A Model for Determining the Dependability of Continuous Subsystems in Coal Mines Using the Fuzzy Logic Approach

1. Introduction

Mining operations, crucial to numerous economies worldwide, are undergoing a transformative phase, marked by heightened environmental concerns, technological advancements, 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 influencing 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 like electric and autonomous vehicles [7,8]. Moreover, safety and risk management are paramount, with advanced technologies such as automation and real-time monitoring offering new opportunities for optimizing transport routes and enhancing decision-making [9]. 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 works 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 [10,11,12,13,14]. 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 [15,16,17,18,19]. The scientific literature also highlights the pervasive nature of risk in mining operations [20,21,22,23,24], 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 [25]. 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 [26,27,28].

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 [29].

Given the evolving challenges of environmental sustainability, safety and cost optimization, 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 minimizing energy consumption, reducing carbon emissions and increasing worker safety, continuous transport systems support transformative changes in the mining industry [30].

The continuous part of the combined system is used at the coal open pit Gacko, Republic Srpska. 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. Continuous Parts of the Combined System

The CCS system (crusher - belt conveyors - landfill) consists of two semi-mobile primary crushers SB 1315 and SB 1515, 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 power plant. Figure 1 shows a view of the open pit Gacko. Figure 2 shows the position of the CCS system at the open pit Gacko.

3. Dependability

Dependability is a common term used to describe the availability and factors affecting it: reliability, maintainability, and level of maintainability [31,32]. The term availability is commonly used as a measure of operational safety [31,33]. The availability is expressed in quantitative indicators, and as such represents a measure of operational safety and thus a measure of quality in use [34]. 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 [31,34].

Dependability is a complex function that depends on the following performances [35]:

• 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" [35]

The dependability of technical systems is conceptually stipulated by ISO-IEC standards [36,37].

4. Materials and Methods

4.1. Development Fuzzy Model

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 [11,38].

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 management 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 [35,36] the Standards of the IEC 300 series deal with the concept of logistic support for maintenance [37].

Figure 5. Presentation of partial indicators of dependability.

Figure 5. Presentation of partial indicators of dependability.

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 [39].

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 is presented in the following figure.

Corresponding fuzzy numbers of the mentioned linguistic variables are defined by (according to Figure 6):

$${\mu }_{poor}=\left(1,0.25,0,0,0\right),$$

$${\mu }_{adeq}=\left(0.25,1,0.25,0,0\right),$$

$${\mu }_{aver}=\left(0,0.25,1,0.25,0\right),$$

(1)

$${\mu }_{good}=\left(0,0,0.25,1,0.25\right),$$

$${\mu }_{exc}=\left(0,0,0,0.25,1\right).$$

Partial indicators t, e, u, d, m, s more closely determines the partial indicator M- maintenance convenience, while M – maintainability together with R-reliability and F- logistic support determine the D- dependability of the system. It will be shown in the following how the dependability D is determined based on indicators of maintainability M, reliability R and logistical support F, while the maintenance convenience M is obtained similarly based on partial indicators t, e, u, d, m, 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, F be shown in the form of the following triangular fuzzy numbers

$${\mu }_R\left({\mu }_R^1,{\mu }_R^2,{\mu }_{R,}^3{\mu }_R^4,{\mu }_R^5\right),{\mu }_M\left({\mu }_M^1,{\mu }_M^2,{\mu }_{M,}^3{\mu }_M^4,{\mu }_M^5\right), { \mu }_F\left({\mu }_F^1,{\mu }_F^2,{\mu }_{F,}^3{\mu }_F^4,{\mu }_F^5\right).$$

(2)

In the next step, the max-min composition is performed on them. If the mentioned partial indicators R, M, F are observed, it is possible to make $C=5^3=125$ combinations of corresponding membership functions, which will be further denoted with

$${\mu }^{ijk}\left({\mu }_R^i{,\mu }_M^j, {\mu }_F^k\right), i,j,k\in \left\{1,2,3,4,5\right\}$$

(3)

Each of these combinations represents one possible assessment of the dependability and the following two values can be associate with it

$${\mathsf{\Omega }}_{ijk}={\displaystyle \frac{\left[i+j+k\right]}{3}}$$

(4)

and

$$m^{ijk}=\min \left\{{\mu }_R^i,{\mu }_M^j,{\mu }_F^k\right\}$$

(5)

${\mathsf{\Omega }}_{ijk}$ takes values from the set $\left\{1, 2, 3, 4, 5\right\}$, and each of the mentioned values can be associated with the number ${\mu }^l$ which represents the maximum value of $m^{ijk} \mathrm{o}\mathrm{f}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{w}\mathrm{h}\mathrm{i}\mathrm{c}\mathrm{h}{\mathsf{\Omega }}_{ijk}$ is equal to $l$, za $l\in \left\{1, 2, 3, 4, 5\right\}$, that is

$${\mu }^l=\mathrm{m}\mathrm{i}\mathrm{n}\left\{m^{ijk}:{\mathsf{\Omega }}_{ijk}=l\right\}.$$

(6)

In this way, a rating for the dependability of $D$ is obtained

$$\mu =\left({\mu }^1,{\mu }^2,{\mu }^3,{\mu }^4,{\mu }^5\right)$$

(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

$$d_i=d\left(\mu ,{\mu }_i\right)=\sqrt{\sum _{j=1}^5{({\mu }^j-{\mu }_{i,j})}^2},{\mu }_i=\left({\mu }_{i,1},{\mu }_{i,2},{\mu }_{i,3},{\mu }_{i,4},{\mu }_{i,5}\right),$$

(8)

For ${\mu }_i\in \left\{{\mu }_{poor},{\mu }_{adeq} , {\mu }_{aver},{\mu }_{good} ,{\mu }_{exc} \right\}$. Small values $d_i$ indicate proximity to the linguistic variable ${\mu }_{ i}$. Accordingly, let $d_{min}$ be the minimum value of the obtained distances $d_1,d_2, d_3, d_4, d_5$, then the reciprocal value of the relative distances can be associated to each of them that is determined by:

$${\alpha }_i={\displaystyle \frac{d_{min}}{d_i}},i\in \left\{1,2,3,4,5\right\}.$$

(9)

If for some i the distance value$d_i$ is equal to 0, then the corresponding value of the reciprocal value of relative distance is ${\alpha }_i=1,$while the other values of the reciprocal relative distances are equal to 0. The normalized values of thus obtained reciprocal values of the relative distances are determined by:

$${\beta }_i={\displaystyle \frac{{\alpha }_i}{{\alpha }_1+{\alpha }_2+{\alpha }_3+{\alpha }_4+{\alpha }_5}},i\in \left\{1,2,3,4,5\right\}$$

(10)

and present belonging to the appropriate rating:

$$A=\left\{\left({\beta }_1,"\mathrm{exc}\text{"}\right),\left({\beta }_2,"\mathrm{good}\text{"}\right),\left({\beta }_3,"\mathrm{aver}\text{"}\right),\left({\beta }_4,"\mathrm{adeq}\text{"}\right),\left({\beta }_5,"\mathrm{poor}\text{"}\right)\right\}$$

(11)

In the end, the appropriate linguistic rating is obtained as follows:

$$Z={\displaystyle \frac{{5\beta }_1+{4\beta }_2+{3\beta }_3+{2\beta }_4+{1\beta }_5}{{\beta }_1+{\beta }_2+{\beta }_3+{\beta }_4+{\beta }_5}}$$

(12)

In a similar way, a rating for maintainability M is obtained from the linguistic variables t, e, u, d, m, s which is later used to determine the dependability D.

Figure 7 shows the fuzzy model algorithm for dependability evaluation.

4.2. Case Study – Open Pit Gacko

4.2.1. Results of Expert Evaluation

Determination of the dependability of the system and its partial indicators was processed through the results obtained through questionnaires related to the expert evaluation of the partial indicators of operational safety. The questionnaire contained detailed descriptions of the partial indicators themselves. In the expert evaluation, 10 experts were surveyed. The first 5 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 5 experts are external experts with many years of experience in the field of open pit mining. 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 Figure 8.

Table 1. 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
	m	0.5	0.5	0	0	0		m	0	0	0.2	0.8	0
	s	0	0.7	0.3	0	0		s	0	0	0.3	0.7	0
	F	0	0.3	0.7	0	0		F	0	0.4	0.6	0	0
3	R	0	0	0.3	0.7	0	8	R	0	0	0	0.8	0.2
	t	0	0	0.4	0.6	0		t	0	0.4	0.6	0	0
	e	0	0	0.45	0.55	0		e	0	0.3	0.7	0	0
	u	0	0.25	0.75	0	0		u	0	0.6	0.4	0	0
	d	0	0.1	0.9	0	0		d	0	0	0.2	0.8	0
	m	0.4	0.6	0	0	0		m	0	0	0.7	0.3	0
	s	0	0.6	0.4	0	0		s	0	0.4	0.6	0	0
	F	0	0.3	0.7	0	0		F	0	0.1	0.9	0	0
4	R	0	0	0.1	0.9	0	9	R	0	0	0	0.9	0.1
	t	0	0	0.2	0.8	0		t	0	0.3	0.7	0	0
	e	0	0.5	0.5	0	0		e	0	0	0.2	0.8	0
	u	0.4	0.6	0	0	0		u	0	0	0.4	0.6	0
	d	0	0.4	0.6	0	0		d	0	0	0.2	0.8	0
	m	0.3	0.7	0	0	0		m	0	0	0.7	0.3	0
	s	0.25	0.75	0	0	0		s	0	0.3	0.7	0	0
	F	0.15	0.85	0	0	0		F	0.2	0.8	0	0	0
5	R	0	0	0.3	0.7	0	10	R	0	0	0.6	0.4	0
	t	0	0.3	0.7	0	0		t	0	0.3	0.7	0	0
	e	0	0.7	0.3	0	0		e	0	0.4	0.6	0	0
	u	0	0.4	0.6	0	0		u	0	0.6	0.4	0	0
	d	0.3	0.7	0	0	0		d	0	0.1	0.9	0	0
	m	0	0.6	0.4	0	0		m	0	0.7	0.3	0	0
	s	0.3	0.7	0	0	0		s	0	0.2	0.8	0	0
	F	0	0.3	0.7	0	0		F	0	0.4	0.6	0	0

Table 1. 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
	m	0.5	0.5	0	0	0		m	0	0	0.2	0.8	0
	s	0	0.7	0.3	0	0		s	0	0	0.3	0.7	0
	F	0	0.3	0.7	0	0		F	0	0.4	0.6	0	0
3	R	0	0	0.3	0.7	0	8	R	0	0	0	0.8	0.2
	t	0	0	0.4	0.6	0		t	0	0.4	0.6	0	0
	e	0	0	0.45	0.55	0		e	0	0.3	0.7	0	0
	u	0	0.25	0.75	0	0		u	0	0.6	0.4	0	0
	d	0	0.1	0.9	0	0		d	0	0	0.2	0.8	0
	m	0.4	0.6	0	0	0		m	0	0	0.7	0.3	0
	s	0	0.6	0.4	0	0		s	0	0.4	0.6	0	0
	F	0	0.3	0.7	0	0		F	0	0.1	0.9	0	0
4	R	0	0	0.1	0.9	0	9	R	0	0	0	0.9	0.1
	t	0	0	0.2	0.8	0		t	0	0.3	0.7	0	0
	e	0	0.5	0.5	0	0		e	0	0	0.2	0.8	0
	u	0.4	0.6	0	0	0		u	0	0	0.4	0.6	0
	d	0	0.4	0.6	0	0		d	0	0	0.2	0.8	0
	m	0.3	0.7	0	0	0		m	0	0	0.7	0.3	0
	s	0.25	0.75	0	0	0		s	0	0.3	0.7	0	0
	F	0.15	0.85	0	0	0		F	0.2	0.8	0	0	0
5	R	0	0	0.3	0.7	0	10	R	0	0	0.6	0.4	0
	t	0	0.3	0.7	0	0		t	0	0.3	0.7	0	0
	e	0	0.7	0.3	0	0		e	0	0.4	0.6	0	0
	u	0	0.4	0.6	0	0		u	0	0.6	0.4	0	0
	d	0.3	0.7	0	0	0		d	0	0.1	0.9	0	0
	m	0	0.6	0.4	0	0		m	0	0.7	0.3	0	0
	s	0.3	0.7	0	0	0		s	0	0.2	0.8	0	0
	F	0	0.3	0.7	0	0		F	0	0.4	0.6	0	0

Table 2. Results of expert evaluation for Crusher SB 1315.

Expert	Type	poor	adeq	aver	good	exc	Expert	Type	poor	adeq	aver	good	exc
1	R	0	0	0	0.6	0.4	6	R	0	0	0	0.6	0.4
	t	0	0	0.2	0.8	0		t	0	0.4	0.6	0	0
	e	0	0	0	0.7	0.3		e	0	0.2	0.8	0	0
	u	0.45	0.55	0	0	0		u	0	0.1	0.9	0	0
	d	0	0	0.1	0.9	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	0.2	0.8	0	0		s	0	0.7	0.3	0	0
	F	0	0	0.4	0.6	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	0.3	0.7		t	0	0	0.2	0.8	0
	e	0	0	0	0.4	0.6		e	0	0	0	0.4	0.6
	u	0	0	0.2	0.8	0		u	0	0.4	0.6	0	0
	d	0	0	0.4	0.6	0		d	0	0	0	0.6	0.4
	m	0.5	0.5	0	0	0		m	0	0	0.2	0.8	0
	s	0	0	0.8	0.2	0		s	0	0	0.3	0.7	0
	F	0	0	0.2	0.8	0		F	0	0.4	0.6	0	0
3	R	0	0	0.3	0.7	0	8	R	0	0	0	0.8	0.2
	t	0	0	0.4	0.6	0		t	0	0.4	0.6	0	0
	e	0	0	0.45	0.55	0		e	0	0.3	0.7	0	0
	u	0	0.25	0.75	0	0		u	0	0.6	0.4	0	0
	d	0	0.1	0.9	0	0		d	0	0	0.2	0.8	0
	m	0.4	0.6	0	0	0		m	0	0	0.7	0.3	0
	s	0	0.6	0.4	0	0		s	0	0.4	0.6	0	0
	F	0	0.3	0.7	0	0		F	0	0.1	0.9	0	0
4	R	0	0	0.1	0.9	0	9	R	0	0	0	0.9	0.1
	t	0	0	0.2	0.8	0		t	0	0.3	0.7	0	0
	e	0	0.5	0.5	0	0		e	0	0	0.2	0.8	0
	u	0.4	0.6	0	0	0		u	0	0	0.4	0.6	0
	d	0	0.4	0.6	0	0		d	0	0	0.7	0.3	0
	m	0.3	0.7	0	0	0		m	0	0	0.4	0.6	0
	s	0.25	0.75	0	0	0		s	0	0.3	0.7	0	0
	F	0.15	0.85	0	0	0		F	0.2	0.8	0	0	0
5	R	0	0	0.3	0.7	0	10	R	0	0	0.6	0.4	0
	t	0	0.3	0.7	0	0		t	0	0.3	0.7	0	0
	e	0	0.7	0.3	0	0		e	0	0.4	0.6	0	0
	u	0	0.4	0.6	0	0		u	0	0.6	0.4	0	0
	d	0.3	0.7	0	0	0		d	0	0.1	0.9	0	0
	m	0	0.6	0.4	0	0		m	0	0.7	0.3	0	0
	s	0.3	0.7	0	0	0		s	0	0.2	0.8	0	0
	F	0	0.3	0.7	0	0		F	0	0.4	0.6	0	0

Table 2. Results of expert evaluation for Crusher SB 1315.

Expert	Type	poor	adeq	aver	good	exc	Expert	Type	poor	adeq	aver	good	exc
1	R	0	0	0	0.6	0.4	6	R	0	0	0	0.6	0.4
	t	0	0	0.2	0.8	0		t	0	0.4	0.6	0	0
	e	0	0	0	0.7	0.3		e	0	0.2	0.8	0	0
	u	0.45	0.55	0	0	0		u	0	0.1	0.9	0	0
	d	0	0	0.1	0.9	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	0.2	0.8	0	0		s	0	0.7	0.3	0	0
	F	0	0	0.4	0.6	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	0.3	0.7		t	0	0	0.2	0.8	0
	e	0	0	0	0.4	0.6		e	0	0	0	0.4	0.6
	u	0	0	0.2	0.8	0		u	0	0.4	0.6	0	0
	d	0	0	0.4	0.6	0		d	0	0	0	0.6	0.4
	m	0.5	0.5	0	0	0		m	0	0	0.2	0.8	0
	s	0	0	0.8	0.2	0		s	0	0	0.3	0.7	0
	F	0	0	0.2	0.8	0		F	0	0.4	0.6	0	0
3	R	0	0	0.3	0.7	0	8	R	0	0	0	0.8	0.2
	t	0	0	0.4	0.6	0		t	0	0.4	0.6	0	0
	e	0	0	0.45	0.55	0		e	0	0.3	0.7	0	0
	u	0	0.25	0.75	0	0		u	0	0.6	0.4	0	0
	d	0	0.1	0.9	0	0		d	0	0	0.2	0.8	0
	m	0.4	0.6	0	0	0		m	0	0	0.7	0.3	0
	s	0	0.6	0.4	0	0		s	0	0.4	0.6	0	0
	F	0	0.3	0.7	0	0		F	0	0.1	0.9	0	0
4	R	0	0	0.1	0.9	0	9	R	0	0	0	0.9	0.1
	t	0	0	0.2	0.8	0		t	0	0.3	0.7	0	0
	e	0	0.5	0.5	0	0		e	0	0	0.2	0.8	0
	u	0.4	0.6	0	0	0		u	0	0	0.4	0.6	0
	d	0	0.4	0.6	0	0		d	0	0	0.7	0.3	0
	m	0.3	0.7	0	0	0		m	0	0	0.4	0.6	0
	s	0.25	0.75	0	0	0		s	0	0.3	0.7	0	0
	F	0.15	0.85	0	0	0		F	0.2	0.8	0	0	0
5	R	0	0	0.3	0.7	0	10	R	0	0	0.6	0.4	0
	t	0	0.3	0.7	0	0		t	0	0.3	0.7	0	0
	e	0	0.7	0.3	0	0		e	0	0.4	0.6	0	0
	u	0	0.4	0.6	0	0		u	0	0.6	0.4	0	0
	d	0.3	0.7	0	0	0		d	0	0.1	0.9	0	0
	m	0	0.6	0.4	0	0		m	0	0.7	0.3	0	0
	s	0.3	0.7	0	0	0		s	0	0.2	0.8	0	0
	F	0	0.3	0.7	0	0		F	0	0.4	0.6	0	0

Table 3. Results of expert evaluation for belt conveyors.

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
	m	0.5	0.5	0	0	0		m	0	0	0.2	0.8	0
	s	0	0.7	0.3	0	0		s	0	0	0.3	0.7	0
	F	0	0.3	0.7	0	0		F	0	0.4	0.6	0	0
3	R	0	0	0.3	0.7	0	8	R	0	0	0	0.8	0.2
	t	0	0	0.4	0.6	0		t	0	0.4	0.6	0	0
	e	0	0	0.45	0.55	0		e	0	0.3	0.7	0	0
	u	0	0.25	0.75	0	0		u	0	0.6	0.4	0	0
	d	0	0.1	0.9	0	0		d	0	0	0.2	0.8	0
	m	0.4	0.6	0	0	0		m	0	0	0.7	0.3	0
	s	0	0.6	0.4	0	0		s	0	0.4	0.6	0	0
	F	0	0.3	0.7	0	0		F	0	0.1	0.9	0	0
4	R	0	0	0.1	0.9	0	9	R	0	0	0	0.9	0.1
	t	0	0	0.2	0.8	0		t	0	0.3	0.7	0	0
	e	0	0.5	0.5	0	0		e	0	0	0.2	0.8	0
	u	0.4	0.6	0	0	0		u	0	0	0.4	0.6	0
	d	0	0.4	0.6	0	0		d	0	0	0.7	0.3	0
	m	0.3	0.7	0	0	0		m	0	0	0.4	0.6	0
	s	0.25	0.75	0	0	0		s	0	0.3	0.7	0	0
	F	0.15	0.85	0	0	0		F	0.2	0.8	0	0	0
5	R	0	0	0.3	0.7	0	10	R	0	0	0.6	0.4	0
	t	0	0.3	0.7	0	0		t	0	0.3	0.7	0	0
	e	0	0.7	0.3	0	0		e	0	0.4	0.6	0	0
	u	0	0.4	0.6	0	0		u	0	0.6	0.4	0	0
	d	0.3	0.7	0	0	0		d	0	0.1	0.9	0	0
	m	0	0.6	0.4	0	0		m	0	0.7	0.3	0	0
	s	0.3	0.7	0	0	0		s	0	0.2	0.8	0	0
	F	0	0.3	0.7	0	0		F	0	0.4	0.6	0	0

Table 3. Results of expert evaluation for belt conveyors.

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
	m	0.5	0.5	0	0	0		m	0	0	0.2	0.8	0
	s	0	0.7	0.3	0	0		s	0	0	0.3	0.7	0
	F	0	0.3	0.7	0	0		F	0	0.4	0.6	0	0
3	R	0	0	0.3	0.7	0	8	R	0	0	0	0.8	0.2
	t	0	0	0.4	0.6	0		t	0	0.4	0.6	0	0
	e	0	0	0.45	0.55	0		e	0	0.3	0.7	0	0
	u	0	0.25	0.75	0	0		u	0	0.6	0.4	0	0
	d	0	0.1	0.9	0	0		d	0	0	0.2	0.8	0
	m	0.4	0.6	0	0	0		m	0	0	0.7	0.3	0
	s	0	0.6	0.4	0	0		s	0	0.4	0.6	0	0
	F	0	0.3	0.7	0	0		F	0	0.1	0.9	0	0
4	R	0	0	0.1	0.9	0	9	R	0	0	0	0.9	0.1
	t	0	0	0.2	0.8	0		t	0	0.3	0.7	0	0
	e	0	0.5	0.5	0	0		e	0	0	0.2	0.8	0
	u	0.4	0.6	0	0	0		u	0	0	0.4	0.6	0
	d	0	0.4	0.6	0	0		d	0	0	0.7	0.3	0
	m	0.3	0.7	0	0	0		m	0	0	0.4	0.6	0
	s	0.25	0.75	0	0	0		s	0	0.3	0.7	0	0
	F	0.15	0.85	0	0	0		F	0.2	0.8	0	0	0
5	R	0	0	0.3	0.7	0	10	R	0	0	0.6	0.4	0
	t	0	0.3	0.7	0	0		t	0	0.3	0.7	0	0
	e	0	0.7	0.3	0	0		e	0	0.4	0.6	0	0
	u	0	0.4	0.6	0	0		u	0	0.6	0.4	0	0
	d	0.3	0.7	0	0	0		d	0	0.1	0.9	0	0
	m	0	0.6	0.4	0	0		m	0	0.7	0.3	0	0
	s	0.3	0.7	0	0	0		s	0	0.2	0.8	0	0
	F	0	0.3	0.7	0	0		F	0	0.4	0.6	0	0

4.3. Determination the Partial Indicator of Maintainability M

On the basis of the submitted results, the following estimates were obtained for each analyzed part of the CCS system.

Table 4. 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

Table 4. 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

Table 5. Final rating for partial indicators t, e, u d, m, 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

Table 5. Final rating for partial indicators t, e, u d, m, 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.

Table 6. 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

Table 6. 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

Figure 9. Distribution of output values for indicator M maintainability for Crusher SB 1515 using max-min composition.

Figure 9. Distribution of output values for indicator M maintainability for Crusher SB 1515 using max-min composition.

Figure 10. Distribution of output values for indicator M maintainability for Crusher SB 1315 using max-min composition.

Figure 10. Distribution of output values for indicator M maintainability for Crusher SB 1315 using max-min composition.

Figure 11. Distribution of output values for indicator M maintainability for belt conveyors using max-min composition.

Figure 11. Distribution of output values for indicator M maintainability for belt conveyors using max-min composition.

4.4. 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.

Table 9. 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

Table 9. 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 F for Crusher SB 1515, Crusher SB 1315 and belt conveyors in the fuzzy number form.

Table 10. 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

Table 10. 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 number, the ratings obtained using the max-min composition for the specified parts of the CCS system are shown in the following table.

Table 11. Obtained ratings for operational safety 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

Table 11. Obtained ratings for operational safety 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

Figure 12. Distribution of output values for D dependability for Crusher SB 1515 using max-min composition.

Figure 12. Distribution of output values for D dependability for Crusher SB 1515 using max-min composition.

Figure 13. Distribution of output values for D dependability for Crusher SB 1315 using max-min composition.

Figure 13. Distribution of output values for D dependability for Crusher SB 1315 using max-min composition.

Figure 14. Distribution of output values for D dependability for belt conveyors using max-min composition.

Figure 14. Distribution of output values for D dependability for belt conveyors using max-min composition.

4.5. Dependability of the CCS System at the Open Pit Gacko

On the basis of obtained ratings for dependability of the system parts, the overall rating of dependability was obtained using the max-min composition and reads as follows:

(0.07125, 0.3033, 0.30333, 0.30333, 0.105).

Further analysis shows that the corresponding values obtained by the best fit method are equal to:

(1.02977, 0.78942, 0.71215, 0.77866, 0.99645).

The corresponding reciprocal values of the relative distances ${\alpha }_i$ are:

(0.69156, 0.90211, 1, 0.91458, 0.71468),

while the values of normalized reciprocal values ${\beta }_i$ are equal to:

(0.16376, 0.21362, 0.23680, 0.21657, 0.16923).

Appropriate linguistic evaluation $Z={\displaystyle \frac{{5\beta }_1+{4\beta }_2+{3\beta }_3+{2\beta }_4+{1\beta }_5}{{\beta }_1+{\beta }_2+{\beta }_3+{\beta }_4+{\beta }_5}}=2.9860.$

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%.

Figure 15. Distribution of output values for D dependability for CCS system using max-min composition.

Figure 15. Distribution of output values for D dependability for CCS system using max-min composition.

5. 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 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.

Failures are categorized into the following groups:

• technological failures,
• electrical failures,
• mechanical failures,
• shift of workers,
• equipment overhaul,
• daily review,
• weather conditions.

Figure 16. The authors of the article with representatives of the Gacko mine during a tour of the field (private archive).

Figure 16. The authors of the article with representatives of the Gacko mine during a tour of the field (private archive).

The following figure shows the percentage participation by types of failures for the CCS system by year.

Figure 17. The percentage of failures of the CCS system in the period from 2018-2023. years.

Figure 17. The percentage of failures of the CCS system in the period from 2018-2023. years.

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 varies 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, shift of workers and equipment overhaul are the most dominant factors in the operation of the CCS system, while weather conditions are the least significant.

Dependability of the CCS system in the period 2018-2023 is shown in the following figure (Figure 18).

Figure 18. Dependability of the continuous part of the CCS system in the period from 2018-2023. years.

Figure 18. Dependability of the continuous part of the CCS system in the period from 2018-2023. years.

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 others years. In 2021 and 2022, dependability was stable at 53%, while 2023 saw a slight drop to 51%. Overall, system dependability varies between 46% and 55% over the observed period. The average value of dependability for the period of 6 years is 52.16%.

6. Conclusions

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.

Unlike conventional models that rely on IT monitoring systems, this approach incorporates 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 recommendations, 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 the model is 59 %, 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 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.