HEART Hybrid Methods for Assessing Human Reliability in Coal-Fired Thermal Power Plant Process

Abstract

The assessment of human reliability is crucial in serious processes and operations, such as planned maintenance, unplanned maintenance, and troubleshooting in a coal-fired thermal power plant, as the nature of these processes poses significant threats. When the literature is examined, the evaluation of human reliability in any type of power plant, especially coal-fired thermal power plants, is limited. In order to fill this gap, we systematically assessed human reliability in an accident that occurred during a repair of a tube failure in a boiler in a coal-fired thermal power plant. The HEART (human error assessment and reduction technique) method was used in a hybrid way alongside the fuzzy AHP and SWARA (step weight assessment ratio analysis) methods. Although the HEART method is a practical, understandable, and easy-to-implement human reliability assessment method, the APOE (assessment of the proportion effect) value depends on the decision of a single decision maker. This study aimed to eliminate this deficiency and compare human error possibilities using HEART–fuzzy AHP and HEART–SWARA methods. This hybrid method can be used in the operation of all coal-fired thermal power plants and provides practical contributions to minimize human error.

1. Introduction

Despite thorough training and motivation, mistakes can still be made. In the workplace, the consequences of human failure have always been severe. According to statistics, more than 60% of deaths and accidents that occur globally each year are caused by human error [1]. Accident and incident analyses have shown that human failure contributes to increased exposure to all accidents and health-hazardous substances. Human reliability analysis (HRA) has been investigated more effectively in recent years due to increased human failure events. Estimates of human error in road transport are 85%, 50–70% in nuclear power plants, 60–90% in the chemical industry, 70–80% in aviation, and 80–85% in freighters [2]. Therefore, researchers have tackled human error to reveal the causes of these results.

Many studies have been undertaken to assess the role of human error in different industrial accidents. A series of studies have been undertaken to determine the initial possibility of a failure occurring. Current research involves the study of human error in the marine industry as the cause of marine accidents [3]; maintenance operations in the marine industry [4]; calculation of human error that will cause specific grounding events [5]; the evaluation of human error in railway accidents [6,7]; human-induced actions with the potential to expose operators working in a radiation-emitting facility to radiation [8,9]; human error during the steam boiler operation [10,11]; and the human error probability in a probability security assessment of the reactor in nuclear power plants [12]. Research has demonstrated that the human factor is an important risk factor in an industry, regardless of production and process.

Human reliability refers to the possibility that system operations will be undertaken by an individual accurately, within a certain timeframe, and without errors. A human reliability analysis (HRA) is used to predict human error in activities. A human reliability analysis (HRA) is one of the most powerful methods in risk assessments. Human error is the most significant factor affecting safety. The results of research have demonstrated that current reliability is not the same as expected reliability, and the root cause of this deficit is human error. The HRA is carried out as part of an analysis of system safety to estimate and analyze the possibility of human error in each sector. One of the most significant steps in the evaluation of human reliability is to define the factors that increase the likelihood of human error occurring and those that influence human performance [13].

The first generation of human reliability analysis methods supposed that human behavior could be separated like a data computer. These models were largely adapted from expert analyses, such as the human error assessment and reduction technique (HEART) method. The second generation concentrated on human cognitive methods and modeling. Third-generation human reliability analysis methods, which are dynamic models, are grounded on cognitive simulation models [1].

Electricity is the principal product of power plants and an essential component of contemporary life. According to the International Energy Agency, coal is the largest source of electricity production [14]. The situation is similar in Turkey, where coal is important for the production of electricity [15]. Despite all technological developments and processes, as in many industries, detrimental and devastating accidents still occur in coal-fired thermal power plants within the energy sector. Despite the popularity of coal compared to other power sources, very few studies have considered the different risks of coal-fired thermal power plants. Human behavior and manufacturing procedures play a significant role in crisis and accident management in thermal power plants, as well as in making human decisions.

Unexpected problems can occur in complex and high-tech equipment in a thermal power plant. Problems can often be caused by production error, material fatigue, human error, and other problems. In the event of a system failure, it is necessary to avoid human error. Despite the fact that accidents or incidents in coal-fired thermal power plants are often caused by human factors, there is not enough effort to increase safety and reduce the number of incidents in coal-fired thermal power plants.

Many researchers use multi-criteria decision making (MCDM) methods; to compensate for the shortcomings of one method, they combine two or more methods. Expressing risks based on personal views and value decisions, rather than numerical size, leads to uncertainty. In some cases, if there is no numeric data, there is a verbal language in risk assessment methods where terms can be given as vague expressions. Due to this feature of risk assessment methods, various studies [8,9,16,17,18] have used the fuzzy AHP approach. Researchers and scientists have created a series of recent MCDM methods in the last decade [19]. A new step weight assessment ratio analysis (SWARA) technique has been recommended by Kersulien [20]. Although this is a new method, the choice of packaging design, architect selection, product design [19], rational dispute resolution [20], analysis of risks in coal supply chain management [21], recruitment and staff selection [22], and the power plant was used to solve many problems, such as location selection [23].

This article provides more information on the relationship between accidents and risks in coal-fired thermal power plants, which are very dangerous and complex, by taking into consideration the literature. The study examined an incident that occurred in a coal-fired thermal power plant that was operating in Turkey. As this research was sectoral and based on specialist opinion and experience, this study used the human error assessment and reduction technique (HEART), a common approach often used to determine the human error probability (HEP). In addition, fuzzy analytical hierarchy process (fuzzy AHP) methods and step weight assessment ratio analysis (SWARA) from MCDM were used together. The purpose of using MCDM is the need for expert judgment. The weight of the error-producing conditions that constitute each risk was calculated with SWARA and fuzzy AHP, and the probability of human error was compared using the HEART method.

2. Materials and Methods

2.1. HEART Technique

The human error assessment and reduction technique (HEART) was developed by Williams to identify human error values and to calculate human error probability (HEP). The HEART method uses the experience and knowledge of experts for the assignment of operational utilization [24]. The HEART method can be defined by two basic parameters. These are EPCs and GEP. The GEP parameter indicates a generic error probability value that is performed by an expert choosing a generic task type (GTT). The generic task type (GTT) states the generic description of the task. There is a total of nine GTTs as shown in

Table 1. GTT and GEP value.

Generic Task Type (GTT)		Nominal Human
		Unreliability (GEP)
		(5th–95th Percentile Bounds)
A	Totally unfamiliar; performed at speed with	0.55
	no real idea of likely consequences	(0.35–0.97)
B	Shift or restore system to a new or original	0.26
	state on a single attempt	(0.14–0.42)
C	Complex task requiring high level of	0.16
	comprehension and skill	(0.12–0.28)
D	Fairly simple task performed rapidly or	0.09
	given scant attention	(0.06–0.13)
E	Routine, highly practiced, rapid task	0.02
	involving relatively low level of skill	(0.07–0.045)
F	Restore or shift a system to original or	0.003
	new state following procedures with	(0.0008–0.007)
	some checking
G	Completely familiar, well- designed, highly	0.0004
	practiced, routine task occurring several	(0.00008–0.009)
	times per day, performed to highest possible
	standards by highly motivated, highly trained,
	and experienced personnel, with time to correct
	potential error, but without the benefit of
	significant job aid
H	Respond correctly to system command even	0.00002
	when there is an augment or automated	(0.000006–0.0009)
	supervisory system providing accurate
	interpretation of system state
M	Miscellaneous task for which no description	0.003
	can be found	(0.008–0.11)

. Among the GTTs described in the method, the proper GTT for the task is chosen and the allocated generic error probability (GEP) is appointed in relation to the human error probability value [5,24].

The second basis parameter is the error-producing condition (EPC), which shows the related performance-shaping factors for humans and is able to influence the HEP value. The EPC parameters can relate to any internal human characteristic, management, environment, machine, etc.

Table 2. List of error-producing conditions (EPCs).

Code	Error-Producing Condition	Maximum Effect
EPC1	Unfamiliarity	17
EPC2	Time shortage	11
EPC3	Low signal-noise ratio	10
EPC4	Features over-ride allowed	9
EPC5	Spatial and functional incompatibility	8
EPC6	Model mismatch	8
EPC7	Irreversibility	8
EPC8	Channel overload	6
EPC9	Technique unlearning	6
EPC10	Knowledge transfer	5.5
EPC11	Performance ambiguity	5
EPC12	Misperception of risk	4
EPC13	Poor feedback	4
EPC14	Delayed/incomplete feedback	4
EPC15	Operator inexperience	3
EPC16	Impoverished information	3
EPC17	Inadequate checking	3
EPC18	Objectives conflict	2.5
EPC19	No diversity	2.5
EPC20	Educational mismatch	2
EPC21	Dangerous incentives	2
EPC22	Lack of exercise	1.8
EPC23	Unreliable instruments	1.6
EPC24	Absolute judgements required	1.6
EPC25	Unclear allocation of function	1.6
EPC26	Progress tracking lack	1.4
EPC27	Physical capabilities	1.4
EPC28	Low meaning	1.4
EPC29	Emotional stress	1.3
EPC30	ill- health	1.2
EPC31	Low morale	1.2
EPC32	Inconsistency of displays	1.15
EPC33	Poor environment	1.1
EPC34	Low mental workload	1.1
EPC35	Sleep cycles disruption	1.06
EPC36	Task pacing	1.03
EPC37	Supernumeraries	1.03
EPC38	Age	1.02

shows the list of error-producing conditions (EPCs) and their maximum effect on HEP. There are 38 EPCs identified for the HEART method, and the maximum impact value of each EPC is defined to calculate the HEP value [18,24].

In consideration of the above, the human error probability (HEP) in the HEART method is forecasted by the following form:

$$HEP{ }_{value}=GE{P}_{value} x \left\{{\displaystyle \prod }_i\left[(EP{C}_i-1)APO{E}_i+1\right]\right\}$$

where $GE{P}_{value}$ is the error probability value of the related GTT, $EP{C}_i$ is the ith (i = 1, 2, 3, …, n) EPC, and $APO{E}_i$ (from 0 to 1) shows a specialist’s assessment of the proportion effect for each ith EPC, which is determined as the significance of each error-producing condition [6,7,24].

2.2. Fuzzy AHP Method

Fuzzy AHP creates a hierarchical structure that reduces complex problems to simple problems so that the problem can be resolved in less time. It considers both qualitative and quantitative factors and is an easy and simple method. This method is often used to solve complex decision problems by analyzing pairwise comparisons, options, and criteria for their meaning and dominance [25]. The FAHP method combines the fuzzy set theory and hierarchical layout analysis concepts. In many industries, decision-making issues with uncertain conditions have been resolved through studies that help to develop and improve this method [26]. This study used Chang’s fuzzy AHP method. Chang’s fuzzy AHP method is a preferred method because it does not require a lot of math, and it is also the preferred method because of the implementation of classic AHP steps. The steps of an extent analysis method known as a fuzzy AHP developed by Chang are as follows. According to Chang’s extent analysis method, the method uses triangular fuzzy numbers in

Table 3. Triangular fuzzy comparison number.

Linguistic Scale	Triangular	Triangular Fuzzy
	Fuzzy Number	Reciprocal Number
Just Equal	(1, 1, 1)	(1, 1, 1)
Equally important	(1/2, 1, 3/2)	(2/3, 1, 2)
Weakly important	(1, 3/2, 2)	(1/2, 2/3, 1)
Strongly more important	(3/2, 2, 5/2)	(2/5, 1/2, 2/3)
Very strongly more important	(2, 5/2, 3)	(1/3, 2/5, 1/2)
Absolutely more important	(5/2, 3, 7/2)	(2/7, 1/3, 2/5)

instead of exact values as in the classic AHP when making pair comparisons [27]. The conversion scale was used for converting the linguistic judgments into the triangular fuzzy numbers (TFNs), which is given in Table 3 [28,29].

The steps of Chang’s analysis are explained below:

Step 1. The fuzzy synthetic extent $\left(S_i\right)$ value with respect to ith criterion is defined as:

$$S_i={\displaystyle \sum }_{j=1}^m{M}_{gi}^j{\left[{\displaystyle \sum }_{i=1}^n{\displaystyle \sum }_{j=1}^m{M}_{gi}^j\right]}^{-1}$$

(1)

$${\displaystyle \sum }_{j=1}^m{M}_{gi}^j=\left({\displaystyle \sum }_{j=1}^m{l}_j, {\displaystyle \sum }_{j=1}^m{m}_j, {\displaystyle \sum }_{j=1}^m{u}_j\right)$$

To obtain the value ${\left[{\displaystyle \sum }_{i=1}^n{\displaystyle \sum }_{j=1}^m{M}_{gi}^j\right]}^{-1}$, the fuzzy addition of $M_{gi}^j, \left(j=1, 2, \dots , m\right)$ values is carried out using the equation ${\displaystyle \sum }_{i=1}^n{\displaystyle \sum }_{j=1}^m{M}_{gi}^j=\left({\displaystyle \sum }_{j=1}^m{l}_j, {\displaystyle \sum }_{j=1}^m{m}_j, {\displaystyle \sum }_{j=1}^m{u}_j\right)$.

$${\left[{\displaystyle \sum }_{i=1}^n{\displaystyle \sum }_{j=1}^m{M}_{gi}^J\right]}^{-1}=\left(\frac{1}{{{\displaystyle \sum }}_{i=1}^n{u}_i}, \frac{1}{{{\displaystyle \sum }}_{i=1}^n{m}_i}, \frac{1}{{{\displaystyle \sum }}_{i=1}^n{l}_i}\right)$$

where l is the lower limit value, m is the most promising value, and u is the upper limit value.

Step 2. The degree of the possibility of $S_2=\left(l_2,m_2, u_2\right)\ge \left(l_1, m_1, u_1\right)$ can be defined as:

$$\mathrm{V}\left(S_2\ge S_1\right){=}_{y\ge x}^{sup}\left[min\left({\mu }_{s_1}\left(x\right), {\mu }_{s_2}\left(y\right)\right)\right]$$

where x and y represent the values on an axis of the membership function of each criterion; this expression can be found in Equation (2) below:

$$\mathrm{V}=\left(S_2\ge S_1\right)=\left\{ \begin{array}{c} 1 if m_2\ge m_1\\ 0 if l_1\ge u_2\\ \frac{l_1-u_2}{\left(m_2-u_2\right)-\left(m_1-l_1\right)} otherwise\end{array}\right.$$

(2)

To compare $S_1 \mathrm{and} S_2$, both V $\left(S_2\ge S_1\right)$ and V $\left(S_1\ge S_2\right)$ values need to be calculated.

Step 3. The degree of possibility for a convex fuzzy number S to be greater than k convex fuzzy numbers $S_i=\left(i=1, 2, 3,\dots , k\right)$ can be described as:

$$\mathrm{V}\left(S\ge S_1, S_2, \dots , S_k\right)=\mathrm{V} \left[\left(S\ge S_1\right), \left(S\ge S_2\right),\dots \left(S\ge S_k\right)\right]=min \mathrm{V}\left(S\ge S_i\right), i=1,2,3,\dots ,k$$

(3)

Suppose that $d^{\prime }\left(A_i\right)=min \mathrm{V} \left(S_i\ge S_k\right)$.

For k = 1, 2, 3, …, n k$\ne i,$ the weight vectors are given in Equation (4) as

$${\mathrm{W}}^{\prime } ={\left(d^{\prime }\left(A_1\right),d^{\prime }\left(A_2\right),\dots , d^{\prime }\left(A_m\right) \right)}^T$$

(4)

Step 4. By way of normalization, the normalized weight vectors are given in Equation (5) as

$$\mathrm{W}={\left(d \left(A_1\right),d \left(A_2\right),\dots , d \left(A_m\right) \right)}^T$$

(5)

where W is the non-fuzzy number.

These weights are scaled (dividing each weight by the sum of the weights), and the total of the weights is equal to one [27].

2.3. SWARA Method

The step-wise weight assessment ratio analysis method was developed by Kersuliene et al., in 2010. The criteria that should be used in the evaluation of alternatives are gradual from the most significant weight value to the least significant value; each criterion is voted by experts, and the insignificant ones are eliminated with this method [23].

The process of the determination of the relative weights of criteria using the SWARA method can correctly be displayed according to the following steps [19,22]:

Step 1. Defining the criteria on which the sorting of criteria in decreasing order and the assessment will be based. Gradation is performed dependent upon the significance that the administrator designates to a certain criterion.

Step 2. Specification of the relative significance of the criteria j in relation to the previous criterion (j − 1). The relative significance is denoted for every criterion individually, and it begins with the second criterion.

Step 3. Determining $k_j$ by using the following Equation:

$$k_j= \left\{\begin{array}{c}1 j=1\\ s_{j } j>1\end{array}\right.$$

Step 4. Determining the recalculated weight $q_j$ as follows:

$$q_j= \left\{\begin{array}{c} 1 j=1\\ \frac{k_j-1}{k_j} j>1\end{array}\right.$$

Step 5. The relative weights of the assessment criteria are specified as follows:

$$w_j=\frac{q_j}{{{\displaystyle \sum }}_{k=1}^n{q}_k}$$

where $w_j$ expresses the relative weight of criterion j.

The convenience of implementation of the SWARA method has contributed to its popularity and implementation for the troubleshooting and definition of the significance of assessment criteria in several areas of business and life.

3. Case Study

3.1. Assessment of Human Reliability: An Accident during Planned Maintenance at a Coal-Fired Thermal Plant

In this section, a real thermal plant accident scenario was selected to implement the proposed approach. The X Coal-Fired Thermal Power Plant consists of four units and operates in Turkey. The power of each unit is 360 MW. When the unit was deactivated in a planned manner (repair of the boiler tube failure), the turbine speed had reached 4500 rpm uncontrollably due to incorrect operator contact. As a result, the turbine and the generator were badly damaged. The thermal plant has been disabled for months.

Hierarchical task analysis (HTA) was used to gather information through interviews and observation. The hierarchical task analysis (HTA) of the process required to repair the boiler tube failure was prepared by five experts with extensive knowledge and experience. The experts had a certain competence. The HTA was prepared by two occupational safety experts, an occupational safety manager, a boiler maintenance chief engineer, and a mechanical maintenance manager. The HTA is shown in

Table 4. HTA of the boiler tube failure process.

1. Readiness for starting scheduled maintenance (the boiler tube failure)

1.1 The system must be deactivated to repair the boiler tube failure

1.2 Ensure that the relevant unit has approved the plan to deactivate the system for scheduled maintenance

1.3 Before starting scheduled maintenance, it must be determined how long the maintenance will last, when it will end, and when the system will be activated

1.4 This decision and the necessary procedures must be again approved by the department

2. Start to deactivate the system in accordance with the instructions for deactivating the system

2.1 The load must be decreased by reducing the steam flow to the turbine and then the mill must be disabled in the boiler

2.2 You have to be sure that the appropriate conditions in the instructions are reached (steam flow rate, pressure, etc.)

2.3 Make sure that the steam to the turbine is stopped

2.4 Make sure that the unit cutter is switched on and that there is no power generation by checking by both the operator in the control room and the observer in the location

2.5 After the steam is stopped, the boiler pressure must be checked and the boiler must be extinguished when the suitable conditions

3. Checking the valves, alarm system and system breakers before starting maintenance

3.1 Make sure that all warning signs exist

3.2 Ensure that the alarm system is operational

3.3 Check the turbine governing valves for problems

3.4 Check the Emergency Trip buttons and Fire Trip buttons

3.5 Check that the control valves are closed and opened according to the values in the main control room and the location

4. Completion of pre-maintenance preparations

4.1 Ensure the environmental security

4.2 Ensure that personnel have protective equipment prior to maintenance

4.3 Checking the condition of the explosion in the boiler and start to maintenance and repair by means of proper work after check

5. Ensure that the necessary supervision during maintenance

5.1 Ensure that the operating personnel are on work site and are monitoring the operation

5.2 The operator has to provided good communication with the observer

6. Turbine speed reaches an uncontrolled level during the maintenance process, resulting in the turbine and generator being blown up in flames

6.1 Check that the turbine load is reset with the control valves during system deactivation

6.2 Check that the turbine is disable or not

7. Completion of the operations required to reduce the turbine speed

7.1 Ensure that the operating personnel are in the knowledge and experience required to intervene in the situation

7.2 Operating personnel must be provided support with auxiliary staff

7.3 To reduce turbine speed, the operating personnel must be checked for correct initial intervention

7.4 Personnel must have followed the appropriate sequence to reduce turbine speed

7.5 Make sure that operating personnel close the control valves with the correct decision

. The process of HTA begins with preparations that are required to be performed before the start of the process. It proceeds with sub-tasks that have to be finished throughout the process. The process ends off with sub-tasks that have to be finalized after the process.

Experts are requested to determine the EPCs affecting each task and choose the most suitable GTT for each sub-task. Experts are able to select different EPC(s) and GTTs. There must be a consensus between experts to achieve a consistent outcome. The GTTs, GEP value, EPCs, and the sub-steps of boiler maintenance are given in

Table 5. Chosen GTTs and EPC(s).

Sub-Tasks	GTT	GEP Value	Chosen EPC or EPCs
1
1.1	F	3.0 × 10−3	EPC13,14,19,26
1.2	H	2.0 × 10−5	EPC14,18
1.3	F	3.0 × 10−3	EPC2,11,18,35
1.4	E	2.0 × 10−2	EPC26
2
2.1	E	2.0 × 10−2	EPC11,13,17,19
2.2	E	2.0 × 10−2	EPC14,18,19
2.3	H	2.0 × 10−5	EPC2,13,14,17
2.4	H	2.0 × 10−5	EPC8,10,15,16,20,25
2.5	F	3.0 × 10−3	EPC2,13,17,21
3
3.1	G	4.0 × 10−4	EPC2,18,32
3.2	H	2.0 × 10−5	EPC14,17
3.3	H	2.0 × 10−5	EPC14,17,32
3.4	D	9.0 × 10−2	EPC17
3.5	E	2.0 × 10−2	EPC17,34
4
4.1	G	4.0 × 10−4	EPC5,13
4.2	G	4.0 × 10−4	EPC2,17,26
4.3	F	3.3 × 10−3	EPC2,17,18
5
5.1	G	4.0 × 10−4	EPC15,17,24,26
5.2	G	4.0 × 10−4	EPC13,16
6
6.1	H	2.0 × 10−5	EPC2,7,13
6.2	H	2.0 × 10−5	EPC1,2,7,13
7
7.1	G	4.0 × 10−4	EPC6,15,20
7.2	G	4.0 × 10−4	EPC25,37
7.3	F	3.0 × 10−3	EPC7,12,15,29,31
7.4	F	3.0 × 10−3	EPC2,7,21,26
7.5	F	3.0 × 10−3	EPC2,15,20,29,31

. Experts can choose several EPCs for each sub-task. $APO{E}_i$ is calculated for each sub-task. In this study, the APOE calculation was performed using the fuzzy AHP and SWARA methods.

3.2. Fuzzy AHP Pairwise Comparison Matrix

This section creates a pairwise comparison matrix for the EPC selected for each of the seven steps. Firstly, the fuzzy AHP is used to specify the significant weights of the main criteria and sub-criteria. Chang’s extent analysis is utilized for fuzzy pairwise comparisons of the main criteria and sub-criteria. The stages of the extent analysis are described below.

Table 6. Comparison matrix of EPC selected for step 1.1.

	EPC13	EPC14	EPC19	EPC26
EPC13	(1, 1, 1)	(3/2, 2, 5/2)	(2, 5/2, 3)	(1, 3/2, 2)
EPC14	(2/5, 1/2, 2/3)	(1, 1, 1)	(1/2, 1, 3/2)	(1/2, 2/3, 1)
EPC19	(1/3, 2/5, 1/2)	(2/3, 1, 2)	(1, 1, 1)	(2/3, 1, 2)
EPC26	(1/2, 2/3, 1)	(1, 3/2, 2)	(1/2, 1, 3/2)	(1, 1, 1)

shows that APOE weights are calculated using the fuzzy AHP method for each EPC. The result of the fuzzy pairwise comparison matrix for the criteria layer (EPC13,14,19,26) is shown in Table 6. The value of fuzzy synthetic extent with respect to the four criteria can be obtained. The computational process is described below. The fuzzy synthetic grade values for the pair comparison matrix of criteria are found as follows.

$$\begin{gathered} S_{EPC13}=\left(5.5, 7, 8.5\right)\otimes {\left(13.56, 17.72, 23.66\right)}^{-1} \\ =(5.5, 7, 8.5)\otimes (1/23.66, 1/17.72, 1/13.56) \\ =(0.2325, 0.3950, 0.6268) \\ {S}_{EPC14}=(0.1014, 0.1783, 0.3068) \\ {S}_{EPC19}=(0.1124, 0.1919, 0.4056) \\ {S}_{EPC26}=(0.1268, 0.2348, 0.4056) \end{gathered}$$

The importance weights of attributes were found using fuzzy synthetic grade values from the pair comparison matrix. The degree of possibility (V ($S_2\ge S_1$)) among these four fuzzy synthetic extent values can be acquired. Equation (2) is used in the calculation process.

$$\begin{gathered} \mathrm{V} (S_{EPC13}\ge S_{EPC14})=m_1\ge m_2=1 \\ \mathrm{V} (S_{EPC13}\ge S_{EPC19})=m_1\ge m_3=1 \\ \mathrm{V} (S_{EPC13}\ge S_{EPC26})=m_1\ge m_4=1 \end{gathered}$$

$$\begin{gathered} \mathrm{V} (S_{EPC14}\ge S_{EPC13})=(l_1-u_2)/\left[\left(m_2-u_2\right)-(m_1-l_1\right)]=0.2553 \\ \mathrm{V} (S_{EPC14}\ge S_{EPC19})=(l_3-u_2)/\left[\left(m_2-u_2\right)-(m_3-l_3\right)]=0.9346 \\ \mathrm{V} (S_{EPC14}\ge S_{EPC26})=(l_4-u_2)/[\left(m_2-u_2\right)-(m_4-l_4)]=0.7610 \end{gathered}$$

$$\begin{gathered} \mathrm{V} (S_{EPC19}\ge S_{EPC13})=(l_1-u_3)/[\left(m_3-u_3\right)-(m_1-l_1)]=0.4601 \\ \mathrm{V} (S_{EPC19}\ge S_{EPC14})=m_3\ge m_2=1 \\ \mathrm{V} (S_{EPC19}\ge S_{EPC26})=(l_4-u_3)/[\left(m_3-u_3\right)-(m_4-l_4)]=0.8666 \end{gathered}$$

$$\begin{gathered} \mathrm{V} (S_{EPC26}\ge S_{EPC13})=(l_1-u_4)/[\left(m_4-u_4\right)-(m_1-l_1)]=0.5193 \\ \mathrm{V} (S_{EPC26}\ge S_{EPC14})=m_4\ge m_2=1 \\ \mathrm{V} (S_{EPC26}\ge S_{EPC19})=m_4\ge m_3=1 \end{gathered}$$

Using the equation of $d^{\prime }\left(A_i\right)=\min \left\{\mathrm{V}\left(S_i\ge S_k\right)\right\}$, the weight vector and normalized weight vector of the criteria layer can be obtained. Weights showing the degree of preference of an attribute compared to the others are obtained by means of Equation (3).

$$\begin{gathered} \mathrm{V} (S_{EPC13}\ge S_{EPC14},S_{EPC19},S_{EPC26})=\min (1,1,1)=1 \\ \mathrm{V} (S_{EPC14}\ge S_{EPC13},S_{EPC19},S_{EPC26})=\min (0.2553, 0.9346, 0.7610)=0.2553 \\ \mathrm{V} (S_{EPC19}\ge S_{EPC13},S_{EPC14},S_{EPC26})=\min (0.4601, 1, 0.8666)=0.4601 \\ \mathrm{V} (S_{EPC26}\ge S_{EPC13},S_{EPC14},S_{EPC19})=\min (0.5193, 1, 1)=0.5193 \end{gathered}$$

$W^{\prime }$=$\left(d^{\prime }(EP{C}_{13}\right), d^{\prime }(EP{C}_{14}),d^{\prime }(EP{C}_{19}),d^{\prime }(EP{C}_{26}){)}^T$ = ${\left(1, 0.2553, 0.4601, 0.5193\right)}^T$. The weight vectors are obtained by means of the Equation (4) formula.

$$\mathrm{W}={(\frac{1}{1+0.2553+0.4601+0.5193}, \frac{0.2553}{2.2348}, \frac{0.4601}{2.2348},\frac{0.5193}{2.2348})}^T$$

$W_{Adım 1.1}$ = ${\left(0.448, 0.114, 0.206, 0.232\right)}^T$. The normalized weight vectors are obtained as in Equation (5).

3.3. Calculating Weights Using the SWARA Method

Average severity percentages are given as a result of the assessment of all participants for the specified criteria. The relative values of the criteria obtained as a result of the co-decisions of five experts are shown in

Table 7. Weights of the criteria obtained from 5 expert participants in the common view for step 1.1.

Criteria	${\mathit{s}}_{\mathit{i}}$	${\mathit{k}}_{\mathit{i}}$	${\mathit{q}}_{\mathit{i}}$	${\mathit{w}}_{\mathit{i}}$
EPC13		1	1	0.385
EPC26	0.60	1.6	0.625	0.240
EPC19	0.10	1.1	0.568	0.219
EPC14	0.40	1.4	0.406	0.156

. Table 7 shows the calculated weights of the weight calculation procedure and criteria using the SWARA method.

Using the fuzzy AHP and SWARA methods, the APOE weight account is calculated from step 1 to step 7 and up to all sub-steps.

Afterwards, calculations of the APOE are carried out, and the calculation of HEP for each sub-task of the boiler tube failure repair operation is carried out in compliance with equation HEP.

Table 8. HEP and APOE results of the boiler explosion repair process.

Sub-Task	EPC(s)	Fuzzy AHP APOE	SWARA APOE	Fuzzy AHP–HEART	SWARA–HEART
				HEP	HEP
1.1	EPC13	0.448	0.385	1.35 × 10−2	1.38 × 10−2
	EPC14	0.114	0.156
	EPC19	0.206	0.219
	EPC26	0.232	0.240
1.2	EPC14	0.685	0.643	9.00 × 10−5	9.00 × 10−5
	EPC18	0.315	0.357
1.3	EPC2	0.388	0.338	2.96 × 10−2	2.89 × 10−2
	EPC11	0.007	0.119
	EPC18	0.365	0.307
	EPC35	0.240	0.236
1.4	EPC26	1.000	1.000	2.80 × 10−2	2.80 × 10−2
2.1	EPC11	0.311	0.297	1.56 × 10−1	1.54 × 10−1
	EPC13	0.330	0.326
	EPC17	0.257	0.247
	EPC19	0.102	0.130
2.2	EPC14	0.139	0.251	7.00 × 10−2	8.42 × 10−2
	EPC18	0.750	0.500
	EPC19	0.111	0.249
2.3	EPC2	0.391	0.426	3.29 × 10−4	3.47 × 10−4
	EPC13	0.084	0.113
	EPC14	0.226	0.225
	EPC17	0.299	0.236
2.4	EPC8	0.160	0.157	1.91 × 10−2	1.84 × 10−2
	EPC10	0.124	0.112
	EPC15	0.163	0.165
	EPC16	0.124	0.111
	EPC20	0.225	0.257
	EPC25	0.204	0.198
2.5	EPC2	0.544	0.487	4.00 × 10−2	4.17 × 10−2
	EPC13	0.055	0.129
	EPC17	0.346	0.256
	EPC21	0.055	0.128
3.1	EPC2	0.345	0.294	2.20 × 10−3	2.09 × 10−3
	EPC18	0.095	0.148
	EPC32	0.560	0.558
3.2	EPC14	0.685	0.655	9.96 × 10−5	1.00 × 10−4
	EPC17	0.315	0.345
3.3	EPC14	0.095	0.144	5.73 × 10−5	6.39 × 10−5
	EPC17	0.560	0.570
	EPC32	0.345	0.286
3.4	EPC17	1.000	1.000	2.70 × 10−1	2.70 × 10−1
3.5	EPC17	0.685	0.643	4.89 × 10−2	4.74 × 10−2
	EPC34	0.315	0.357
4.1	EPC5	0.685	0.643	4.51 × 10−3	4.56 × 10−3
	EPC13	0.315	0.357
4.2	EPC2	0.365	0.301	4.09 × 10−3	3.55 × 10−3
	EPC17	0.560	0.541
	EPC26	0.095	0.158
4.3	EPC2	0.365	0.294	3.38 × 10−2	3.06 × 10−2
	EPC17	0.560	0.558
	EPC18	0.095	0.148
5.1	EPC15	0.234	0.229	1.10 × 10−3	1.11 × 10−3
	EPC17	0.243	0.252
	EPC24	0.204	0.191
	EPC26	0.319	0.328
5.2	EPC13	0.479	0.456	1.99 × 10−3	1.98 × 10−3
	EPC16	0.521	0.544
6.1	EPC2	0.527	0.545	4.39 × 10−4	5.08 × 10−4
	EPC7	0.090	0.152
	EPC13	0.383	0.303
6.2	EPC1	0.298	0.321	1.56 × 10−3	1.45 × 10−3
	EPC2	0.175	0.134
	EPC7	0.229	0.227
	EPC13	0.298	0.318
7.1	EPC6	0.144	0.157	2.19 × 10−3	2.27 × 10−3
	EPC15	0.530	0.531
	EPC20	0.326	0.312
7.2	EPC25	0.685	0.655	5.69 × 10−4	5.62 × 10−4
	EPC37	0.315	0.345
7.3	EPC7	0.162	0.155	1.45 × 10−2	1.34 × 10−2
	EPC12	0.137	0.104
	EPC15	0.217	0.217
	EPC29	0.242	0.263
	EPC31	0.242	0.261
7.4	EPC2	0.055	0.132	2.04 × 10−2	2.66 × 10−2
	EPC7	0.346	0.263
	EPC21	0.055	0.131
	EPC26	0.544	0.474
7.5	EPC2	0.162	0.171	1.37 × 10−2	1.37 × 10−2
	EPC15	0.137	0.114
	EPC20	0.217	0.223
	EPC29	0.242	0.247
	EPC31	0.242	0.245

and Figure 1 demonstrate the calculation results of HEP. For each sub-task, Figure 1 is a graph that shows HEP distribution. Human reliability is increasing toward the center of the graph. Step 3.4 has the lowest human reliability value, but step 3.2 has the highest human reliability value. The APOE weights obtained as a result of expert knowledge and experience are provided in Table 8.

4. Results and Discussion

For the way of the boiler tube failure repair operation, human reliability assessment (HRA) can be calculated in accordance with the rule to find the HEP of operation tasks by the HEPs of sub-tasks given in

Table 9. Calculating the HEP of a task from the HEPs of its sub-tasks.

Logic Relation between Sub-Tasks	Dependence between Sub-Tasks	HEP of the Task
Parallel system	High dependency	$HE{P}_{Task}\approx Min\left\{HE{P}_{Sub-task i}\right\}$
	Low or no dependency	$HE{P}_{Task}=\Pi \left(HE{P}_{Sub-task i}\right)$
Serial system	High dependency	$HE{P}_{Task}=Max\left\{HE{P}_{Sub-task i}\right\}$
	Low or no dependency	$HE{P}_{Task}=Ʃ\left(HE{P}_{Sub-task i}\right)$

. In light of this information in Table 9, the sub-tasks of a system of dependencies are designated in parallel or series. If failure of any sub-tasks makes the system completely inoperable, sub-tasks that form the system are identified as a serial system. For the system to operate, the achievement of either of the sub-tasks is adequate, and thus the sub-tasks are evaluated to be parallel. In the system, if serial sub-tasks have got a high dependence, the maximum HEP value is chosen. If the dependencies of serial sub-tasks have no or low dependencies, the values of HEP are summed. On the other hand, in the system, if the parallel sub-tasks have a high dependence, the minimum value of HEP is chosen. If the dependencies of parallel sub-tasks have no or low dependencies, the values of HEP are multiplied [24,30,31,32].

The overall HEP was calculated for each boiler tube failure repair operation for 7 essential tasks and 26 sub-tasks, with the aid of Table 9. When analyzing step 1, four sub-steps should be performed appropriately to carry out step 1 successfully. Step 1 is considered a serial system when any of these four sub-steps fail. For this reason, the summed HEP value is found to be 7.11 × 10⁻² since four sub-steps have a low dependency. Similarly, step 2 will fail in the case any of the five sub-steps fail (high dependency, serial system). For this reason, the HEP value for step 2 is 1.56 × 10⁻¹. For step 3, the total HEP value is found to be 3.21 × 10⁻¹ (low dependency, serial system). For step 4, the total HEP value is obtained as 4.51 × 10⁻³ (high dependency, parallel system), 1.99 × 10⁻³ (high dependency, parallel system) for step 5, 1.56 × 10⁻³ (high dependency, serial system) for step 6, and 1.37 × 10⁻² (high dependency, serial system) for step 7.

To calculate the failure (HEP) value of the boiler tube failure repair process, the 7 basic steps and the 26 sub-steps must be calculated precisely and successfully. If any of the steps are not successful, the operation does not take place properly. The final HEP value is 3.21 × 10⁻¹ because there is a high dependency between them.

The relation between reliability (R) and failure (HEP) can be easily described with the formula R = 1 − HEP. Based on the precise calculation carried out, the reliability of the boiler tube failure repair was found to be 6.79 × 10⁻¹. Therefore, recovery is performed to reduce the HEP value and improve performance reliability.

In accordance with the findings, the estimated failure (HEP) values of each sub-task for the boiler tube failure repair operation are in the range of 9.96 × 10⁻⁵ to 2.70 × 10⁻¹. According to the results, sub-tasks that make a contribution to decreasing reliability are 2.1 (The load must be decreased by reducing the steam flow to the turbine and then the mill must be disabled in the boiler) and 3.4 (Check the Emergency Trip buttons and Fire Trip buttons). Remedial measures for sub-tasks 2.1 and 3.4 are proposed in

Table 10. Proposed remedial measures for sub-tasks 2.1 and 3.4.

Sub-Task	EPC(s)	Remedial Measures
2.1	EPC11	The planning must be carried out properly, it must be clear
		who is responsible for what task, and unnecessary work
		and confusion must be eliminated
		Teamwork and constructive feedback must be provided
	EPC17	The work program is a factor that can affect the
		course of the work, and the staff should be informed of the
		work to be done and the method to be used
		General operating parameters of the thermal power plant
		(boiler inlet temperature, main steam temperature, etc.)
		must be predetermined and known to the staff
	EPC19	Personnel should be required and given sufficient
		information
		Personnel must follow the instructions after adequate
		information has been given
3.4	EPC17	Emergency trip and fire trip buttons must be in working order
		The frequency of control of the emergency trip and fire trip buttons must be increased

.

Table 10 presents actions to decrease human error rates with the highest human reliability (HEP) values for the boiler tube failure repair process among the overall sub-steps. Actions of control were generated with the co-decision of five specialists participating in the work since they have extensive experience and knowledge about thermal power plant operations. Thus, the safety level of the process is increased, and the probability of human error is decreased.

5. Conclusions

There is a limited amount of research that explores the relationship between the causes of human error and the negative consequences. The underwork on human reliability in operations in thermal power plants illustrates the importance of working. To enhance the level of operational safety in the thermal power plant, it is of major significance to increase the reliability of operations.

This article presented an HRA of boiler tube failure repair operation, one of the most serious processes in a thermal power plant, to enhance human reliability and safety because possible dangerous incidents generated as a consequence of weaknesses in safety experienced in the thermal power plant are fundamentally connected to human error. The boiler tube failure repair process, which is one of the most serious processes and operations that can cause damage to the system and accidents, was analyzed using a hybrid of the HEART with the fuzzy AHP and SWARA methods. The HEP values obtained by both methods were identical. Within this scope, the research findings are reasonable and consistent.

The HEART has deficiencies in the calculation of the APOE due to individual characteristics of experts that influence their decision. In this study, to work around these shortcomings and acquire an APOE value with high reliability and accuracy, the HEART was merged with the SWARA and fuzzy AHP to combine the decision of the expert group.

Operations should identify and implement appropriate control strategies and methods for each activity and risk. In this hybrid approach, linked to the knowledge and experience of the five experts in the coal-fired thermal power plant, experts can achieve the desired low-risk value by conducting regular reviews, verification by sampling, reporting, analyses, and supervision. Consequently, in order to decrease the human error probability, it is required to take appropriate actions depending on the task-specific error-producing condition (EPC). Table 10 provides solution recommendations for sub-tasks 2.1 and 3.4. The conditions that generate errors in steps 2.1 and 3.4 were revised, and the human error probability was completely eliminated.

In the HEART method, it is difficult to obtain the assessed proportion effect value (APOE) because this value is obtained subjectively by the researcher or assessor. The APOE impact value in the study was evaluated with the opinion of more experts instead of a single expert. The common views of experts and the APOE values obtained through both the fuzzy AHP and SWARA methods were compared and obtained with close-to-one values. The contribution of the proposed methods in comparison to the conventional HEART method continues as follows:

• In the expert-based fuzzy AHP–HEART hybrid method, experts used the linguistic terms independently and made the value of criteria more reliable and consistent.
• In the SWARA–HEART hybrid method, five experts first sorted the criteria in order of importance and then weighted the criteria to analyze the risk. This method had changed risk values, unlike the conventional HEART method.
• With the two recommended hybrid methods, hazards were analyzed precisely and accurately. In addition, this study highlighted the availability of the fuzzy AHP–HEART and SWARA–HEART hybrid methods to conduct human-focused risk assessments on coal-fired thermal power plants in Turkey.
• In addition to this, the recommended method can also be practiced in several other serious processes in thermal power plants.
• Consequently, the findings of this study can help develop the safety indicators and achieve the sustainable objectives of thermal power plants by offering practical solutions to control and eliminate errors.

The most remarkable limitation of the study is the use of just five types of expert experience and knowledge. Therefore, further research can be carried out using different multi-criteria decision-making methods and empirical studies with the opinion of more experts. The outcomes of the research will aid managers, experts, and safety researchers in achieving the lowest possible human error in the energy industry.