Determining the Dependability of
Continuous Subsystems in Coal
Mines Using the Fuzzy Logic
Approach. Appl. Sci. 2024,14, 7947.
https://doi.org/10.3390/
app14177947
Received: 19 July 2024
Revised: 29 August 2024
Accepted: 2 September 2024
Published: 6 September 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
applied
sciences
Article
A Model for Determining the Dependability of Continuous
Subsystems in Coal Mines Using the Fuzzy Logic Approach
Nikola Stanic 1, *, Miljan Gomilanovic 1, Petar Markovic 2, Daniel Krzanovic 1, Aleksandar Doderovic 1
and Sasa Stepanovic 1
1Mining and Metallurgy Institute Bor, 19210 Bor, Serbia; miljan.gomilanovic@irmbor.co.rs (M.G.);
daniel.krzanovic@irmbor.co.rs (D.K.); aleksandar.doderovic@irmbor.co.rs (A.D.);
sasa.stepanovic@irmbor.co.rs (S.S.)
2Faculty of Mining and Geology, University of Belgrade, 11000 Belgrade, Serbia; petar.markovic@rgf.bg.ac.rs
*Correspondence: nikola.stanic@irmbor.co.rs
Abstract: This study presents a unique model for assessing the dependability of continuous parts
of combined systems in open-pit mining through the application of fuzzy logic. Continuous sub-
systems as part of the combined system of coal exploitation in surface mines have the basic function
of ensuring safe operation, high capacity with high reliability, and low costs. These subsystems
are usually part of the thermal power plant’s coal supply system and ensure stable fuel supply.
The model integrates various independent partial indicators of dependability into an expert system
specifically designed for evaluating these systems. It deconstructs the complex parameter of system
dependability into distinct partial indicators: reliability, maintainability, and logistical support. These
indicators are then integrated using fuzzy composition (max-min composition). Historical data
from 2018 to 2023 are utilized alongside the fuzzy model to provide a retrospective analysis of
system dependability, serving to validate the model’s effectiveness. What sets this model apart
from conventional approaches is its consideration of practical dependability indicators, thereby
obviating the need for extensive long-term monitoring and data collection to portray the system’s
status accurately over time. This model serves as a valuable tool for assisting decision-makers in open-
pit mining operations, facilitating planning, exploitation control, and the selection of maintenance
strategies to ensure consistent production and cost reduction. Designed for quick assessment, the
model relies on expert judgments and assessments to determine system dependability efficiently.
Keywords: fuzzy logic; max-min composition; continuous part of combined system (CCS); open pit;
mining; dependability
1. Introduction
Mining operations, crucial to numerous economies worldwide, are undergoing a
transformative phase, marked by heightened environmental concerns, technological ad-
vancements, and a growing emphasis on operational efficiency [
1
,
2
]. These operations
include a wide range of activities, from excavation and material extraction to transportation
and processing. Within the complex structure of mining activities, transport systems are
one of the key components, enabling the smooth movement of materials across large mining
sites [3].
Material transportation is a critical aspect of mining operations, significantly influ-
encing costs, efficiency, safety, and environmental impact [
4
,
5
]. Considering that loading
and transportation costs amount to 60% of the total operating costs, it is essential that
these systems are efficient and reliable [
6
]. The environmental footprint of traditional
diesel-powered transport methods necessitates research into sustainable alternatives such
as electric and autonomous vehicles [
7
,
8
]. Moreover, safety and risk management are
paramount, with advanced technologies such as automation and real-time monitoring offer-
ing new opportunities for optimizing transport routes and enhancing decision-making [
9
].
Appl. Sci. 2024,14, 7947. https://doi.org/10.3390/app14177947 https://www.mdpi.com/journal/applsci
Appl. Sci. 2024,14, 7947 2 of 23
Given the complex and variable conditions of mining environments, tailored solutions are
essential, making continuous research in this area crucial for achieving greater sustainability,
operational excellence, and economic viability in the mining industry.
Various methods and models are used for the purposes of this research in the field of
mining, which provide the possibility of dealing with the complex and changing conditions
of the mining environment. One of the most widely applied mathematical approaches is
the theory of fuzzy sets, which is suitable for the analysis of processes in which uncertainty,
ambiguity, subjectivity, and indeterminacy prevail [10].
The application of this method enables the aforementioned problem to be successfully
analyzed, and the analysis results reflect the previous expert experiences and results of
experimental measurements in a good way. To assess the success of using this method,
prior knowledge of the behavior of the analyzed systems and processes is necessary. By
comparing the experience and experimental data with the analysis results of the fuzzy logic
method, its verification is carried out. Below is an overview of works with the application
of fuzzy logic in mining and similar topics.
The largest number of studies is related to the field of mechanization in mining, where
fuzzy logic was used to evaluate the performance of mining equipment under different
operating conditions. The approach takes into account multiple criteria such as reliability,
efficiency, and maintenance costs [
10
–
16
]. For example, the dependability of bucket wheel
excavators, which are complex hierarchical systems, has been analyzed using fuzzy sets to
synthesize information from the component level to the entire system, applying evident
reasoning theory [
17
]. This mathematical approach has also found application in various
parts of the production process in surface and underground mines, where processes such
as loading, transportation, drilling, and blasting are adequately optimized [
18
–
22
]. The
scientific literature also highlights the pervasive nature of risk in mining operations [
23
–
28
],
emphasizing the need for robust risk management strategies to mitigate the impact of
potential failures, where risk assessment methodologies such as failure mode and effects
analysis (FMEA) and risk priority number (RPN) calculations are used very effectively in
combination with fuzzy logic [
29
]. New approaches for assessing maintenance support
and integrating it into the dependability concept have been developed, with fuzzy algebra
playing a key role in this process. This involves using fuzzy composition to incorporate
maintenance support into dependability, alongside the fuzzification of probability functions
related to reliability and maintainability [
30
]. Fuzzy logic can also be applied to analyze
environmental data collected from mining sites to assess the impact of mining activities
on air and water quality, soil stability, and biodiversity. This information can help in
developing strategies to minimize environmental degradation and comply with regulatory
requirements [31–33].
When it comes to transport systems, the evolution of mining practices has witnessed a
change that has entailed the adoption of continuous haulage systems, marking a departure
from conventional discontinuous methods. While traditional transportation systems that
rely on trucks and loaders still predominate in certain contexts, the advent of continuous
systems ushered in a new era of efficiency and productivity. Continuous conveyor systems,
characterized by crushers, conveyor belts, and integrated automation technologies, offer
countless advantages over discontinuous technologies [
34
]. A fuzzy approach to depend-
ability performance evaluation allows for the analysis of technical systems from multiple
perspectives, including design, construction, maintenance, and logistics. This approach is
particularly useful when available data are limited to expert judgments, as demonstrated
in the dependability analysis of mechanical systems within bucket wheel excavators [35].
Appl. Sci. 2024,14, 7947 3 of 23
Given the evolving challenges of environmental sustainability, safety, and cost op-
timization, the role of continuous transport systems is gaining increasing importance in
mining operations. These systems, characterized by their ability to operate 24/7 without
interruption, offer a path towards sustainable and responsible mining practices. By min-
imizing energy consumption, reducing carbon emissions, and increasing worker safety,
continuous transport systems support transformative changes in the mining industry [4].
Scientific articles in areas of maintainability and reliability engineering are very cur-
rent [16,36–43].
The continuous part of the combined system is used at the coal open pit Gacko,
Republic Srpska, Bosnia and Herzegovina. This paper presents a model that predicts the
dependability of the continuous part of the combined system (CCS system) at the open pit
Gacko applying the fuzzy theory. More precisely, this paper deals with the development of
a model for predicting the dependability of the continuous part of the combined system
at the open pit using the max-min composition. The basic idea of this paper is an expert
assessment of partial indicators that affect the dependability and their synergy in order
to determine the dependability of the CCS systems with the help of fuzzy models. In
addition to the fuzzy model, a historical overview (period 2018–2023) of data related to
the dependability of these systems is given. These historical data served to verify the
fuzzy model.
2. Case Study: Open Pit Gacko, Continuous Parts of the Combined System
The lignite basin Gacko is located in the north-eastern part of Herzegovina, a region
of Bosnia and Herzegovina, and has an area of about 30 km
2
. It is divided into four
exploitation fields: Western, Central, Eastern, and Southern. Coal mining in this basin
began in 1954, with a smaller capacity, and since 1982, with a capacity of 1.8 Mt/year for
the needs of the power plant. Coal production currently takes place with a capacity of
2.3 Mt/year. Exploitation has been completed in West Field, it is currently taking place
in Central and South, and it is planned to continue in East Field. The coal mining system
is combined with hydraulic bucket excavators, with a bucket volume of 4–6 m
3
, truck
transportation to the crusher, with a load capacity of 110 t, and further transport with belt
conveyors. Two continuous systems with rotary excavators with a theoretical capacity of
1600 m
3
/h and suitable belt conveyors and spreaders are engaged in the excavation of
the overburden. In addition to continuous systems, hydraulic excavators, buckets with a
bucket volume of 10–12 m
3
, trucks with a load capacity of 110 t, a crusher with a theoretical
capacity of 2000 m
3
/h, appropriate conveyors, and a spreader within the combined system
are engaged in the excavation of overburden. The geological structure of the deposits and
the great variety of mining equipment make exploitation conditions more complex.
The CCS system (crusher-belt conveyors-landfill) consists of two semi-mobile primary
crushers, SB 1315 and SB 1515, and belt conveyors TU-3, TU-2, TU-1, and PTU. Coal brought
by truck to the SB 1515 crusher is directly shaken onto the same rake, and that brought to
the SB 1315 crusher is deposited at the landfill and dosed to the rake using a loader where,
after crushing and pulverization by the conveyor system, it is handed over to the power
plant. Figure 1shows the position of the CCS system at the open pit Gacko. Figure 2shows
a view of the open pit Gacko.
Appl. Sci. 2024,14, 7947 4 of 23
Appl. Sci. 2024, 14, x FOR PEER REVIEW 4 of 24
Figure 1. View of the CCS system and position of open pit Gacko (Source: Google Earth,
hps://philarcher.org/diary/2013/euromap/, accessed on 10 July 2024).
Figure 2. Gacko open pit (photographed by the author of the article: N.S.).
Figure 1. View of the CCS system and position of open pit Gacko (Source: Google Earth, https:
//philarcher.org/diary/2013/euromap/, accessed on 10 July 2024).
Appl. Sci. 2024, 14, x FOR PEER REVIEW 4 of 24
Figure 1. View of the CCS system and position of open pit Gacko (Source: Google Earth,
hps://philarcher.org/diary/2013/euromap/, accessed on 10 July 2024).
Figure 2. Gacko open pit (photographed by the author of the article: N.S.).
Figure 2. Gacko open pit (photographed by the author of the article: N.S.).
Appl. Sci. 2024,14, 7947 5 of 23
3. Methodology
3.1. Dependability
Dependability is a common term used to describe the availability and factors affecting
reliability, maintainability, and the level of maintainability [
44
,
45
]. The term availability is
commonly used as a measure of operational safety [
44
,
46
]. The availability is expressed in
quantitative indicators and, as such, represents a measure of operational safety and thus
a measure of quality in use [
47
]. The performance of availability has a decisive effect on
operational safety and quality in use due to the well-known fact that the machine should
first of all be available for work, in order to realize the other performances as well [44,47].
Dependability is a complex function that depends on the following performances [
48
]:
•performances of reliability;
•performances of maintainability;
•performances of logistic support for maintenance.
Operational safety: “A collective term used to describe the availability performance
and factors that determine these performances: reliability performances, maintainability
performances, and logistics support performances” [37].
The dependability of technical systems is conceptually stipulated by ISO-IEC stan-
dards [49,50].
3.2. Development Fuzzy Model
The model for determining dependability will be presented through a hierarchical
structure consisting of synthetic and partial indicators. In this sense, dependability (
D
) will
be defined through partial indicators that are classified in the domain of reliability (
R
) and
the domain of maintenance convenience (
M
) and logistical support (
F
), where the specified
domains are synthetic indicators. Partial indicators of dependability are shown in Figure 3
and should include most of the phenomena and influential factors that lead to failure of the
observed system.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 6 of 24
D -Dependability
R -Reliability M -Maintainability F -Logistical support
t -Technological
e -Tools and equipment
u -Unif icatio n
d -Diagnostic
m -Manipulativness
s -Standardization
Figure 3. Presentation of partial indicators of dependability.
In terms of the number of linguistic variables, it can be inferred that seven is the max-
imum count of variables that a person can rationally recognize simultaneously while re-
taining the same meaning [52].
Taking this statement into account, the five ratings (linguistic variables), defined as
follows: excellent (exc), good (good), average (aver), adequate (adeq), and poor (poor),
will be considered in this paper. Linguistic variables (ratings) are given in the form of
triangular fuzzy numbers, and their graphic representation are presented in the following
Figures 4 and 5.
Figure 4. Fuzzy sets.
Corresponding fuzzy numbers of the mentioned linguistic variables are defined by
(according to Figure 6):
Figure 3. Presentation of partial indicators of dependability.
Appl. Sci. 2024,14, 7947 6 of 23
The first step when creating a fuzzy model is the definition of linguistic variables that
refer to the partial indicators of dependability, namely:
Reliability represents the probability, at a certain level of confidence, that the system
(machine) will successfully perform the function for which it is intended, without failure
and within the specified performance limits, taking into account the previous time of
system use, during the specified duration of a task. When it is used in the prescribed
manner and for the purpose for which it is intended, under the specified load levels [11].
Maintainability, as a set of structural characteristics that affect the time to eliminate
failures or the time of performing other maintenance procedures, is an internal property
of the observed technical system; therefore, it is called structural maintainability. The
following parameters affect the maintainability: t—technology, e—tools and equipment,
u—unification, d—diagnostics, m—manipulativeness, s—standardization [11,51].
For the technical system to successfully perform the set tasks, it is necessary to provide
logistical support and numerous conditions. The logistic support combines the manage-
ment process with appropriate technical measures to define the necessary support and
create conditions for the realization of the given function of the technical system goal.
Logistical support performances according to the ISO-IEC Standard are defined as:
“The ability of maintenance system, i.e., the organization that performs maintenance,
to provide under given conditions the required maintenance of the technical system in
accordance with the maintenance policy” [
48
,
49
], the Standards of the IEC 300 series deal
with the concept of logistic support for maintenance [50].
In terms of the number of linguistic variables, it can be inferred that seven is the
maximum count of variables that a person can rationally recognize simultaneously while
retaining the same meaning [52].
Taking this statement into account, the five ratings (linguistic variables), defined as
follows: excellent (exc), good (good), average (aver), adequate (adeq), and poor (poor),
will be considered in this paper. Linguistic variables (ratings) are given in the form of
triangular fuzzy numbers, and their graphic representation are presented in the following
Figures 4and 5.
Corresponding fuzzy numbers of the mentioned linguistic variables are defined by
(according to Figure 6):
µpoor =(1, 0.25, 0, 0, 0),
µadeq =(0.25, 1, 0.25, 0, 0),
µaver =(0, 0.25, 1, 0.25, 0),
µgood =(0, 0, 0.25, 1, 0.25),
µexc =(0, 0, 0, 0.25, 1).
(1)
Appl. Sci. 2024, 14, x FOR PEER REVIEW 6 of 24
D -Dependability
R -Reliability M -Maintainability F -Logistical support
t -Technological
e -Tools and equipment
u -Unif icatio n
d -Diagnostic
m -Manipulativness
s -Standardization
Figure 3. Presentation of partial indicators of dependability.
In terms of the number of linguistic variables, it can be inferred that seven is the max-
imum count of variables that a person can rationally recognize simultaneously while re-
taining the same meaning [52].
Taking this statement into account, the five ratings (linguistic variables), defined as
follows: excellent (exc), good (good), average (aver), adequate (adeq), and poor (poor),
will be considered in this paper. Linguistic variables (ratings) are given in the form of
triangular fuzzy numbers, and their graphic representation are presented in the following
Figures 4 and 5.
Figure 4. Fuzzy sets.
Corresponding fuzzy numbers of the mentioned linguistic variables are defined by
(according to Figure 6):
Figure 4. Fuzzy sets.
Appl. Sci. 2024,14, 7947 7 of 23
Appl. Sci. 2024, 14, x FOR PEER REVIEW 7 of 24
Figure 5. Distribution of output values for indicator M maintainability for the CCS system, Crusher
SB 1515 (a), Crusher SB 1315 (b), and belt conveyors (c) using max-min composition.
Figure 6. Display results for parts of the CCS system.
Figure 5. Distribution of output values for indicator Mmaintainability for the CCS system, Crusher
SB 1515 (a), Crusher SB 1315 (b), and belt conveyors (c) using max-min composition.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 7 of 24
Figure 5. Distribution of output values for indicator M maintainability for the CCS system, Crusher
SB 1515 (a), Crusher SB 1315 (b), and belt conveyors (c) using max-min composition.
Figure 6. Display results for parts of the CCS system.
Figure 6. Display results for parts of the CCS system.
Partial indicators t,e,u,d,m, and smore closely determine the partial indicator
M-maintenance convenience, while M-maintainability together with R-reliability and F-
Appl. Sci. 2024,14, 7947 8 of 23
logistic support determine the D-dependability of the system. It is shown in the following
how the dependability Dis determined based on indicators of maintainability M, reliability
R, and logistical support F, while the maintenance convenience Mis obtained similarly
based on partial indicators t,e,u,d,m, and s.
The idea of this work is to obtain a more accurate assessment of the dependability of
CCS systems at the open pit Gacko. This assessment was identified as the best possible
among the worst expected ratings of the partial availability indicators (R,M, and F).
Let the partial indicators R,M, and Fbe shown in the form of the following triangular
fuzzy numbers
µRµ1
R,µ2
R,µ3
R,µ4
R,µ5
R,µMµ1
M,µ2
M,µ3
M,µ4
M,µ5
M,µFµ1
F,µ2
F,µ3
F,µ4
F,µ5
F. (2)
In the next step, the max-min composition is performed on them. If the mentioned
partial indicators R,M, and Fare observed, it is possible to make
C=
5
3=
125 combinations
of corresponding membership functions, which will be further denoted with
µijk µi
R,µj
M,µk
F),i,j,k∈{1, 2, 3, 4, 5}(3)
Each of these combinations represents one possible assessment of the dependability
and the following two values can be associated with it
Ωijk =[i+j+k]
3(4)
and
mijk =minnµi
R,µj
M,µk
Fo(5)
Ωijk
takes values from the set
{1, 2, 3, 4, 5}
, and each of the mentioned values
can be associated with the number
µl
, which represents the maximum value of
mijk
of all those combinations for which Ωijk is equal to l, za l∈{1, 2, 3, 4, 5}, that is
µl=minnmijk :Ωijk =lo. (6)
In this way, a rating for the dependability of Dis obtained
µ=µ1,µ2,µ3,µ4,µ5(7)
Using the best-fit method, see [
11
], to transform the obtained ratings into belonging to
the fuzzy set, determined by (2), the distance is used that is defined by
di=d(µ,µi)=v
u
u
t
5
∑
j=1µj−µi,j2,µi=(µi,1,µi,2,µi,3,µi,4,µi,5), (8)
For
µi∈nµpoor ,µadeq,µaver,µgood ,µexc o
. Small values
di
indicate proximity to the
linguistic variable
µi
. Accordingly, let
dmin
be the minimum value of the obtained distances
d1
,
d2
,
d3
,
d4
,
d5
, and then the reciprocal value of the relative distances can be associated to
each of them that is determined by:
αi=dmin
di
,i∈{1, 2, 3, 4, 5}. (9)
If for some ithe distance value
di
is equal to 0, then the corresponding value of the
reciprocal value of relative distance is
αi=
1, while the other values of the reciprocal
Appl. Sci. 2024,14, 7947 9 of 23
relative distances are equal to 0. The normalized values of the therefore obtained reciprocal
values of the relative distances are determined by:
βi=αi
α1+α2+α3+α4+α5,i∈{1, 2, 3, 4, 5}(10)
and present belonging to the appropriate rating:
A={(β1, “exc”),(β2, “good”),(β3, “aver”),(β4, “adeq”),(β5, “poor”)}(11)
In the end, the appropriate linguistic rating is obtained as follows:
Z=5β1+4β2+3β3+2β4+1β5
β1+β2+β3+β4+β5(12)
In a similar way, a rating for maintainability Mis obtained from the linguistic variables
t,e,u,d,m, and s, which are later used to determine the dependability D.
Initially, experts were provided with a questionnaire to gather their opinions on
various indicators. These responses were then subjected to statistical analysis, a crucial
step before moving on to the fuzzification process. The fuzzy proposal marks the initial
application of artificial intelligence (AI) by assigning each indicator a corresponding fuzzy
number. Subsequently, using fuzzy composition max–min, fuzzy numbers were determined
for the indicators included in the final model, which are based on the indicators from the
questionnaire. Finally, the grades were identified using appropriate methods, such as the
best fit method.
Results of Expert Evaluation
Determination of the dependability of the system and its partial indicators was pro-
cessed through the results obtained through questionnaires related to the expert evaluation
of the partial indicators of operational safety. The questionnaire contained detailed de-
scriptions of the partial indicators themselves. In the expert evaluation, 10 experts were
surveyed. The first five experts are representatives of the Gacko Mine (experts from this
field with many years of work on these systems-minimum 10 years of work experience),
and the other five experts are external experts with many years of experience in the field
of open pit mining. It is expected that the assessment of internal experts will be formed
considering different and specific working conditions. The inclusion of external experts
was achieved with the intention of reducing subjectivity in the assessment and to use the
experiences in other mines and in other conditions. In this way, it is ensured that the given
ratings reflect both the specific impacts on the Gacko open pit and the general impacts oc-
curring in mining in general. By engaging internal and external experts, a synergetic effect
was obtained, expressed in the given ratings. Ratings are expressed using membership
functions representing predefined linguistic variables ranging from ‘poor’ to ‘excellent’
within a scale of 0 to 1. Additionally, a parameter can be associated with multiple linguistic
variables simultaneously, ensuring that the total sum of ratings equals 1. The following
tables give the results of expert evaluation for each part of the CCS system. The layout of
one questionnaire is given in Appendix A. The results of the expert evaluation for the CCS
system are given in Appendix B.
3.3. Determination the Partial Indicator of Maintainability M
On the basis of the submitted results, the following estimates were obtained as the
arithmetic mean of the corresponding grades for the corresponding sub-indicators for
each analyzed part of the CCS system, shown in Tables A1–A3. Ratings of maintainability
indicators for Crusher SB 1515, Crusher SB 1315, and belt conveyors are shown in Table 1.
Appl. Sci. 2024,14, 7947 10 of 23
Table 1. Ratings of maintainability indicators for Crusher SB 1515, Crusher SB 1315, and belt
conveyors.
Crusher SB 1515 Crusher SB 1315 Belt Conveyors
poor adeq aver good exc poor adeq aver good exc poor adeq aver good exc
t
0.0000 0.2850 0.5250 0.1900 0.0000 0.1300 0.4800 0.3200 0.0700 0.0000 0.0700 0.3550 0.4450 0.1300 0.0000
e
0.0600 0.2550 0.4150 0.2700 0.0000 0.3400 0.4300 0.2000 0.0300 0.0000 0.0800 0.3850 0.4150 0.1200 0.0000
u
0.0000 0.1000 0.4650 0.3750 0.0600 0.0000 0.3600 0.3500 0.2450 0.0450 0.0000 0.1400 0.5300 0.3300 0.0000
d
0.0400 0.1700 0.4400 0.3000 0.0500 0.1200 0.4300 0.3500 0.1000 0.0000 0.0040 0.2200 0.4900 0.2500 0.0000
m
0.0000 0.1700 0.3400 0.3700 0.1200 0.0700 0.3000 0.3300 0.2100 0.0900 0.0070 0.1800 0.2700 0.3700 0.1100
s
0.0000 0.0700 0.4300 0.4450 0.0055 0.0000 0.1700 0.4500 0.3250 0.0550 0.0000 0.0800 0.4300 0.4600 0.0300
Using a linear combination of ratings described by (1), the coefficients of which are
given in the previous table, fuzzy ratings for partial indicators for each part of the system
are obtained. And, in this case, we will demonstrate this process using the example of the
partial indicator tfor the Crusher SB 1515.
µt=0.0000·µpoor +0.2850·µadeq +0.5250·µaver +0.1900·µgood +0.0000·µexc
µt=(0, 0, 0, 0, 0)+(0.0713, 0.285, 0.0713, 0, 0)+(0, 0.1313, 0.525, 0.1313, 0)
+(0, 0, 0.0475, 0.19, 0.0475)+(0, 0, 0, 0, 0)
µt=(0.0713, 0.4163, 0.6438, 0.3213, 0.0475)
Similarly, fuzzy ratings are obtained for other indicators and other parts of the system,
which are shown in Table 2.
Table 2. Final rating for partial indicators t,e,u,d,m, and s, for Crusher SB 1515, Crusher SB 1315,
and belt conveyors in the form of fuzzy number.
Crusher SB 1515 Crusher SB 1315 Belt Conveyors
poor adeq aver good exc poor adeq aver good exc poor adeq aver good exc
t
0.0713 0.4163 0.6438 0.3213 0.0475 0.2500 0.5925 0.4575 0.1500 0.0175 0.1588 0.4838 0.5663 0.2413 0.0325
e
0.1238 0.3738 0.5463 0.3738 0.0675 0.4475 0.5650 0.3150 0.0800 0.0075 0.1763 0.5088 0.5413 0.2238 0.0300
u
0.0250 0.2163 0.5838 0.5063 0.1538 0.0900 0.4475 0.5013 0.3438 0.1063 0.0350 0.2725 0.6475 0.4625 0.0825
d
0.8250 0.2900 0.5575 0.4255 0.1250 0.2275 0.5475 0.4825 0.1875 0.0250 0.0950 0.3525 0.6075 0.3725 0.0625
m
0.0425 0.2550 0.4750 0.4850 0.2125 0.1450 0.4000 0.4575 0.3150 0.1425 0.1150 0.2650 0.4075 0.4650 0.2025
s
0.0175 0.1775 0.5588 0.5663 0.1663 0.0425 0.2825 0.5738 0.4513 0.1363 0.0200 0.1875 0.5650 0.5750 0.1450
On the basis of the obtained ratings in the form of fuzzy numbers, the ratings obtained
using the max-min composition for the specified parts of the system are shown in the
following table.
Using Formulas (3)–(5), the max-min composition values for indicator
M
are obtained
for each part of the system and they are shown in Table 3.
Table 3. Ratings obtained for the partial indicator of maintainability using the max-min composition.
M-Maintainability poor adeq aver good exc
Crusher SB 1515 0.1250 0.4845 0.4850 0.4163 0.0713
Crusher SB 1315 0.0250 0.3150 0.4575 0.4575 0.2275
Belt conveyors 0.0625 0.4650 0.4650 0.4650 0.0950
Appl. Sci. 2024,14, 7947 11 of 23
3.4. Determination of Partial Indicators of Reliability and Logistical Support of Parts of the
Continuous Prats of Combined System R and F
On the basis of the submitted results, the following estimates were obtained for each
analyzed part of the continuous system when these two partial indicators are concerned.
These estimates are shown in the Table 4.
Table 4. Ratings of partial reliability and logistical support for Crusher SB 1515, Crusher SB 1315, and
belt conveyors.
Crusher SB 1515 Crusher SB 1315 Belt Conveyors
poor adeq aver good exc poor adeq aver good exc poor adeq aver good exc
R
0.0700 0.6400 0.2400 0.0500 0.0000 0.2700 0.6200 0.1100 0.0000 0.0000 0.0700 0.6500 0.2400 0.0400 0.0000
F
0.0000 0.0000 0.4200 0.4850 0.0950 0.0000 0.2600 0.3700 0.3250 0.0450 0.0000 0.0000 0.4600 0.5000 0.0400
Using the estimated values for the partial indicators for system maintainability, the
final ratings for the partial indicators R,M, and Ffor Crusher SB 1515, Crusher SB 1315,
and belt conveyors in the fuzzy number form were obtained. These ratings are shown in
the Table 5.
Table 5. Corresponding fuzzy numbers for Crusher SB 1515, Crusher SB 1315, and belt conveyors.
Crusher SB 1515 Crusher SB 1315 Belt Conveyors
poor adeq aver good exc poor adeq aver good exc poor adeq aver good exc
R
0.2300 0.7175 0.4125 0.1100 0.1250 0.4250 0.7150 0.2650 0.0275 0.0000 0.2325 0.7275 0.4125 0.1000 0.0100
M
0.1250 0.4845 0.4850 0.4163 0.0713 0.0250 0.3150 0.4575 0.4575 0.2275 0.0625 0.4650 0.4650 0.4650 0.0950
F
0.0000 0.1050 0.5413 0.6138 0.2163 0.0650 0.3525 0.5163 0.4288 0.1263 0.0000 0.1150 0.5850 0.6250 0.1650
Based on the obtained ratings in the form of fuzzy numbers, the ratings obtained
using the max-min composition for the specified parts of the CCS system are shown in the
following table. These ratings are shown in the Table 6. The distribution of output values is
also shown graphically in the Figure 7.
Table 6. Obtained ratings for dependability using the max-min composition.
D-Dependability poor adeq aver good exc
Crusher SB 1515 0.0713 0.4125 0.4850 0.4850 0.1050
Crusher SB 1315 0.0275 0.2650 0.3033 0.3033 0.2478
Belt conveyors 0.0950 0.4125 0.4650 0.4650 0.6250
3.5. Dependability of the CCS System at the Open Pit Gacko
On the basis of the obtained ratings for dependability of the system parts, the overall
rating of dependability was obtained using the max-min composition and reads as follows
(Their distribution is shown in Figure 8and also the results in Figure 9):
(0.07125, 0.30333, 0.30333, 0.30333, 0.105).
Further analysis shows that the corresponding values obtained by the best fit method,
by (8), are equal to:
d1=q(0.071 −1)2+(0.303 −0.25)2+(0.303 −0)2+(0.303 −0)2+(0.105 −0)2=1.02977
d2=q(0.071 −0.25)2+(0.303 −1)2+(0.303 −0.25)2+(0.303 −0)2+(0.105 −0)2=0.78942
d3=q(0.071 −0)2+(0.303 −0.25)2+(0.303 −1)2+(0.303 −0.25)2+(0.105 −0)2=0.71215
Appl. Sci. 2024,14, 7947 12 of 23
d4=q(0.071 −0)2+(0.303 −0)2+(0.303 −0.25)2+(0.303 −1)2+(0.105 −0.25)2=0.77866
d5=q(0.071 −0)2+(0.303 −0)2+(0.303 −0)2+(0.303 −0.25)2+(0.105 −1)2=0.99645
So, we have
(d1,d2,d3,d4,d5) = (1.02977, 0.78942, 0.71215, 0.77866, 0.99645).
Note that dmin =d3=0.71215, so the corresponding reciprocal values of the relative
distances αi, as described in (9), are:
(α1,α2,α3,α4,α5)= (0.69156, 0.90211, 1, 0.91458, 0.71468).
Appl. Sci. 2024, 14, x FOR PEER REVIEW 12 of 24
Figure 7. Distribution of output values for D dependability for the CCS system, Crusher SB 1515 (a),
Crusher SB 1315 (b), and belt conveyors (c) using max-min composition.
3.5. Dependability of the CCS System at the Open Pit Gacko
On the basis of the obtained ratings for dependability of the system parts, the overall
rating of dependability was obtained using the max-min composition and reads as follows
(Their distribution is shown in Figure 8 and also the results in Figure 9):
(0.07125, 0.30333, 0.30333, 0.30333, 0.105).
Further analysis shows that the corresponding values obtained by the best fit method,
by (8), are equal to:
𝑑=
(0.071−1)+(0.303−0.25)+(0.303−0)+(0.303−0)+(0.105−0)=1.02977
𝑑=
(0.071−0.25)+(0.303−1)+(0.303−0.25)+(0.303−0)+(0.105−0)=0.78942
Figure 7. Distribution of output values for D dependability for the CCS system, Crusher SB 1515 (a),
Crusher SB 1315 (b), and belt conveyors (c) using max-min composition.
Appl. Sci. 2024,14, 7947 13 of 23
Appl. Sci. 2024, 14, x FOR PEER REVIEW 13 of 24
𝑑=
(0.071−0)+(0.303−0.25)+(0.303−1)+(0.303−0.25)+(0.105−0)=0.71215
𝑑=
(0.071−0)+(0.303−0)+(0.303−0.25)+(0.303−1)+(0.105−0.25)=0.77866
𝑑=
(0.071−0)+(0.303−0)+(0.303−0)+(0.303−0.25)+(0.105−1)=0.99645
So, we have
(𝑑, 𝑑, 𝑑, 𝑑, 𝑑) = (1.02977, 0.78942, 0.71215, 0.77866, 0.99645).
Note that 𝑑 = 𝑑= 0.71215, so the corresponding reciprocal values of the rela-
tive distances 𝛼, as described in (9), are:
(𝛼,𝛼,𝛼,𝛼,𝛼) = (0.69156, 0.90211, 1, 0.91458, 0.71468).
The values of normalized reciprocal values 𝛽, described in (10), are equal to:
𝛽=0.69156
0.69156+0.90211+1+0.91458+0.71468=0.16376
𝛽=0.90211
0.69156+0.90211+1+0.91458+0.71468=0.21362
𝛽=1
0.69156+0.90211+1+0.91458+0.71468=0.23680
𝛽=0.91458
0.69156+0.90211+1+0.91458+0.71468=0.21657
𝛽=0.71468
0.69156+0.90211+1+0.91458+0.71468=0.16923
Appropriate linguistic evaluation
𝑍=5𝛽+4𝛽+3𝛽+2𝛽+1𝛽
𝛽+𝛽+𝛽+𝛽+𝛽 = 2.9860.
On a scale of 1–5, the mentioned system in operation has a center of gravity of lin-
guistic assessment for the max-min composition of 2.9860. Dependability is 59%.
Figure 8. Distribution of output values for D dependability for the CCS system using max-min com-
position.
Figure 8. Distribution of output values for D dependability for the CCS system using max-min
composition.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 14 of 24
Figure 9. Display results for CCS system.
One of the ways to determine the dispersion that occurs in the output result is the
standard deviation, which is calculated according to the formula:
𝑆=∑(𝛽−𝛽)
𝑁−1 (13)
where 𝑁-is the number of grades, and 𝛽 is the mean value of values 𝛽, 𝛽, 𝛽,
𝛽, and 𝛽. In the case of max-min composition, the value of the standard deviation is:
S=(0.16376−0.19)+(0.21362−0.19)+(0.23680−0.19)+(0.21657−0.19)+(0.16923−0.19)
5−1
S=
√
0.0020=0.0458
In a similar way, dispersions and Z (center of gravity of linguistic assessment) values
can be obtained for each part of the system separately. The obtained values are shown in
the following Table 7.
Table 7. Dispersions and Z (center of gravity of linguistic assessment) values for parts of the system.
SB 1515 SB 1315 Belt Conveyors
Z 2.9753 2.8754 2.7372
S 0.0599 0.0278 0.0463
If the final Z score was calculated as a linear combination of Z scores for each part of
the system with coefficients corresponding to the participation of the corresponding dis-
persion, the following value would be obtained.
𝑍= 0.0599
0.0599+0.0278+0.0463× 2.9753 + 0.0278
0.0599+0.0278+0.0463× 2.8754
+0.0463
0.0599+0.0278+0.0463× 2.7372= 2.8723
On a scale of 1–5, the mentioned system in operation has a center of gravity of lin-
guistic assessment for the max-min composition of 2.8723. The corresponding dependa-
bility in this case is 57%.
0.000
0.100
0.200
0.300
0.400 1
2
34
5
CCS system
Figure 9. Display results for CCS system.
The values of normalized reciprocal values βi, described in (10), are equal to:
β1=0.69156
0.69156 +0.90211 +1+0.91458 +0.71468 =0.16376
β2=0.90211
0.69156 +0.90211 +1+0.91458 +0.71468 =0.21362
β3=1
0.69156 +0.90211 +1+0.91458 +0.71468 =0.23680
β4=0.91458
0.69156 +0.90211 +1+0.91458 +0.71468 =0.21657
β5=0.71468
0.69156 +0.90211 +1+0.91458 +0.71468 =0.16923
Appropriate linguistic evaluation
Z=5β1+4β2+3β3+2β4+1β5
β1+β2+β3+β4+β5=2.9860.
On a scale of 1–5, the mentioned system in operation has a center of gravity of linguistic
assessment for the max-min composition of 2.9860. Dependability is 59%.
Appl. Sci. 2024,14, 7947 14 of 23
One of the ways to determine the dispersion that occurs in the output result is the
standard deviation, which is calculated according to the formula:
S=s∑N
i=1(βi−βmean )2
N−1(13)
where
N
-is the number of grades, and
βmean
is the mean value of values
β1
,
β2
,
β3
,
β4
, and
β5. In the case of max-min composition, the value of the standard deviation is:
S2=(0.16376 −0.19)2+(0.21362 −0.19)2+(0.23680 −0.19)2+(0.21657 −0.19)2+(0.16923 −0.19)2
5−1
S=√0.0020 =0.0458
In a similar way, dispersions and Z (center of gravity of linguistic assessment) values
can be obtained for each part of the system separately. The obtained values are shown in
the following Table 7.
Table 7. Dispersions and Z(center of gravity of linguistic assessment) values for parts of the system.
SB 1515 SB 1315 Belt Conveyors
Z2.9753 2.8754 2.7372
S0.0599 0.0278 0.0463
If the final Zscore was calculated as a linear combination of Zscores for each part
of the system with coefficients corresponding to the participation of the corresponding
dispersion, the following value would be obtained.
Z=0.0599
0.0599+0.0278+0.0463 ×2.9753 +0.0278
0.0599+0.0278+0.0463 ×2.8754
+0.0463
0.0599+0.0278+0.0463 ×2.7372 =2.8723
On a scale of 1–5, the mentioned system in operation has a center of gravity of linguistic
assessment for the max-min composition of 2.8723. The corresponding dependability in
this case is 57%.
The grade obtained in this way is approximate to the value using the max-min com-
position of the system parts, but unlike it, this one also includes information about the
dispersions of the system parts grades.
4. Verification of Fuzzy Model
The verification model is based on the results of systematic monitoring of the work of
the continuous part of the combined system, which is carried out by a specially designated
service within Gacko Mine and Thermal Power Plant. The data were collected in order
to prepare a special expertise of the condition of the surface mines of Mixed Holding
Power Utility of Republic of Srpska, jointly verified by the investor and the designers. The
performed verification gives a high degree of reliability to the data used in this article.
The effective system operating time represents the total operating time in the observed
period and is calculated by subtracting the total downtime (failures) from the calendar
fund. The operation of each system is accompanied by certain failures that have a direct
impact on the utilization and reliability of the system. These failures can be planned or
unplanned. Planned downtime refers to predefined technological operations and regular
service maintenance. Unplanned failures are unpredictable and are not an integral part of
the system’s working hours. The department in charge of monitoring the operation of the
analyzed system keeps records that include the beginning, duration, and type of failures.
These records are maintained on a shift or daily basis, and an official monthly report is
issued on the operation of the system as a whole, including the continuous part.
Appl. Sci. 2024,14, 7947 15 of 23
Failures are categorized into the following groups:
•technological failures;
•electrical failures;
•mechanical failures;
•shift of workers;
•equipment overhaul;
•daily review;
•weather conditions.
The following Figure 10 shows the percentage participation by types of failures for the
CCS system by year.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 15 of 24
The grade obtained in this way is approximate to the value using the max-min com-
position of the system parts, but unlike it, this one also includes information about the
dispersions of the system parts grades.
4. Verification of Fuzzy Model
The verification model is based on the results of systematic monitoring of the work
of the continuous part of the combined system, which is carried out by a specially desig-
nated service within Gacko Mine and Thermal Power Plant. The data were collected in
order to prepare a special expertise of the condition of the surface mines of Mixed Holding
Power Utility of Republic of Srpska, jointly verified by the investor and the designers. The
performed verification gives a high degree of reliability to the data used in this article.
The effective system operating time represents the total operating time in the ob-
served period and is calculated by subtracting the total downtime (failures) from the cal-
endar fund. The operation of each system is accompanied by certain failures that have a
direct impact on the utilization and reliability of the system. These failures can be planned
or unplanned. Planned downtime refers to predefined technological operations and reg-
ular service maintenance. Unplanned failures are unpredictable and are not an integral
part of the system’s working hours. The department in charge of monitoring the operation
of the analyzed system keeps records that include the beginning, duration, and type of
failures. These records are maintained on a shift or daily basis, and an official monthly
report is issued on the operation of the system as a whole, including the continuous part.
Failures are categorized into the following groups:
• technological failures;
• electrical failures;
• mechanical failures;
• shift of workers;
• equipment overhaul;
• daily review;
• weather conditions.
The following Figure 10 shows the percentage participation by types of failures for
the CCS system by year.
Figure 10. The percentage of failures of the CCS system in the period 2018–2023.
This graph shows the percentage participation of different types of failures in the
operation of the CCS system in the period from 2018 to 2023. The key indicators of the
graph are as follows:
Figure 10. The percentage of failures of the CCS system in the period 2018–2023.
This graph shows the percentage participation of different types of failures in the
operation of the CCS system in the period from 2018 to 2023. The key indicators of the
graph are as follows:
•
Technological failures are consistently high and vary from 20.1% to 33.4% per year,
which accounts for the largest part of total downtime (29% for a period of 6 years).
•
Shift of workers and equipment overhaul are also significant downtime factors, with
overall percentages of 23% and 22%.
•
Electrical failures and mechanical failures have a relatively smaller share, but show
variations between years.
•
Weather conditions have the least participation in total downtime (0.5% for a period of
6 years).
•
Daily review varies by year, but records a significant participation of 17% for the entire
observed period.
Overall data show that technological failures, the shifts of workers, and equipment
overhaul are the most dominant factors in the operation of the CCS system, while weather
conditions are the least significant.
The dependability of the CCS system in the period 2018–2023 is shown in the following
figure (Figure 11).
Data on the dependability of the CCS system in percentages for the period from 2018
to 2023 show slight variations. In 2018 and 2020, the system had the highest dependability
of 55%. In 2019, dependability was the lowest, at 46%. This was the result of a significant
percentage of failures related to the daily inspection of equipment, which was significantly
higher in 2019 compared to all other years. In 2021 and 2022, dependability was stable at
53%, while 2023 saw a slight drop to 51%. Overall, system dependability varied between
Appl. Sci. 2024,14, 7947 16 of 23
46% and 55% over the observed period. The average value of dependability for the period
of 6 years was 52.16%.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 16 of 24
• Technological failures are consistently high and vary from 20.1% to 33.4% per year,
which accounts for the largest part of total downtime (29% for a period of 6 years).
• Shift of workers and equipment overhaul are also significant downtime factors, with
overall percentages of 23% and 22%.
• Electrical failures and mechanical failures have a relatively smaller share, but show
variations between years.
• Weather conditions have the least participation in total downtime (0.5% for a period
of 6 years).
• Daily review varies by year, but records a significant participation of 17% for the en-
tire observed period.
Overall data show that technological failures, the shifts of workers, and equipment
overhaul are the most dominant factors in the operation of the CCS system, while weather
conditions are the least significant.
The dependability of the CCS system in the period 2018–2023 is shown in the follow-
ing figure (Figure 11).
Figure 11. The dependability of the continuous part of the CCS system in the period 2018–2023.
Data on the dependability of the CCS system in percentages for the period from 2018
to 2023 show slight variations. In 2018 and 2020, the system had the highest dependability
of 55%. In 2019, dependability was the lowest, at 46%. This was the result of a significant
percentage of failures related to the daily inspection of equipment, which was significantly
higher in 2019 compared to all other years. In 2021 and 2022, dependability was stable at
53%, while 2023 saw a slight drop to 51%. Overall, system dependability varied between
46% and 55% over the observed period. The average value of dependability for the period
of 6 years was 52.16%.
5. Discussion and Conclusions
In order to develop a model for determining the dependability of complex technical
systems in mining, a combination of several research methods was necessary, such as a
statistical analysis method, a conventional method for calculating dependability, and
methods based on the application of fuzzy logic. These methods do not limit the use of
some others. The goal is for them to show a match with historical data in their results.
The main goal of the research in this paper is to identify important parameters that
affect the dependability of these technical systems and to synthesize these indicators and
determine dependability by applying fuzzy logic. The initial basis of the model is repre-
sented by expert evaluations obtained by a survey that combines the evaluation of the
Figure 11. The dependability of the continuous part of the CCS system in the period 2018–2023.
5. Discussion and Conclusions
In order to develop a model for determining the dependability of complex technical
systems in mining, a combination of several research methods was necessary, such as
a statistical analysis method, a conventional method for calculating dependability, and
methods based on the application of fuzzy logic. These methods do not limit the use of
some others. The goal is for them to show a match with historical data in their results.
The main goal of the research in this paper is to identify important parameters that
affect the dependability of these technical systems and to synthesize these indicators and
determine dependability by applying fuzzy logic. The initial basis of the model is repre-
sented by expert evaluations obtained by a survey that combines the evaluation of the
dependability as a whole as well as the evaluation of individual parts of the system. Synthe-
sis assessment allows the behavior of the production system to be described with a relevant
assessment even when not all its elements are known. In this way, a relatively quick assess-
ment is possible by applying the presented model in the function of production planning,
maintenance system planning, and evaluation of exploitation effects, where the assessment
depends on important indicators assessed by experts, for a complex technological system
and in complex exploitation conditions. This is proven by the presented model verification
by comparison with historical data. Once the model is set, it no longer requires a lengthy
analysis of a large set of historical data. The model itself can be improved over time by
taking into account additional indicators that turn out to have a significant impact. This
model will improve the operation of the CCS system and indicate a possible reduction in
maintenance costs and coal exploitation costs.
The presented model contributes to the assessment, understanding, and optimization
of the dependability of the CCS system in surface coal mines. This model was developed
using the example of the Gacko open pit, but it is also applicable to other open pits and
can be especially significant for open pits where very different mining equipment is used,
which requires specific types of maintenance and reacts differently to external influences.
Therefore, it can be expected that the presented model can be successfully applied in cases
where the mining equipment is unified to a greater extent and in different geological or
climatic conditions. The model presented in this paper can be applied in other areas of the
industry where similar production systems are applied.
This paper presents a model for evaluating the dependability of technical systems
using fuzzy logic. It breaks down dependability into different indicators and combines
them using the max-min composition method.
Appl. Sci. 2024,14, 7947 17 of 23
Unlike conventional models that rely on IT monitoring systems, this approach incor-
porates expert assessments from individuals directly involved in machine operation and
maintenance. Its simplicity and reliance on expert judgment make it easy to implement
without extensive data collection.
This model offers a fast way to assess system safety and provides valuable insights for
enhancing specific indicators and overall dependability. By following the model’s recom-
mendations, companies can streamline maintenance activities, analyze workflows, pinpoint
weaknesses, and optimize the lifecycles of machinery to lower operational expenses.
Field experience confirms that the model accurately reflects the dependability of
analyzed systems, considering factors such as system components, structure, age, working
conditions, and organizational influences. When comparing the reliability data obtained
through the fuzzy logic model with the actual field data collected over the period from
2018 to 2023, there is a strong correlation. The dependability obtained by two different
methods using the model are 59% and 57%, and based on historical data for a period of
6 years, the average value of dependability is 52.6%. This consistency underscores the
model’s effectiveness in capturing the real-world performance and dependability of the
CCS systems.
Moreover, the historical data’s alignment with the model’s output validates the use of
fuzzy logic in predicting and improving dependability. This approach not only facilitates
proactive maintenance and risk management but also supports strategic decision-making
by providing a sophisticated understanding of system vulnerabilities. The adaptability
of the model to different mining contexts and its reliance on expert knowledge further
enhance its practicality and robustness. Ultimately, this model serves as a valuable tool for
mining companies aiming to achieve greater sustainability, efficiency, and cost-effectiveness
in their operations.
Future research could explore the further refinement of this model by integrating
it with advanced data analytics and machine learning techniques to enhance predictive
accuracy and adaptability. Additionally, expanding the application of this model to other
industries beyond mining could reveal broader insights and benefits, establishing it as a
versatile tool for dependability assessment across various sectors. The continued evolution
and validation of this model will ensure its relevance and efficacy in the ever-changing
landscape of technical system management.
Author Contributions: Conceptualization, N.S. and M.G.; methodology N.S., M.G. and P.M.; Writing—
review and editing N.S., P.M., D.K., A.D. and M.G., supervision S.S., N.S. and M.G. All authors have
read and agreed to the published version of the manuscript.
Funding: This work was financially supported by the Ministry of Science, Technological Development
and Innovation of the Republic of Serbia, Contract on realization and financing the scientific research
work of the Mining and Metallurgy Institute Bor in 2024, Contract No.: 451-03-66/2024-03/200052.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The original contributions presented in the study are included in the
article, further inquiries can be directed to the corresponding author.
Acknowledgments: Gratitude to Ministry of Science, Technological Development and Innovation of
the Republic of Serbia; Mining and Metallurgy Institute Bor, Zeleni bulevar 35, Bor; Gacko Mine and
Thermal Power Plant.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
Layout of questionnaire
Appl. Sci. 2024,14, 7947 18 of 23
Appl. Sci. 2024, 14, x FOR PEER REVIEW 19 of 24
Appendix B
Tab le A1 . Results of expert evaluation for Crusher SB 1515.
Expert Type poor adeq aver good exc Expert Type poor adeq aver good exc
1
R 0 0.5 0.5 0 0
6
R 0 0 0 0.6 0.4
t 0 0.2 0.8 0 0 t 0 0.4 0.6 0 0
e 0 0.6 0.4 0 0 e 0 0.2 0.8 0 0
u 0.2 0.8 0 0 0 u 0 0.1 0.9 0 0
d 0 0.5 0.5 0 0 d 0 0.4 0.6 0 0
m 0 0.3 0.7 0 0 m 0 0.3 0.7 0 0
s 0 0.1 0.9 0 0 s 0 0.7 0.3 0 0
F 0.4 0.6 0 0 0 F 0.2 0.8 0 0 0
2
R 0 0 0.3 0.7 0
7
R 0 0 0.3 0.7 0
t 0 0 0.35 0.65 0 t 0 0 0.2 0.8 0
e 0 0 0.2 0.8 0 e 0 0 0 0.4 0.6
u 0 0 0.6 0.4 0 u 0 0.4 0.6 0 0
d 0.2 0.8 0 0 0 d 0 0 0 0.6 0.4
Appendix B
Table A1. Results of expert evaluation for Crusher SB 1515.
Expert
Type poor adeq aver good exc
Expert
Type poor adeq aver good exc
1
R0 0.5 0.5 0 0
6
R0 0 0 0.6 0.4
t0 0.2 0.8 0 0 t0 0.4 0.6 0 0
e0 0.6 0.4 0 0 e0 0.2 0.8 0 0
u0.2 0.8 0 0 0 u0 0.1 0.9 0 0
d0 0.5 0.5 0 0 d0 0.4 0.6 0 0
m0 0.3 0.7 0 0 m0 0.3 0.7 0 0
s0 0.1 0.9 0 0 s0 0.7 0.3 0 0
F0.4 0.6 0 0 0 F0.2 0.8 0 0 0
Appl. Sci. 2024,14, 7947 19 of 23
Table A1. Cont.
Expert
Type poor adeq aver good exc
Expert
Type poor adeq aver good exc
2
R0 0 0.3 0.7 0
7
R0 0 0.3 0.7 0
t0 0 0.35 0.65 0 t0 0 0.2 0.8 0
e0 0 0.2 0.8 0 e0 0 0 0.4 0.6
u0 0 0.6 0.4 0 u0 0.4 0.6 0 0
d0.2 0.8 0 0 0 d0 0 0 0.6 0.4
m0.5 0.5 0 0 0 m0 0 0.2 0.8 0
s0 0.7 0.3 0 0 s0 0 0.3 0.7 0
F0 0.3 0.7 0 0 F0 0.4 0.6 0 0
3
R0 0 0.3 0.7 0
8
R0 0 0 0.8 0.2
t0 0 0.4 0.6 0 t0 0.4 0.6 0 0
e0 0 0.45 0.55 0 e0 0.3 0.7 0 0
u0 0.25 0.75 0 0 u0 0.6 0.4 0 0
d0 0.1 0.9 0 0 d0 0 0.2 0.8 0
m0.4 0.6 0 0 0 m0 0 0.7 0.3 0
s0 0.6 0.4 0 0 s0 0.4 0.6 0 0
F0 0.3 0.7 0 0 F0 0.1 0.9 0 0
4
R0 0 0.1 0.9 0
9
R0 0 0 0.9 0.1
t0 0 0.2 0.8 0 t0 0.3 0.7 0 0
e0 0.5 0.5 0 0 e0 0 0.2 0.8 0
u0.4 0.6 0 0 0 u0 0 0.4 0.6 0
d0 0.4 0.6 0 0 d0 0 0.2 0.8 0
m0.3 0.7 0 0 0 m0 0 0.7 0.3 0
s0.25 0.75 0 0 0 s0 0.3 0.7 0 0
F0.15 0.85 0 0 0 F0.2 0.8 0 0 0
5
R0 0 0.3 0.7 0
10
R0 0 0.6 0.4 0
t0 0.3 0.7 0 0 t0 0.3 0.7 0 0
e0 0.7 0.3 0 0 e0 0.4 0.6 0 0
u0 0.4 0.6 0 0 u0 0.6 0.4 0 0
d0.3 0.7 0 0 0 d0 0.1 0.9 0 0
m0 0.6 0.4 0 0 m0 0.7 0.3 0 0
s0.3 0.7 0 0 0 s0 0.2 0.8 0 0
F0 0.3 0.7 0 0 F0 0.4 0.6 0 0
Appl. Sci. 2024,14, 7947 20 of 23
Table A2. Results of expert evaluation for Crusher SB 1315.
Expert
Type poor adeq aver good exc
Expert
Type poor adeq aver good exc
1
R0 0 0 0.6 0.4
6
R0 0 0 0.6 0.4
t0 0 0.2 0.8 0 t0 0.4 0.6 0 0
e0 0 0 0.7 0.3 e0 0.2 0.8 0 0
u0.45 0.55 0 0 0 u0 0.1 0.9 0 0
d0 0 0.1 0.9 0 d0 0.4 0.6 0 0
m0 0.3 0.7 0 0 m0 0.3 0.7 0 0
s0 0.2 0.8 0 0 s0 0.7 0.3 0 0
F0 0 0.4 0.6 0 F0.2 0.8 0 0 0
2
R0 0 0.3 0.7 0
7
R0 0 0.3 0.7 0
t0 0 0 0.3 0.7 t0 0 0.2 0.8 0
e0 0 0 0.4 0.6 e0 0 0 0.4 0.6
u0 0 0.2 0.8 0 u0 0.4 0.6 0 0
d0 0 0.4 0.6 0 d0 0 0 0.6 0.4
m0.5 0.5 0 0 0 m0 0 0.2 0.8 0
s0 0 0.8 0.2 0 s0 0 0.3 0.7 0
F0 0 0.2 0.8 0 F0 0.4 0.6 0 0
3
R0 0 0.3 0.7 0
8
R0 0 0 0.8 0.2
t0 0 0.4 0.6 0 t0 0.4 0.6 0 0
e0 0 0.45 0.55 0 e0 0.3 0.7 0 0
u0 0.25 0.75 0 0 u0 0.6 0.4 0 0
d0 0.1 0.9 0 0 d0 0 0.2 0.8 0
m0.4 0.6 0 0 0 m0 0 0.7 0.3 0
s0 0.6 0.4 0 0 s0 0.4 0.6 0 0
F0 0.3 0.7 0 0 F0 0.1 0.9 0 0
4
R0 0 0.1 0.9 0
9
R0 0 0 0.9 0.1
t0 0 0.2 0.8 0 t0 0.3 0.7 0 0
e0 0.5 0.5 0 0 e0 0 0.2 0.8 0
u0.4 0.6 0 0 0 u0 0 0.4 0.6 0
d0 0.4 0.6 0 0 d0 0 0.7 0.3 0
m0.3 0.7 0 0 0 m0 0 0.4 0.6 0
s0.25 0.75 0 0 0 s0 0.3 0.7 0 0
F0.15 0.85 0 0 0 F0.2 0.8 0 0 0
5
R0 0 0.3 0.7 0
10
R0 0 0.6 0.4 0
t0 0.3 0.7 0 0 t0 0.3 0.7 0 0
e0 0.7 0.3 0 0 e0 0.4 0.6 0 0
u0 0.4 0.6 0 0 u0 0.6 0.4 0 0
d0.3 0.7 0 0 0 d0 0.1 0.9 0 0
m0 0.6 0.4 0 0 m0 0.7 0.3 0 0
s0.3 0.7 0 0 0 s0 0.2 0.8 0 0
F0 0.3 0.7 0 0 F0 0.4 0.6 0 0
Appl. Sci. 2024,14, 7947 21 of 23
Table A3. Results of expert evaluation for belt conveyors.
Expert
Type poor adeq aver good exc
Expert
Type poor adeq aver good exc
1
R0 0.5 0.5 0 0
6
R0 0 0 0.6 0.4
t0 0.2 0.8 0 0 t0 0.4 0.6 0 0
e0 0.6 0.4 0 0 e0 0.2 0.8 0 0
u0.2 0.8 0 0 0 u0 0.1 0.9 0 0
d0 0.5 0.5 0 0 d0 0.4 0.6 0 0
m0 0.3 0.7 0 0 m0 0.3 0.7 0 0
s0 0.1 0.9 0 0 s0 0.7 0.3 0 0
F0.4 0.6 0 0 0 F0.2 0.8 0 0 0
2
R0 0 0.3 0.7 0
7
R0 0 0.3 0.7 0
t0 0 0.35 0.65 0 t0 0 0.2 0.8 0
e0 0 0.2 0.8 0 e0 0 0 0.4 0.6
u0 0 0.6 0.4 0 u0 0.4 0.6 0 0
d0.2 0.8 0 0 0 d0 0 0 0.6 0.4
m0.5 0.5 0 0 0 m0 0 0.2 0.8 0
s0 0.7 0.3 0 0 s0 0 0.3 0.7 0
F0 0.3 0.7 0 0 F0 0.4 0.6 0 0
3
R0 0 0.3 0.7 0
8
R0 0 0 0.8 0.2
t0 0 0.4 0.6 0 t0 0.4 0.6 0 0
e0 0 0.45 0.55 0 e0 0.3 0.7 0 0
u0 0.25 0.75 0 0 u0 0.6 0.4 0 0
d0 0.1 0.9 0 0 d0 0 0.2 0.8 0
m0.4 0.6 0 0 0 m0 0 0.7 0.3 0
s0 0.6 0.4 0 0 s0 0.4 0.6 0 0
F0 0.3 0.7 0 0 F0 0.1 0.9 0 0
4
R0 0 0.1 0.9 0
9
R0 0 0 0.9 0.1
t0 0 0.2 0.8 0 t0 0.3 0.7 0 0
e0 0.5 0.5 0 0 e0 0 0.2 0.8 0
u0.4 0.6 0 0 0 u0 0 0.4 0.6 0
d0 0.4 0.6 0 0 d0 0 0.7 0.3 0
m0.3 0.7 0 0 0 m0 0 0.4 0.6 0
s0.25 0.75 0 0 0 s0 0.3 0.7 0 0
F0.15 0.85 0 0 0 F0.2 0.8 0 0 0
5
R0 0 0.3 0.7 0
10
R0 0 0.6 0.4 0
t0 0.3 0.7 0 0 t0 0.3 0.7 0 0
e0 0.7 0.3 0 0 e0 0.4 0.6 0 0
u0 0.4 0.6 0 0 u0 0.6 0.4 0 0
d0.3 0.7 0 0 0 d0 0.1 0.9 0 0
m0 0.6 0.4 0 0 m0 0.7 0.3 0 0
s0.3 0.7 0 0 0 s0 0.2 0.8 0 0
F0 0.3 0.7 0 0 F0 0.4 0.6 0 0
Appl. Sci. 2024,14, 7947 22 of 23
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