A modified HEART method with FANP for human error assessment in high-speed railway dispatching tasks

International Journal of Industrial Ergonomics 67 (2018) 242–258

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International Journal of Industrial Ergonomics journal homepage: www.elsevier.com/locate/ergon

A modified HEART method with FANP for human error assessment in highspeed railway dispatching tasks

T

Weizhong Wanga,b,∗∗, Xinwang Liua,∗, Yong Qinc a

School of Economics and Management, Southeast University, Nanjing, Jiangsu, 211189, China School of Management, Anhui Science and Technology University, Bengbu, Anhui, 233090, China c State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Human error Fuzzy ANP Interdependence EPC High-speed railway

Human error is recognized as one of the main leading causes of high-speed railway accidents. Human error Assessment and Reduction Technique (HEART) as a human error probability assessment technique has been widely employed in various fields. However, the traditional HEART possess limitations in modelling the dependence relationships among Error Producing Conditions (EPCs) and the uncertainty of experts' estimation in practical application, which may affect its evaluation accuracy. In this paper, a modified HEART method with Railway Action Reliability Assessment (RARA) technique and fuzzy analytic network process (FANP) is proposed to assess human error probability in high-speed railway dispatching tasks. Firstly, the parameters Generic Error Probability (GEP) and Error Producing Conditions (EPCs) from the RARA technique are introduced into conventional HEART technique. Secondly, The FANP is utilized to handle the problems of interdependences and interaction among EPCs and the uncertainty exists in the experts' judgment. The proportion effect of each EPC is determined through ANP by consideration of correlation among EPCs. In addition, the triangle fuzzy number is used to simulate vagueness and uncertainty of expert's opinion. Finally, train occupancy loss in high-speed railway dispatching tasks is selected as an example to illustrate the applicability of the proposed method, and a sensitivity analysis is also performed to test the impact level of the importance degree of experts.

1. Introduction The high-speed railway with advantages of timesaving, low energy consumption and high punctuality rate has been regarded as the development direction of railway (Liu et al., 2015; Zhan et al., 2017). Nevertheless, some high-speed railway risk events and safety incidents have occurred in recent years (Liu et al., 2015). In order to effectively prevent risk in high-speed railway system, many automated operation control systems have been used (Wang and Fang, 2014). The presence of these systems displaces the dispatcher's routine work by system functions, however the dispatching tasks still heavily depend on highspeed railway dispatchers' capabilities in emergency situations. As the complexity of innovative technologies, the uncertainty of driving circumstance, and the frequency of human-machine interaction increases (Pan et al., 2016), so the Probabilistic Safety Assessments for highspeed railway systems should consider not only the contributions of hardware failures and environmental events but also the influence of human error. In addition, the human error has been recognized as a predominant

∗

causal factor in the occurrence of many accidents in numerous domains, and many researchers have devoted to developing and facilitating models and theories related to Human Reliability Analysis (HRA) (Dsouza and Lu, 2017; Pasquale et al., 2013). These HRA methodologies can be divided into three categories (Preischl and Hellmich, 2013; Reer, 2008): the first generation methodologies, the second generation methodologies and the third generation methodologies. In the literature of the first generation methodologies, there are a number of approaches proposed to measure the human operation reliability. The relatively widespread methods are the Human Cognitive Reliability Correlation (HCR), the Technique for Human Error Rate Prediction (THERP), the Success Likelihood Index Method (SLIM), the Human Error Assessment and Reduction Technique (HEART) and the Simplified Plant Analysis Risk-Human Reliability Assessment (SPAR-H). The second generation methodologies take into consideration the internal and external factors and the cognitive context that may affect the reliability of human operation. The Cognitive Reliability and Error Analysis Method (CREAM) and the A Technique for Human Event Analysis (ATHEANA) are the main second generation techniques applied to evaluate human error

Corresponding author. Corresponding author. School of Economics and Management, Southeast University, Nanjing, Jiangsu, 211189, China. E-mail addresses: [email protected] (W. Wang), [email protected] (X. Liu).

∗∗

https://doi.org/10.1016/j.ergon.2018.06.002 Received 28 September 2017; Received in revised form 9 March 2018; Accepted 1 June 2018 0169-8141/ © 2018 Elsevier B.V. All rights reserved.

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paper. Section 3 shows how proposed method can be employed to determine human error probability in high-speed railway dispatching task. The final section gives the conclusion and contribution of this study.

probability in industries (Maniram Kumar et al., 2017). The third generation methodologies are being improved in the base of shortcomings and limitations of the first and second generation HRA techniques. And besides, the third generation HRA techniques utilize present methods and/or tools to develop pre-existing approaches in HRA. According to Dsouza and Lu (2017), the third generation methods Nuclear Action Reliability Assessment (NARA) and Railway Action Reliability Assessment (RARA) are examples of the advanced versions of HEART known as the first generations HRA method. Since the method HEART is a simple and effective technique for human error likelihood assessment, it has been a common approach used in various scenarios with complex systems, such as energy plants, petrochemicals, off-shore platforms, maritime transportation, railway industries, etc.(Akyuz et al., 2016; Castiglia and Giardina, 2013; Castiglia et al., 2015; Deacon et al., 2013; Gibson et al., 2013; Petrillo et al., 2017). In the literature, some papers have developed advanced versions of HEART of the specific fields. Kirwan et al. (2004) introduced a method termed as nuclear action reliability assessment (NARA). The method is an improved version of the traditional HEART for monitoring human error in the nuclear field. Chadwick and Fallon (2012) applied the HEART technique to assess the reliability of tasks in healthcare, and proposed a modified HEART for human error probability evaluation of tasks related to healthcare. Similarly, Gibson et al. (2013) presented a railway human error analysis method called Railway Action Reliability Assessment (RARA) which is based on the specific rail context. Akyuz et al. (2016) developed a synthetic model to determine the marine specific EPCs for human error probability analysis in shipboard operations. In addition, there are some modified approaches applied to handle the inherent limitations of some EPCs in the literature. Regarding to uncertainty of experts' judgment in human error probability (HEP) calculation, some approaches have been applied in the literature to modify the HAERT method. Casamirra et al. (2009) and Castiglia and Giardina (2011) incorporated fault tree analysis, fuzzy set theory and HEART method to determine the human error probability in irradiation plants. Castiglia and Giardina (2013) employed a modified HEART based on fuzzy set theory, to assess operators' operation error probability in hydrogen refueling stations. Akyuz and Celik (2015) presented a developed HEART, which integrated the Analytic Hierarchy Process (AHP) method with the calculation of the proportion of the effect for calculating Error Producing Conditions (EPCs). Akyuz and Celik (2016a) proposed an extended HEART which incorporated with interval type-2 fuzzy sets to overcome the uncertainty of experts’ judgment. Maniram Kumar et al. (2017) combined the fuzzy logic theory and the conventional HEART to handle the linguistic expressions of expert elicitation approach which was used to distribute appropriate weight to EPCs. In the light of literature review, great headway about HEART has been made in various areas. In fact, this technique really applied in analysis for human error in high-speed railway dispatching system related issues has not gathered required attention. On the other hand, although many modified approaches have been applied to overcome the limitations and shortcomings of the HEART method, most of these works suffer from an obvious limitation: an inability to take into consideration dependent relationship among EPCs. To remedy the gap, this paper proposes a synthesis analytic method by incorporating RARA technique and FANP into conventional HEART method to evaluate HEP in High-speed railway. The two fundamental parameters Generic Error Probability (GEP) and EPCs from RARA technique are introduced into traditional HEART method by consideration of human error in railway. The FANP is introduced to handle the dependent relationship among EPCs and the uncertainties of expert elicitation. A modified HEART with RARA technique and FANP to assess human error probability will be presented for high-speed railway dispatching tasks. The reminder of this study is organized as follows. Section 2 expresses the method theory and proposed quantitative approach in this

2. Methodology This paper proposes a hybrid framework to evaluate HEP by incorporating HEART technique, RARA technique and FANP method in high-speed railway dispatching tasks. Therefore, the flowing sub-sections introduce the methodologies. 2.1. HEART technique The Human Error Assessment and Reduction Technique (HEART), preliminary put forward by Williams (1988), is a method enables rapid evaluation HEP with define probability failure values. The HEART method can be descripted by two fundamental parameters, which are the GEP and EPCs. The parameter GEP provides values of generic error probability which is carried out by analyst selecting a generic task type (GTT). There are eight qualitative descriptions of generic task type (from R1 to R8) corresponding to eight GEP values. The other parameter EPCs is Performance -Shaping Factors for human during the course of task that may influence the possibility of human error. The EPCs provides with a maximum amount by which the predicted nominal HEP can be multiplied. In the light of above, the human error probability in the HEART method is estimated by the following form:

HEPvalue = GEPvalue ×

⎧ ∏ [(EPCi − 1) Api + 1] ⎫⎬. ⎨ i ⎩ ⎭

(1)

where GEPvalue is the error probability value of relevant GTT, and EPCi is the ith (i = 1,2,3, ⋯n ) error promoting condition and Api (from 0 to 1) indicates expert's evaluation of the proportion effect for each ith EPC, which is termed as the importance of each EPC. As mentioned above, the conventional HEART method possess limitations in modelling dependence relationships among EPCs and uncertainties in error probability assessment. Thus, a framework proposed to modify the HEART technique by employing fuzzy linguistic expression and ANP for simulating the fuzzy judgment of analysts and developing an assessment method for the proportion effect factor Api . 2.2. RARA technique The Railway Action Reliability Assessment (RARA) technique is a methodological extension of traditional HEART technique, which was introduced by Gibson et al. (2013) as a quantitative approach for human error probability evaluation in railway industry. In the RARA technique, the human error probability calculation method is the same as Eq. (1), however, the fundamental parameters GEP and EPCs are redefined according to the context of operations in railway industry. The redefined fundamental parameters GEP and EPCs in RARA technique are provided in Table 1 and Table 2. According to the aforementioned RARA technique, the values of GEP and EPCs are more suitable for human error probability assessment in high-speed railway dispatching tasks. Therefore, the GEP and EPCs from the list of RARA are used to modify the traditional HEART for human error probability assessment in high-speed railway. 2.3. Analytic network process (ANP) The ANP method was preliminary introduced as an extension of AHP by (Saaty, 1996), and it is one of the most widely used methods applied in Multi-criteria Decision Making (MCDM) problems. The typical structural model for ANP is composed of the control level and network level two parts. The control level includes one analysis 243

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Table 1 Human generic error probability for generic task. Process

Code

Generic task

GEP

Thinking outside procedures More effortful and rule-based processes

R1 R2 R3 R4 R5 R6 R7 R8

Complex task requiring a high level of understanding and skill Identification of situation requiring interpretation of alarm or indication patterns Restore or shift a system to original or new state, following procedures with some checking. Fairly simple task performed rapidly or given insufficient or inadequate attention Skill-based tasks (manual, visual or communication) when there is some opportunity for confusion Simple response to a dedicated alarm and execution of actions covered in procedures Completely familiar, well designed, highly practiced task which is routine Respond correctly to system command even when there is an automated system providing accurate interpretation of system state

0.16 0.07 0.003 0.09 0.003 0.0004 0.0004 0.00002

More automated and skill-based processes

objective and some criteria, and the network level consists of clusters and the interdependence and feedback relationship among elements in the clusters (Cagri Tolga et al., 2013). As mentioned above, the schematic representation of the typical structural model for ANP can be shown as Fig. 1. The ANP method fundamentally comprises of a couple of main steps (Akyuz, 2017; Xu et al., 2015); (i) decomposing problem and constructing ANP model structure, (ii) forming the pair-wise comparison matrices and calculating the local and relative weights of criteria and sub-factors, (iii) establishing super matrix, (iv) obtaining final priorities weights of criteria and sub-factors by calculating limit super matrix. Since the ANP method can be implemented to model the interdependence and feedback between criteria factors and sub-factors, it is applied to define the interaction and dependence among the performance shaping factors of human error identified by EPCs in this paper.

Fig. 1. The typical structural model of ANP. x−l

⎧ m − l , l ≤ x ≤ m, ⎪ ∼ μ A (x ) = x − u , m ≤ x ≤ u, ⎨m−u ⎪ 0, x < l or x > m . ⎩

(2)

∼ Assume two triangular fuzzy numbers A1 = (l1, m1, u1) and ∼ A2 = (l2, m2 , u2) , the main algebraic operation for the two triangular fuzzy numbers can be provided as follows (Chou and Cheng, 2012):

2.4. Triangular fuzzy number (TFN)

∼ The TFN can be represented as A = (l, m , u) , where l and u denote fuzzy possibility between the lower and upper possible value of evaluation information (Chen, 2001). The membership function of this TFN can be represented as Eq. (2) and Fig. 2.

∼ ∼ A1 ⊕ A2 = (l1, m1, u1) ⊕ (l2, m2 , u2) = (l1 + l2, m1 + m2 , u1 + u2)

(3)

∼ ∼ A1 ⊗ A2 = (l1, m1, u1) ⊗ (l2, m2 , u2) = (l1 l2, m1 m2 , u1 u2)

(4)

Table 2 Consolidation of error producing conditions. Aspect

Code

Error promoting condition, EPC

Value

Task design (A)

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 B1 B2 B3 B4 B5 B6 B7 C1 D1 D2 E1 E2 E3 E4 E5 E6 F1

Unfamiliarity with a situation which is potentially important but which only occurs infrequently or which is novel A shortage of time available for error detection and correction A need to unlearn a technique and apply one which requires the application of an opposing philosophy The need to transfer specific knowledge from task to task without loss An impoverished quality of information conveyed by person-person interaction Little or no independent checking or testing of output. A conflict between immediate and long-term objectives Unclear allocation of function and responsibility A danger that finite physical capabilities will be exceeded Prolonged inactivity or highly repetitious cycling of half hour low mental workload tasks A low signal-noise ratio A means of suppressing or over-riding information of features which is too easily accessible No means of conveying spatial and functional information to operators in a form which they can readily assimilate A mismatch between an operator's model of the world and that imagined by a designer No obvious means of reversing an unintended action A channel capacity overload, particularly one caused by simultaneous presentation of non-redundant information Poor, ambiguous or ill-matched system feedback Operator inexperience Ambiguity in the required performance standard An impoverished quality of information conveyed by procedures A mismatch between perceived and real risk Fatigue from shift and work patterns High level emotional stress Little opportunity to exercise mind and body outside the immediate confines of a job Little or no intrinsic meaning in a task Low workforce morale A poor or hostile environment

17 11 8 5.5 3 3 2.5 1.6 1.4 1.1 10 9 8 8 8 6 4 3 5 3 4 2.6 2 1.8 1.4 1.2 8

Interface (B)

Competence management (C) Procedures (D) Person (E)

Environment (F)

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∼ ∼ Fig. 3. The degree of Possibility V (A2 ≥ A1 ) .

∼ ∼ ∼ ∼ V (A2 ≥ A1 ) = hgt (A1 ∩ A2 ) = μ A∼2 (z ) ⎧1, ⎪ = 0, ⎨ l1 − u2 ⎪ (m2 − u2) − (m1 − l1) , ⎩

Fig. 2. The triangular fuzzy number.

1 1 1⎞ ∼ −1 (A1 ) = (l1, m1, u1)−1 = ⎛ , , u ⎝ 1 m1 l1 ⎠ ⎜

(13)

where z is the ordinate of the highest intersection point Z between μ A∼1 ∼ ∼ and μ A∼2 (see Fig. 3). To compare A1 and A2 , we need each value of ∼ ∼ ∼ ∼ V (A2 ≥ A1 ) and V (A1 ≥ A2 ) .

⎟

(6) Step 3 The degree possibility for a convex fuzzy number to be greater ∼ than k convex fuzzy numbers Aj (j = 1,2,3, ⋯k ) can be derived as follows: ∼ ∼ ∼ ∼ ∼ ∼ ∼ V (A ≥ A1 , A2 , A3 , ⋯Ak ) = min V (A ≥ Aj ) (14)

2.5. Fuzzy extent analysis method According to the extent analysis method introduced by Chang (Zhu et al., 1999), the method can be formulated as follows: Let X = (x1, x2 , x3, ⋯, x n ) be an object set, and G = (g1, g2 , g3, ⋯gm) be a goal set. Each object is taken and extent analysis for each goal gi is performed, respectively. Therefore, m extent analysis value for each object can be obtained, with the following signs:

∼1 ∼2 ∼1 ∼m Agi , Agi , Agi , ⋯Agi , i = 1,2,3, ⋯n

m1 ≥ m2 ⎫ l1 ≥ u2 ⎪ ⎬ otherwise ⎪ ⎭

Assume that d′ (Pi ) = min V (Si ≥ Sk ) for k = 1,2,3, ⋯n, k ≠ i . Then the weight vector is computed by Eq. (15):

W ′ = (d′ (P1), d′ (P2), d′ (P3), ⋯d′ (Pn ))T

(15)

where Pi (i = 1,2,3, ⋯n) are numbers of elements.

(7)

Step 4 Via normalization, the normalized weight vectors are derived as follows:

∼j where, each Agi (j = 1,2,3, ⋯m) above is a triangular fuzzy number. The extent analysis method proposed by Chang employed in this paper is displayed as following four steps:

W = (d (P1), d (P2), d (P3), ⋯d (Pn ))T

(16)

where W is a non-fuzzy number. Step 1 The fuzzy synthetic extent value about the i th object can be defined as: m

S͠ i =

∼j

∑ Agi

n

⊗

j=1 m

∼j

∑ Agi j=1 n

m

∼j

⎛ l, ⎜∑ j ⎝ j=1

∑ ∑ Agi i=1 j=1

⎛ ∼j ⎞ A ⎜∑ ∑ gi ⎟ ⎝ i=1 j=1 ⎠

m

=

m

n

⎛ = ⎜∑ li , ⎝ i=1

The FANP applied in this paper can be displayed as the following steps:

(8)

m

Step 1 Acquiring the experts to conduct pair-wise comparison matrices of all the criteria and elements by adopting the linguistic scale given in Table 3. Step 2 Calculating the aggregated pair-wise comparison matrices by the following form:

⎞

∑ mj , ∑ u j ⎟ j=1

2.6. Calculation steps of FANP

−1

m

j=1

(9)

⎠

n

n

i=1

i=1

∑ mi , ∑ ui⎞⎟ ⎠

(10)

∼ ∼(t ) Z = φt ∗Z

(17) ∼(t ) where φt denotes the importance weight of tth expert, Z indicates the pair-wise comparison matrix provided by tth expert.

And then the inverse of the vector in Eq. (10) is computed such as Eq. (11): n

m

−1

⎛ ∼j ⎞ A ⎜∑ ∑ gi ⎟ ⎝ i=1 j=1 ⎠

=

1 1 1 ⎞ , n , n ⎟ n u m l ∑ ∑ ∑ i i i=1 i=1 i ⎠ ⎝ i=1 ⎛

⎜

Step 3 Calculating the local and relative importance weights for each element and examining the consistency ration (CR) of each pairwise comparison matrix. Step 4 Constructing the unweighted super-matrix. The unweighted super-matrix is a block matrix which consists of some sub-matrices such as local priorities, interdependence priorities and inner dependence priorities. And interdependence priorities and inner dependence priorities should be assigned as zero if the

(11)

∼ ∼ Step 2 the degree of possibility of A2 = (l2, m2 , u2) ≥ A1 = (l1, m1, u1) is obtained, as shown in the following equation: ∼ ∼ V (A2 ≥ A1 ) = sup [min (μ A∼1 (x ), μ A∼2 (y ) )] (12) y≥x And Eq. (12) can be equivalently expressed as Eq. (13): 245

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Step 2 Scenario station: the goal of this step is to define a set of real scenarios in the light of steps the dispatchers must complete. The scenarios provide information about the factors that may have an effect on the human reliability in all of the steps with high-speed railway dispatching task. These scenarios in highspeed railway dispatching task may include dispatchers' capability and experience, train operation and environment, task type and mental workload, etc. Step 3 Assigning the generic error probability value to each step of the tasks: This step consists of two sub-steps. The first step is to select the relevant generic task type in accordance with the task analysis result by the decision committee. The second step is to assign the relevant nominal value of human error probability to generic task type selected. Step 4 Identifying relevant EPCs: The relevant EPCs are the specific factors that may influence dispatchers' performance of dispatching task required. And the relevant EPCs are ascertained by the decision committee selecting from Table 2. Step 5 Calculating Api for each railway-specific EPC: The step is to deal with the problems that some EPCs possessed in the conventional HEART. Since the computation of Api is conducted by decision-maker with the hypothesis that each EPC is independent from one another in the traditional HEART. This paper provides a solution for the Api calculation by adoption of fuzzy set theory and ANP method to instead of the conventional Api calculation. Step 6 Obtaining the human error probability value: After calculation of Api , the proportion of maximum effect of each EPC can be ascertained, and it enables the decision maker to evaluate human reliability for each step of the defined tasks in the light of Eq. (1).

Table 3 Membership function for linguistic scale (Chou and Cheng, 2012). Linguistic scale

Numerical scale

Triangular fuzzy scale

Inverse of triangular fuzzy scale

Absolute importance Very to absolute Very importance Strong to very Strong importance Moderate to strong Moderate importance Equal to moderate Equal importance

9

(9, 9, 9)

(1/9, 1/9, 1/9)

8 7 6 5 4 3

(7, (6, (5, (4, (3, (2,

(1/9, (1/8, (1/7, (1/6, (1/5, (1/4,

2 1

(1, 2, 3) (1, 1, 1)

8, 7, 6, 5, 4, 3,

9) 8) 7) 6) 5) 4)

1/8, 1/7, 1/6, 1/5, 1/4, 1/3,

1/7) 1/6) 1/5) 1/4) 1/3) 1/2)

(1/3, 1/2, 1) (1, 1, 1)

criterion or sub-factor is determined to have no effect on another criterion or sub-factor. As noted above, the unweighted super-matrix representation of a structural model shown in Fig. 1 is expressed as follows:

Obgective Criteria Subfactors ⎤ ⎡ ⎢ ⎥ Obgective 0 0 0 Ws = ⎢ ⎥ Criteria W W 0 OC CC ⎢ ⎥ 0 WSC WSS ⎥ ⎢ ⎣ Subfactors ⎦

(18)

where WOC is a vector that indicates the effect of the “Objective” on the “Criteria”; WSC is a matrix that represents the impact of the “Criteria” on all elements of the “Sub-factors”. WCC and WSS represent the inner dependence among the “Criteria” on all elements of the “Sub-factors”, respectively. Step 5 Forming the weighted super-matrix. Since the columns in an unweighted super-matrix are possible not stochastic, as regard to ANP method, the unweighted super-matrix columns should be converted to stochastic columns. This transformation forms a weighted super-matrix and it can be performed by Eq. (19).

W = AW s = aij wijs

3. Case study This section presents an illustrative example to demonstrate the hybrid method proposed is applicable. Train occupancy loss is selected to as a case in this paper which has serious potential risks and can cause potential harm to personal security and train operation.

(19)

wijs

indicates the component in unweighted super-matrix; A is a where matrix that represents the corresponding cluster matrix weight. aij is an element of the corresponding weighted matrix.

3.1. Problem definition Train occupancy loss is one of the abnormal and unexpected conditions which will change the normal train operation plan and cause the initial transport plan and normal procedures failing. In this context, the dispatchers should take emergency procedures to resume train operation. However, the possibility of human errors of dispatchers increases significantly than normal conditions during this process. Accordingly, human error probability assessment is a significant support for organizational system to develop measures for risk mitigation in dispatching tasks. Consequently, it is certainly worthwhile to assess the probability of human error for every dispatching operation step during train occupancy loss.

Step 6 Obtaining the priorities for factors. The weights of the factors were derived by a limited matrix, which is formed by achieving the convergence of the weighted super-matrix. The process can be expressed as follows:

Wf = lim W n n →∞

(20)

2.7. Proposed approach for human error probability assessment In this part, a hybrid probability assessment method for human error in high-speed railway dispatching task is introduced. Therefore, the following systematic procedures of the proposed approach are illustrated in Fig. 4. And the general steps for this synthetic methodology are briefly introduced as follows:

3.2. Task analysis In 2014, China Railway Corporation (CRC) released the emergency disposal workflow of train occupancy loss. It also provided the specific steps in the dispatching task. Based on that information, the result of task analysis for train occupancy loss in high-speed railway dispatching tasks can be provided in Table 4.

Step 1 Task analysis: the first step of the proposed framework is to identify the steps that the dispatchers on Centralized Traffic Control System (CTC) must accomplish during an unexpected situation. This step is performed by hierarchical task analysis (HTA) in which the main tasks are broken down into sub-tasks (Akyuz and Celik, 2015; Wang and Fang, 2014). And the Human Error Probability of dispatchers can be calculated for each specific sub-task.

3.3. Definition of scenario As mentioned in Sub-section 2.7, the scenarios can be defined which may be responsible for human errors in train occupancy loss can be defined, as soon as the task analyses are accomplished. The scenarios of 246

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Fig. 4. The process of the proposed approach.

Table 4 HAT of train occupancy loss in high-speed railway dispatching tasks.

Table 5 Scenarios of train occupancy loss.

1. Reading information of train occupancy loss from system alarming signals 2. Handle relevant train with train occupancy loss 2.1 Identify the loss position of train occupancy 2.2 Inform driver of the train running in the sections to stop 2.3 Notify the train driver stopping within stations 2.4 Shift the train route to manual trigger 3. Formulate a plan for the train operation and arrange parking for rear station train 3.1 formulate a plan for the train operation 3.2 Inform the adjacent dispatching station of the receiving plan 3.3 Set the train route of relative train to manual trigger 4.Restore the train operation to original state 4.1 Check the action of de-registration 4.2 Notify the driver to resumed normal operation 4.3 Restore the train route to train automatic route trigger 4.4 Check the dispatching operation registry

Scenario Detail Dispatchers Drivers Environment & Trains Weather

Train occupancy loss scenario being in acceptable level getting a motor vehicle driver's license being in satisfactory level downpour

3.4. Selecting generic task types and identifying EPCs The task 2 (deal with the relevant train) shown in Table 4 is selected as an example to illustrate the proposed model, because of its significance in the disposal procedure for the whole task. The generic task types (GTTs) and EPCs of sub-task 2 in train occupancy loss are ascertained by professors in safety research about high-speed railway industry. Each professor is provided the scenarios shown in Table 5 and invited to select accurate GTTs for the list of each step in the loss of the train occupancy. Assessors are requested to identify the EPCs that may cause human error in each step simultaneously. The determination of GTTs and EPCs should be conducted according to the list of possible

train occupancy loss are given in Table 5. As operation environment, weather and equipment play a significant role in dispatching tasks, the environment and weather as well as equipment condition are designed. The capability of the drivers and dispatchers in the definition of scenario is also specified.

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experience from the literature (Akyuz and Celik, 2015; Zhong and Yao, 2017), the importance weights vector of eight experts is φt0 = (0.125,0.125,0.125,0.125,0.125.0.125,0.125,0.125) . And then, the aggregation results of pair-wise comparison matrices are derived by Eq. (17). Table 7 and Table 8 show a pair-wise comparison matrix of dimensions factors and a pair-wise comparison matrix of Person subfactors, respectively. Form Tables 7 and 8, the local weights for dimensions factors and Person sub-factors are derived by a similar type namely Chang's fuzzy extend analysis method (Section 2.5). In the following section, the process how weight vector of the dimension with respect to the human error probability is obtained in detail is provided. Firstly, the values of fuzzy synthetic extents with respect to the six dimensions are calculated by Eq. (8).

Table 6 Generic tasks and EPCs for task 2 (deal with the relevant train). Sub-task

Selected GTT

2. Handle relevant train with train occupancy loss 2.1 Identify the loss position of train R2 occupancy 2.2 Inform driver of the train R3 running in the sections to stop 2.3 Notify the train driver stopping R3 within stations 2.4 Shift the train route to manual R3 trigger

GEP value

Selected EPCs

7.00E-02

A2, A6, B1, C1 A2, A5, A6

3.00E-03 3.00E-03 3.00E-03

A2, A4, A5, A6 A6, B2, C1

statements in RARA as shown in Tables 1 and 2. Table 6 gives the results of selected GTTs and EPCs for task 2.

S͠ A = (6.540, 8.890, 12.491) ⊗ (1/64.370, 1/46.821, 1/33.332) = (0.102, 0.190, 0.375)

3.5. Calculation Api

S͠ B = (6.386, 8.655, 12.216) ⊗ (1/64.370, 1/46.821, 1/33.332) = (0.099, 0.185, 0.366)

The FANP proposed is utilized for calculation the effect of each railway EPC, which is illustrated in Table 2. For the application, there are three phases to illustrate how to determine the proportion effect of each EPC by FANP. The first phase defines the decision goal. The goal is to derive the weights of each EPC. The second phase establishes an analytical structure of EPCs. The analytical structure focuses on the interaction of dimensions and interdependence of criteria through interviews with professors in safety research about high-speed railway. The analytical structure of EPCs is provided as Fig. 5. In phase 3, a decision committee is established with eight experts. The committee consists of academic researchers and high-speed railway practitioners, who experienced in the field of the human error and human reliability for railway or high-speed railway. And then, the decision committee is invited to make independent pair-wise comparisons for dimension and criteria. (Independent pair-wise comparisons of eight experts are provided in the “Appendix” section). After that, drawing the

S͠ C = (3.219, 4.207, 5.765) ⊗ (1/64.370, 1/46.821, 1/33.332) = (0.050, 0.090, 0.173)

S͠ D = (3.338, 4.374, 5.934) ⊗ (1/64.370, 1/46.821, 1/33.332) = (0.052, 0.093, 0.178) S͠ E = (10.812, 16.607, 22.347) ⊗ (1/64.370, 1/46.821, 1/33.332) = (0.168, 0.355, 0.670)

S͠ F = (3.038, 4.088, 5.626) ⊗ (1/64.370, 1/46.821, 1/33.332) = (0.047, 0.087, 0.169) After that, the degrees of possibility are derived by using Eq. (13) as follows:

Fig. 5. The analytical structure of EPCs. 248

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Table 7 Pair-wise comparison matrix and local weight of dimensions factors.

A B C D E F Local weights

A

B

C

D

E

F

(1,1,1) (0.65,0.91,1.37) (0.33,0.47,0.68) (0.33,0.50,0.70) (1.36,1.83,2.40) (0.33,0.47,0.68) 0.258

(0.73,1.10,1.54) (1,1,1) (0.32,0.48,0.69) (0.33,0.50,0.71) (1.49,1.86,2.58) (0.33,0.48,0.68) 0.250

(1.47,2.11,3.07) (1.46,2.10,3.09) (1,1,1) (0.79,1.10,1.51) (2.53,4.07,5.62) (0.68,0.58,0.91) 0.008

(1.44,2.01,3.07) (1.42,2.00,3.01) (0.66,0.91,1.27) (1,1,1) (2.33,3.76,5.18) (0.63,0.99,1.43) 0.017

(0.42,0.55,0.74) (0.39,0.54,0.67) (0.18,0.25,0.40) (0.19,0.27,0.43) (1,1,1) (0.18,0.24,0.47) 0.464

(1.48,2.13,3.08) (1.47,2.11,3.08) (0.73,1.11,1.72) (0.70,1.01,1.59) (2.11,4.10,5.57) (1,1,1) 0.001

Table 8 Pair-wise comparison matrix and local weight of Person sub-factors.

E1 E2 E3 E4 E5 E6 Local weights

E1

E2

E3

E4

E5

E6

(1,1,1) (0.50,0.72,1.22) (0.49,0.71,1.17) (0.58,0.87,1.28) (0.64,0.81,1.12) (0.64,0.82,1.12) 0.195

(0.82,1.40,1.99) (1,1,1) (0.61,0.93,1.39) (0.82,1.40,1.97) (0.73,1.11,1.72) (0.73,1.11,1.72) 0.149

(0.85,1.42,2.03) (0.72,1.07,1.63) (1,1,1) (0.85,1.41,2.04) (0.78,1.18,1.78) (0.78,1.18,1.79) 0.141

(0.78,1.16,1.73) (0.51,0.72,1.22) (0.49,0.71,1.18) (1,1,1) (0.64,0.82,1.12) (0.64,0.83,1.13) 0.189

(0.89,1.23,1.55) (0.58,0.91,1.37) (0.56,0.85,1.28) (0.89,1.23,1.55) (1,1,1) (0.58,0.87,1.28) 0.166

(0.89,1.22,1.55) (0.58,0.90,1.37) (0.56,0.85,1.28) (0.89,1.21,1.55) (0.78,1.15,1.74) (1,1,1) 0.160

V (S͠ A ≥ S͠ B ) = 1.000 , V (S͠ A ≥ S͠ C ) = 1.000 , V (S͠ A ≥ S͠ E ) = 0.556, V (S͠ A ≥ S͠ F ) = 1.000 V (S͠ B ≥ S͠ A) = 0.981, V (S͠ B ≥ S͠ C ) = 1.000 , V (S͠ B ≥ S͠ E ) = 0.539, V (S͠ B ≥ S͠ F ) = 1.000 V (S͠ C ≥ S͠ A) = 0.415, V (S͠ C ≥ S͠ B ) = 0.436, V (S͠ C ≥ S͠ E ) = 0.018, V (S͠ C ≥ S͠ F ) = 1.000 V (S͠ D ≥ S͠ A) = 0.442 , V (S͠ D ≥ S͠ B ) = 0.463, V (S͠ D ≥ S͠ E ) = 0.037 , V (S͠ D ≥ S͠ F ) = 1.000 V (S͠ E ≥ S͠ A) = 1.000 , V (S͠ E ≥ S͠ B ) = 1.000 , V (S͠ E ≥ S͠ D ) = 1.000 , V (S͠ E ≥ S͠ F ) = 1.000 V (S͠ F ≥ S͠ B ) = 0.416, V (S͠ F ≥ S͠ A) = 0.396, V (S͠ F ≥ S͠ D ) = 0.950 , V (S͠ F ≥ S͠ E ) = 0.003

V (S͠ A ≥ S͠ D ) = 1.000 ,

Finally, the normalized weight vector of the dimension with respect to human error probability is obtained as follows:

V (S͠ B ≥ S͠ D ) = 1.000 ,

WV1 = (d (PA), d (PB ), d (PC ), d (PD ), d (PE ), d (PF ))T

V (S͠ C ≥ S͠ D ) = 0.971,

= (0.258, 0.250, 0.008, 0.017, 0.464, 0.001) By the same token, the normalized weight vector for the criteria with reference to task design is obtained as follows:

V (S͠ D ≥ S͠ C ) = 1.000 ,

V (S͠ E ≥ S͠ C ) = 1.000 ,

WV2 = (d (PA1), d (PA2), d (PA3), d (PA4 ), d (PA5), d (PA6), d (PA7), d (PA8), d (PA9), d (PA10))T = (0.114, 0.094, 0.072, 0.076, 0.118, 0.127, 0.085, 0.123, 0.092, 0.100)

V (S͠ F ≥ S͠ C ) = 0.979,

The normalized weight vector for the criteria with respect to interface is computed as follows:

For every pair-wise comparison, the weight vector can be calculated by Eq. (15) as follows:

WV3 = (d (PB1), d (PB2), d (PB3), d (PB 4 ), d (PB5), d (PB6), d (PB7))T d′ (PA) = min V (S͠ A ≥ S͠ B, S͠ C , S͠ D, S͠ E , S͠ F )

= (0.138, 0.193, 0.106, 0.115, 0.223, 0.127, 0.099)

= min(1.000, 1.000, 1.000, 0.556, 1.000) = 0.556 d′ (PB ) = min V (S͠ B ≥ S͠ A, S͠ C , S͠ D, S͠ E , S͠ F )

The normalized weight vector for the criteria with respect to procedures is calculated as follows:

= min(0.981, 1.000, 1.000, 0.539, 1.000) = 0.539 d′ (PC ) = min V (S͠ C ≥ S͠ A, S͠ B, S͠ D, S͠ E , S͠ F )

WV4 = (d (PD1), d (PD2))T = (0.522, 0.478)

= min(0.415, 0.436, 0.971, 0.018, 1.000) = 0.018 d′ (PD ) = min V (S͠ D ≥ S͠ A, S͠ B, S͠ C , S͠ E , S͠ F )

The normalized weight vector for the criteria with respect to person is obtained as follows:

= min(0.442, 0.463, 1.000, 0.037, 1.000) = 0.037 d′ (PE ) = min V (S͠ E ≥ S͠ A, S͠ B, S͠ C , S͠ D, S͠ F )

WV5 = (d (PE1), d (PE 2), d (PE 3), d (PE 4 ), d (PE5), d (PE 6))T = (0.195, 0.149, 0.141, 0.189, 0.166, 0.160)

= min(1.000, 1.000, 1.000, 1.000, 1.000) = 1.000 d′ (PF ) = min V (S͠ F ≥ S͠ A, S͠ B, S͠ C , S͠ D, S͠ E )

In accordance with the calculation steps of FANP, the eight experts compare the interdependence relationship with respect to criteria, as well as the inner dependence of sub-factors. (Independent importance assessment of interdependence and inner dependence relationships of eight experts are provided in the “Appendix” section). Table 9 and

= min(0.396, 0.416, 0.979, 0.950, 0.003) = 0.003 WV ′ = (0.556, 0.539, 0.018, 0.037, 1.000, 0.003)

Table 9 Importance assessment of interdependence relationship with respect to “A″ Controlled factor: A

A

B

C

D

E

A B C D E Relative weights

(1,1,1) (0.65,0.93,1.37) (0.35,0.49,0.84) (0.33,0.50,0.82) (1.09,1.57,2.45) 0.255

(0.73,1.08,1.54) (1,1,1) (0.34,0.50,1.01) (0.33,0.50,0.99) (1.49,1.86,2.58) 0.241

(1.19,2.01,2.88) (0.99,1.99,2.90) (1,1,1) (0.78,1.09,1.52) (0.78,1.09,1.52) 0.022

(1.21,1.99,3.03) (1.01,1.99,3.01) (0.66,0.91,1.28) (1,1,1) (2.32,3.73,5.13) 0.038

(0.41,0.64,0.91) (0.39,0.54,0.67) (0.18,0.24,0.39) (0.19,0.27,0.43) (1,1,1) 0.444

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Table 10 Importance assessment of inner dependence relationship with controlled factor “B6″ Controlled factor: B6

B1

B3

B4

B7

B1 B3 B4 B7 Relative weights

(1,1,1) (0.62,0.82,1.22) (0.63,0.84,1.14) (0.61,0.75,1.09) 0.290

(0.82,1.23,1.59) (1,1,1) (0.73,1.22,1.69) (0.59,0.82,1.34) 0.238

(0.88,1.19,1.59) (0.59,0.82,1.36) (1,1,1) (0.58,0.99,1.48) 0.252

(0.91,1.34,1.65) (0.75,1.22,1.67) (0.68,1.01,1.69) (1,1,1) 0.219

Fig. 6. Un-weighted super-matrix.

provided in Table 12.

Table 10 show a pair-wise comparison matrix with controlled factors: A (Task design) and B6 (A channel capacity overload, particularly one caused by simultaneous presentation of non-redundant information), respectively. The results of priorities weights for EPCs are derived by calculating the limit matrix. The computation process mention in 2.6 is completed through utilizing ANP version 2.6.0 of Super Decision software. The results of un-weighted super matrix and weighted super matrix can be seen in Fig. 6 and Fig. 7. After accomplishing the steps mentioned, the weight of each EPC in the modified HEART can also be calculated by using the ANP version 2.6.0 of Super Decision software. The result is provided in Fig. 8.

3.7. Analysis of the results In the light of the calculation result of the HEP values for train occupancy loss, the mean value of HEP for the whole dispatching process of train occupancy loss is 3.880E-02. The sub-task “Restore the train operation to original state” seems the most likely to cause human error in the dispatching process of train occupancy loss, because of the mean value of this step is the highest. Accordingly, the lowest mean value of HEP comes from the sub-task “Formulate a plan for the train operation and arrange parking for rear station train”. In addition, Fig. 9 reveals the distribution curve of all dispatching steps of train occupancy loss on the basis of HEP computation. According to Fig. 9, there are eight steps' HEP values significantly below the mean value of HEP. It means that most of the steps of the whole dispatching process of train occupancy loss have relatively low probability to cause human error. According to the GTTs of each step, it also indicates that dispatchers may have better performance for skill-

3.6. Obtaining HEP HEP value of each sub-task for task 2 (deal with the relevant train) are derived by Eq. (1). The calculation results are shown as Table 11. At the same way, we can obtain all the HEP values for the high-speed railway dispatching process of train occupancy loss. The result is 250

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Fig. 7. Weighted super-matrix.

with dispatchers. It indicates that the framework proposed in this paper is applicable. Particularly, the step 4.2 (Notify the driver to resumed normal operation) has the highest HEP value. It is primarily because of the influence of shortage of time available for error detection and correction and mismatch between perceived and real risk. This human error may affect the train operation safety and the normal operation of the following trains. Moreover, the step 4.4 (Restore the train route to train automatic route trigger) has the second highest HEP value. It is mainly because of the GEP value and Api value. The GTT of this step has

based tasks than the rule-based one. On the other hand, 4 of 12 steps’ HEP values are far higher than the mean. It is worthwhile to note that there are 3 of 4 steps whose HEP values higher than the mean appear in the sub-task 4 (Restore the train operation to original state). This may be caused by the sub-task 4 is at the end of the process of the task where human error probability can be influenced by fatigue of shifting work patterns and security awareness decreasing. As mentioned above, there are 4 steps’ HEP values higher than the mean. This calculation result is consistent with the result of interview

Fig. 8. The weight of each EPC. 251

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Table 11 Calculation result for task 2 (deal with the relevant train).

Table 14 The sensitivity according to different experts’ importance weights.

2

GEP value

EPC

EPC value

Api

2.1 Identify the loss position of train occupancy

7.00E-02

2.2 Inform driver of the train running in the sections to stop 2.3 Notify the train driver stopping within stations

3.00E-03

2.4 Shift the train route to manual trigger

3.00E-03

A2 A6 B1 C1 A2 A5 A6 A2 A4 A5 A6 A6 B2 C1

11 3 10 3 11 3 3 11 5.5 3 3 3 9 3

0.0169 0.0067 0.0174 0.0054 0.0169 0.0837 0.0067 0.0169 0.0125 0.0837 0.0067 0.0067 0.0047 0.0054

3.00E-03

value

HEP value

Task

Case 0

Case 1

Case 2

Case 3

9.695E-02

1 2.1 2.2 2.3 2.4 3.1 3.2 3.3 4.1 4.2 4.3 4.4

6.119E-03 9.695E-02 4.149E-03 4.382E-03 3.189E-03 5.025E-04 3.754E-03 6.174E-03 9.121E-02 1.460E-01 3.639E-03 9.952E-02

6.093E-03 9.589E-02 4.117E-03 4.361E-03 3.181E-03 5.013E-04 4.500E-03 6.151E-03 9.131E-02 1.456E-01 3.603E-03 9.966E-02

6.087E-03 9.686E-02 4.146E-03 4.383E-03 3.193E-03 5.031E-04 4.469E-03 6.145E-03 9.117E-02 1.452E-01 3.642E-03 9.954E-02

6.067E-03 9.672E-02 4.155E-03 4.390E-03 3.193E-03 5.033E-04 4.464E-03 6.147E-03 9.112E-02 1.452E-01 3.651E-03 9.973E-02

4.149E-03

4.382E-03

3.189E-03

affect associated with EPC A2. Similarly, the HEP value of step 4.1 is mainly because of the GEP value. The result analysis shows that, human error probability of dispatching tasks depends on GEP value, the maximum affect associated with an EPC and proportion effect. The organizational system should dissect the dependence mechanism and main factors to limit the negative result that increase the possibility of human error. It is also important to improve man-machine interaction by consideration of population stereotypes during the instrumentation design process.

Table 12 HEP computation for HAT of train occupancy loss. Sub-task

GTT

EPC

HEP value

1 2 2.1 2.2 2.3 2.4 3 3.1 3.2 3.3 4 4.1 4.2 4.3 4.4

R5

A2, A7, A10, B7, E1

6.119E-03

R2 R3 R3 R3

A2, A2, A2, A6,

A6, B1, C1 A5, A6 A4, A5, A6 B2, C1

9.695E-02 4.149E-03 4.382E-03 3.189E-03

R7 R3 R3

A2, A4, A6, D2 A2, A4, A6 A2, B2,E1

5.025E-04 3.754E-03 6.174E-03

R4 R2 R3 R4

A6 A2, A6, B2, E1 A2, B2 A6, E5, E6

9.121E-02 1.460E-01 3.639E-03 9.952E-02

3.8. Sensitivity analysis To test the influence of experts' importance weights on the aggregation stage and HEP values, a sensitivity analysis is conducted by changing the vector of experts' importance weights. The different experts' importance weights are shown in Table 13. For each vector of experts' importance weights, we can obtain different HEP values for the whole steps with train occupancy loss by means of the calculation process presented in section 3.5. The sensitivity analysis results according to different experts’ importance weights are shown as Table 14 and Fig. 10. It should be noted that, the case 0 provided in Table 14 means the importance weight of each expert is φt0 = (0.125,0.125,0.125,0.125,0.125.0.125,0.125,0.125) . As it can be seen from Table 14, the HEP value of each subtask is indeed influenced by changing the importance weights of experts. This indicates that the HEP values of these subtasks are different in terms of the degree of importance of each expert. For example, the HEP value of task 2.1 in four case are different according to the experts’ importance weights changing. As depicted in Fig. 10, human error probability of each subtask in four case has the same priority ranking, it means that the importance weights of experts have no impact on determination of the most likely error in high-speed railway dispatching tasks. On the other hand, the HEP values of subtasks in four case are not significant different, it indicates that the importance weights of experts have no significant impact on the HEP calculation. This result is consistent with the relevant Kyriakidis et al. (2018) study.

Fig. 9. HEP values for the whole steps with train occupancy loss.

the highest GEP value in the whole dispatching process, and the Api value of EPC E6 is the second largest. Another important steps are 2.1 (Identify the loss position of train occupancy) and 4.1 (Check the action of de-registration) where HEP values are considerable. The HEP value of step 2.1 is mainly influenced by the GEP value and the maximum

4. Discussion The human error is a main factor of recent high-speed railway accident, the quantification of human error probability is a significant procedure for the control of human error (Castillo et al., 2016). The

Table 13 The importance weights of experts.

Case 1 Case 2 Case 3

expert 1

expert 2

expert 3

expert 4

expert 5

expert 6

expert 7

expert 8

0.125 0.124 0.126

0.126 0.127 0.128

0.131 0.130 0.135

0.120 0.121 0.118

0.117 0.119 0.115

0.127 0.125 0.124

0.128 0.127 0.126

0.126 0.127 0.128

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Fig. 10. Sensitivity according to different experts' importance weights.

that the importance weights of experts have no significant impact on priority ranking of human error priority of each subtask, though it seems that the HEP calculation is influenced by the degree of importance of each expert.

conventional HEART technique is a useful tool to assess human error probability, however, this technique may has some weaknesses during HEP calculation in high-speed railway industry. To overcome these weakness, firstly, this paper selects the GEP and EPCs from the list of RARA technique to make a consistent HEP assessment method for human error across the high-speed railway industry. Secondly, the FANP is used to determine the proportion effect ( Api ) by consideration the dependencies among EPCs. Finally, a modified HEART technique is proposed and applied to evaluate the human error probability in high-speed railway dispatching tasks. The current research provides new insights into the HEART technique for human error analysis in high-speed railway industry. In the past, the Api calculation did not take the dependencies into consideration. However, during this paper, the dependencies among EPCs is highlighted in Api calculation, this is supported by relevant literature (Kyriakidis et al., 2018; Maniram Kumar et al., 2017). This study will also help high-speed railway industry to identify human error operations and to reduce the influence of human error.

4.2. Practical contribution The current study also provides practical contributions to operators, professionals, safety managers and other stakeholders relevant to highspeed railway industry. These practical contributions can be summarized as follows: (i) The proposed method can be utilized to evaluate the influence degree of each EPC on human error, accounting for the interaction and dependence relationships among the EPCs. (ii) The proposed approach can be employed to determine the most erroneous operation in the whole operation tasks by calculating the HEP value. (iii) The proposed framework can be used to assess human reliability for different operations in high-speed railway such as maintenance operations, fault diagnosis operations, etc. Therefore, stakeholders can also adopt the approach to improve safety of high-speed railway operations.

4.1. Academic contribution This paper has a number of academic contributions to the literature on the HEART technique in high-speed railway operations, which can be reported as follows:

4.3. Limitations of the proposed approach

(i) Although some research studies (Akyuz and Celik, 2015, 2016b; Maniram Kumar et al., 2017) in HEART technique have focused on the proportion effect ( Api ) calculation, none of them have provided an weight calculation approach to determine Api value by consideration of dependence relationships among EPCs. This study incorporates the triangular fuzzy number and ANP into the HEART to calculate the Api value. This makes the proposed HEART technique can capture not only the dependencies among EPCs but also the uncertainty of expert judgment. (ii) To the best of author's knowledge, the combination of triangular fuzzy number, ANP and HEART to assess human error probability is not studied in the existing works on human reliability evaluation problems for high-speed railway operations. For the first time, this study combines the HEART technique, RARA technique and FANP method to assess the human error probability in high-speed railway operations from the perspective of modelling the dependencies among EPCs. (iii) The proposed approach undertakes a sensitivity analysis by which to test the influence of the different types of experts, since each expert of the decision committee may possess different priorities. In the case study of this paper, the sensitivity analysis indicates

Although the modified HEART approach is highly beneficial to evaluate human error probability in high-speed railway dispatching operations, but the limitations of this paper should be acknowledged. The main ones are provided as follows: (i) As the CTC in high-speed railway is more automatic and complex than general speed railway, the EPCs used in this paper may cause a bias of human error probability evaluation results. For the calculation of HEP, the values of parameters GEP and EPCs are the most influence factors. This makes the parameters GEP and EPCs from the list of the context of conventional railway operations may not be able to capture unique features of high-speed railway dispatching operations. (ii) There are twenty-seven EPCs in the proposed approach, the complexity of the proportion effect ( Api ) calculation increases. For the Api calculation, a larger number of importance comparison matrices should be conducted by experts, which makes this method slow and difficult, especially for those assessors with no experience in ANP method. 253

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5. Conclusions

human error probability evaluation of high-speed railway dispatchers in dispatching task. In conclusion, the hybrid method proposed in this paper provides a practical application tool to perform human reliability prediction or assessment in high-speed railway dispatching tasks. The current work presents a hybrid method for evaluation human reliability in high-speed railway dispatching tasks based on the railway EPCs. However, as the CTC in high-speed railway is more automatic and complex than general speed railway, the railway EPCs used in this paper may cause a bias of human error probability evaluation results. A more standard and applicable performance shaping factors for the process of human error probability assessment of high-speed railway dispatchers can be a further work.

Human error probability analysis or human reliability assessment is considered as a technique to quantify the possibility of human error and provide decision maker information on making safe decisions in railway tasks. The purpose of this paper is to introduce a hybrid method for human error probability evaluation in high-speed railway dispatching tasks. Despite that HEART has been widely employed to analyze human reliability in various fields on account of its validity and easy accessibility. A number of developments in the framework of HEART techniques have been conducted because of the problems exist in some EPCs. In this paper, a HEART framework based on triangle fuzzy number, FANP and RARA technique is proposed to overcome the shortcoming of EPCs. In the presented framework, the parameters GET and EPCs from the RARA technique are introduced into HEART technique to make a consistent approach to evaluate human error probability in high-speed railway. Triangle fuzzy number is to handle the uncertainty and capture the experts’ subjective judgment information. In addition, utilization of FANP is to deal with the interrelations and dependence among EPCs during the proportion effect ( Api ) calculation. Furthermore, an illustrative example was used to demonstrate the framework is applicable in

Acknowledgments The work was supported by the National Science Foundation of China (71171048, 71371049 and 71771051) and Key Discipline Project (AKZDXK2015B05) and Anhui Province Philosophy and Social Science Planning Youth Project (AHSKQ2016D25).

Appendix A. Supplementary data Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.ergon.2018.06.002. Appendix Table A.1 Pair-wise comparison matrix for dimensions factors of eight experts Experts Expert 1

Expert 2

Expert 3

Expert 4

Expert 5

A B C D E F A B C D E F A B C D E F A B C D E F A B C D E F

A

B

C

D

E

(1,1,1) (0.66,0.93,1.30) (0.34,0.49,0.68) (0.33,0.51,0.69) (1.27,1.64,2.70) (0.34,0.48,0.72) (1,1,1) (0.65,0.87,1.47) (0.32,0.45,0.74) (0.34,0.53,0.72) (1.32,1.72,2.04) (0.32,0.47,0.68) (1,1,1) (0.70,0.83,1.37) (0.33,0.48,0.71) (0.32,0.47,0.66) (1.45,2.04,2.33) (0.33,0.49,0.70) (1,1,1) (0.63,0.95,1.39) (0.32,0.47,0.65) (0.33,0.50,0.68) (1.37,2.22,2.22) (0.33,0.47,0.66) (1,1,1) (0.62,0.97,1.35) (0.35,0.46,0.68) (0.32,0.48,0.69) (1.47,1.82,2.56) (0.32,0.46,0.66)

(0.77,1.08,1.51) (1,1,1) (0.32,0.48,0.71) (0.34,0.49,0.69) (1.45,1.96,2.38) (0.32,0.47,0.66) (0.68,1.15,1.54) (1,1,1) (0.33,0.49,0.67) (0.33,0.48,0.71) (1.61,2.04,2.86) (0.31,0.49,0.67) (0.73,1.21,1.42) (1,1,1) (0.34,0.47,0.70) (0.32,0.52,0.72) (1.49,1.85,2.56) (0.33,0.47,0.70) (0.72,1.05,1.59) (1,1,1) (0.32,0.51,0.68) (0.34,0.51,0.70) (1.47,1.79,2.33) (0.33,0.48,0.69) (0.74,1.03,1.61) (1,1,1) (0.32,0.46,0.67) (0.33,0.50,0.70) (1.59,1.92,2.63) (0.34,0.46,0.65)

(1.47,2.03,2.98) (1.41,2.10,3.17) (1,1,1) (0.79,1.05,1.64) (2.86,3.70,7.69) (0.57,0.93,1.37) (1.35,2.21,3.12) (1.49,2.03,3.05) (1,1,1) (0.81,1.14,1.49) (2.38,4.17,4.76) (0.58,0.90,1.41) (1.41,2.08,3.07) (1.43,2.15,2.98) (1,1,1) (0.76,1.08,1.52) (2.56,4.00,5.26) (0.59,0.88,1.33) (1.53,2.11,3.15) (1.46,1.95,3.09) (1,1,1) (0.78,1.16,1.59) (2.50,3.85,6.67) (0.57,0.90,1.45) (1.47,2.19,2.89) (1.50,2.18,3.15) (1,1,1) (0.80,1.09,1.45) (2.44,3.57,5.88) (0.58,0.93,1.39)

(1.45,1.98,3.01) (1.45,2.03,2.98) (0.61,0.95,1.27) (1,1,1) (2.44,3.45,6.67) (0.65,0.97,1.47) (1.38,1.89,2.98) (1.40,2.07,3.05) (0.67,0.88,1.23) (1,1,1) (2.56,3.85,5.56) (0.62,0.98,1.39) (1.51,2.12,3.09) (1.39,1.93,3.08) (0.66,0.93,1.31) (1,1,1) (2.22,4.00,4.76) (0.63,0.99,1.41) (1.48,2.01,3.07) (1.43,1.98,2.95) (0.63,0.86,1.29) (1,1,1) (2.17,3.70,4.35) (0.64,1.02,1.43) (1.44,2.08,3.12) (1.42,2.00,3.01) (0.69,0.92,1.25) (1,1,1) (2.33,3.57,5.26) (0.63,0.95,1.45)

(0.37,0.61,0.79) (1.39,2.08,2.95) (0.42,0.51,0.69) (1.51,2.11,3.08) (0.13,0.27,0.35) (0.73,1.08,1.75) (0.15,0.29,0.41) (0.68,1.03,1.53) (1,1,1) (2.08,3.98,5.59) (0.18,0.25,0.48) (1,1,1) (0.49,0.58,0.76) (1.48,2.15,3.15) (0.35,0.49,0.62) (1.49,2.05,3.21) (0.21,0.24,0.42) (0.71,1.11,1.72) (0.18,0.26,0.39) (0.72,1.02,1.62) (1,1,1) (2.15,4.08,5.43) (0.18,0.25,0.47) (1,1,1) (0.43,0.49,0.69) (1.42,2.03,2.99) (0.39,0.54,0.67) (1.43,2.14,3.01) (0.19,0.25,0.39) (0.75,1.13,1.69) (0.21,0.25,0.45) (0.71,1.01,1.59) (1,1,1) (2.03,4.15,5.49) (0.18,0.24,0.49) (1,1,1) (0.45,0.45,0.73) (1.52,2.13,3.07) (0.43,0.56,0.68) (1.45,2.08,3.03) (0.15,0.26,0.40) (0.69,1.11,1.76) (0.23,0.27,0.46) (0.70,0.98,1.57) (1,1,1) (2.11,4.21,5.56) (0.18,0.24,0.47) (1,1,1) (0.39,0.55,0.68) (1.51,2.18,3.09) (0.38,0.52,0.63) (1.53,2.16,2.97) (0.17,0.28,0.41) (0.72,1.07,1.72) (0.19,0.28,0.43) (0.69,1.05,1.59) (1,1,1) (2.13,3.93,5.71) (0.18,0.25,0.47) (1,1,1) (continued on next page)

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Table A.1 (continued) Experts Expert 6

Expert 7

Expert 8

A B C D E F A B C D E F A B C D E F

A

B

C

D

E

F

(1,1,1) (0.64,0.85,1.49) (0.32,0.47,0.66) (0.33,0.50,0.68) (1.35,1.75,2.38) (0.31,0.46,0.69) (1,1,1) (0.65,0.99,1.28) (0.31,0.49,0.63) (0.31,0.49,0.71) (1.32,1.79,2.44) (0.32,0.46,0.65) (1,1,1) (0.65,0.91,1.32) (0.33,0.48,0.70) (0.33,0.50,0.72) (1.35,1.82,2.70) (0.33,0.47,0.67)

(0.67,1.18,1.57) (1,1,1) (0.34,0.48,0.68) (0.34,0.52,0.68) (1.45,1.75,2.44) (0.32,0.49,0.69) (0.78,1.01,1.53) (1,1,1) (0.32,0.46,0.72) (0.32,0.49,0.73) (1.47,1.72,2.70) (0.32,0.47,0.68) (0.76,1.10,1.55) (1,1,1) (0.31,0.48,0.66) (0.33,0.48,0.70) (1.49,1.85,2.63) (0.32,0.47,0.68)

(1.51,2.15,3.11) (1.46,2.10,2.91) (1,1,1) (0.81,1.12,1.54) (2.33,4.35,5.56) (0.59,0.87,1.35) (1.59,2.05,3.19) (1.39,2.19,3.12) (1,1,1) (0.78,1.10,1.47) (2.56,3.85,5.26) (0.58,0.88,1.37) (1.42,2.09,3.07) (1.52,2.09,3.21) (1,1,1) (0.78,1.08,1.54) (2.50,4.17,5.56) (0.57,0.89,1.35)

(1.46,1.99,3.07) (1.46,1.91,2.91) (0.65,0.89,1.24) (1,1,1) (2.22,3.85,5.88) (0.62,0.99,1.33) (1.41,2.03,3.19) (1.37,2.03,3.08) (0.68,0.91,1.28) (1,1,1) (2.27,3.45,5.26) (0.62,1.01,1.45) (1.39,2.01,3.01) (1.42,2.07,3.01) (0.65,0.93,1.27) (1,1,1) (2.33,3.70,5.56) (0.63,0.98,1.47)

(0.42,0.57,0.74) (0.41,0.57,0.69) (0.18,0.23,0.43) (0.17,0.26,0.45) (1,1,1) (0.18,0.24,0.48) (0.41,0.56,0.76) (0.37,0.58,0.68) (0.19,0.26,0.39) (0.19,0.29,0.44) (1,1,1) (0.17,0.24,0.46) (0.37,0.55,0.74) (0.38,0.54,0.67) (0.18,0.24,0.40) (0.18,0.27,0.43) (1,1,1) (0.18,0.24,0.48)

(1.45,2.16,3.18) (1.44,2.06,3.15) (0.74,1.15,1.69) (0.75,1.01,1.62) (2.08,4.16,5.46) (1,1,1) (1.54,2.19,3.17) (1.46,2.15,3.11) (0.73,1.13,1.71) (0.69,0.99,1.61) (2.17,4.12,5.75) (1,1,1) (1.49,2.13,3.02) (1.47,2.11,3.09) (0.74,1.12,1.74) (0.68,1.02,1.58) (2.09,4.13,5.57) (1,1,1)

E6

Table A.2 Pair-wise comparison matrix for Person sub-factors of eight experts Experts Expert 1

Expert 2

Expert 3

Expert 4

Expert 5

Expert 6

E1 E2 E3 E4 E5 E6 E1 E2 E3 E4 E5 E6 E1 E2 E3 E4 E5 E6 E1 E2 E3 E4 E5 E6 E1 E2 E3 E4 E5 E6 E1 E2 E3 E4 E5

E1

E2

E3

E4

E5

(1,1,1) (0.49,0.72,1.22) (0.49,0.72,1.18) (0.57,0.89,1.32) (0.66,0.81,1.15) (0.66,0.81,1.15) (1,1,1) (0.51,0.71,1.28) (0.51,0.70,1.23) (0.58,0.85,1.28) (0.65,0.85,1.12) (0.65,0.85,1.12) (1,1,1) (0.50,0.71,1.22) (0.49,0.69,1.15) (0.57,0.86,1.23) (0.65,0.81,1.18) (0.65,0.81,1.18) (1,1,1) (0.51,0.70,1.20) (0.49,0.71,1.18) (0.58,0.88,1.33) (0.64,0.79,1.09) (0.64,0.79,1.09) (1,1,1) (0.50,0.73,1.22) (0.49,0.70,1.20) (0.58,0.85,1.28) (0.63,0.84,1.14) (0.63,0.84,1.14) (1,1,1) (0.49,0.71,1.27) (0.51,0.69,1.12) (0.59,0.86,1.27) (0.66,0.81,1.12)

(0.82,1.38,2.05) (1,1,1) (0.63,0.93,1.45) (0.79,1.39,1.89) (0.71,1.10,1.79) (0.71,1.10,1.79) (0.78,1.14,1.97) (1,1,1) (0.61,0.96,1.39) (0.85,1.33,2.04) (0.74,1.15,1.72) (0.74,1.15,1.72) (0.82,1.40,1.99) (1,1,1) (0.61,0.95,1.41) (0.82,1.37,1.96) (0.73,1.09,1.69) (0.73,1.09,1.69) (0.83,1.42,1.96) (1,1,1) (0.63,0.93,1.47) (0.81,1.41,2.08) (0.72,1.10,1.89) (0.72,1.10,1.89) (0.82,1.37,1.99) (1,1,1) (0.61,0.93,1.39) (0.84,1.39,1.89) (0.76,1.08,1.72) (0.76,1.08,1.72) (0.79,1.40,2.05) (1,1,1) (0.61,0.92,1.33) (0.82,1.45,1.96) (0.73,1.09,1.64)

(0.85,1.39,2.03) (0.69,1.07,1.59) (1,1,1) (0.83,1.47,2.04) (0.76,1.23,1.79) (0.76,1.23,1.79) (0.81,1.42,1.98) (0.72,1.04,1.65) (1,1,1) (0.86,1.41,1.92) (0.79,1.18,1.72) (0.79,1.18,1.72) (0.87,1.45,2.05) (0.71,1.05,1.63) (1,1,1) (0.85,1.37,2.08) (0.78,1.15,1.85) (0.78,1.15,1.85) (0.85,1.41,2.03) (0.68,1.08,1.58) (1,1,1) (0.84,1.41,1.96) (0.79,1.20,1.79) (0.79,1.20,1.79) (0.83,1.42,2.06) (0.72,1.07,1.63) (1,1,1) (0.85,1.45,2.04) (0.76,1.18,1.75) (0.76,1.18,1.75) (0.89,1.45,1.97) (0.75,1.09,1.64) (1,1,1) (0.83,1.39,1.92) (0.78,1.12,1.92)

(0.76,1.12,1.76) (0.53,0.72,1.26) (0.49,0.68,1.21) (1,1,1) (0.63,0.80,1.12) (0.63,0.79,1.12) (0.78,1.18,1.73) (0.49,0.75,1.18) (0.52,0.71,1.16) (1,1,1) (0.66,0.81,1.18) (0.66,0.81,1.18) (0.81,1.16,1.75) (0.51,0.73,1.22) (0.48,0.73,1.18) (1,1,1) (0.65,0.84,1.09) (0.65,0.83,1.09) (0.75,1.14,1.71) (0.48,0.71,1.24) (0.51,0.71,1.19) (1,1,1) (0.65,0.80,1.15) (0.65,0.80,1.15) (0.78,1.17,1.73) (0.53,0.72,1.19) (0.49,0.69,1.18) (1,1,1) (0.64,0.81,1.12) (0.64,0.79,1.12) (0.79,1.16,1.69) (0.51,0.69,1.22) (0.52,0.72,1.21) (1,1,1) (0.65,0.81,1.14)

(0.87,1.23,1.51) (0.87,1.23,1.51) (0.56,0.91,1.41) (0.56,0.91,1.41) (0.56,0.81,1.32) (0.56,0.81,1.32) (0.89,1.25,1.58) (0.89,1.27,1.58) (1,1,1) (0.75,1.08,1.74) (0.57,0.93,1.33) (1,1,1) (0.89,1.18,1.55) (0.89,1.18,1.55) (0.58,0.87,1.35) (0.58,0.87,1.35) (0.58,0.85,1.27) (0.58,0.85,1.27) (0.85,1.23,1.51) (0.85,1.23,1.51) (1,1,1) (0.78,1.15,1.71) (0.58,0.87,1.28) (1,1,1) (0.85,1.23,1.53) (0.85,1.23,1.53) (0.59,0.92,1.37) (0.59,0.92,1.37) (0.54,0.87,1.28) (0.54,0.87,1.28) (0.92,1.19,1.53) (0.92,1.21,1.53) (1,1,1) (0.81,1.17,1.78) (0.56,0.85,1.23) (1,1,1) (0.92,1.26,1.57) (0.92,1.26,1.57) (0.53,0.91,1.39) (0.53,0.91,1.39) (0.56,0.83,1.26) (0.56,0.83,1.26) (0.87,1.25,1.55) (0.87,1.25,1.55) (1,1,1) (0.79,1.11,1.69) (0.59,0.90,1.27) (1,1,1) (0.88,1.19,1.59) (0.88,1.19,1.59) (0.58,0.93,1.32) (0.58,0.93,1.32) (0.57,0.85,1.31) (0.57,0.85,1.31) (0.89,1.23,1.57) (0.89,1.26,1.57) (1,1,1) (0.78,1.15,1.74) (0.57,0.87,1.28) (1,1,1) (0.89,1.23,1.52) (0.89,1.23,1.52) (0.61,0.92,1.37) (0.61,0.92,1.37) (0.52,0.89,1.28) (0.52,0.89,1.28) (0.88,1.24,1.55) (0.88,1.24,1.55) (1,1,1) (0.76,1.16,1.73) (continued on next page)

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Table A.2 (continued) Experts

Expert 7

Expert 8

E6 E1 E2 E3 E4 E5 E6 E1 E2 E3 E4 E5 E6

E1

E2

E3

E4

E5

E6

(0.66,0.81,1.12) (1,1,1) (0.51,0.70,1.19) (0.49,0.70,1.16) (0.57,0.84,1.22) (0.65,0.79,1.10) (0.65,0.79,1.10) (1,1,1) (0.51,0.72,1.22) (0.49,0.70,1.19) (0.58,0.87,1.30) (0.64,0.82,1.15) (0.64,0.83,1.15)

(0.73,1.09,1.64) (0.84,1.43,1.96) (1,1,1) (0.61,0.94,1.37) (0.81,1.41,1.92) (0.72,1.12,1.75) (0.72,1.12,1.75) (0.82,1.38,1.97) (1,1,1) (0.61,0.93,1.39) (0.83,1.39,1.96) (0.74,1.08,1.69) (0.74,1.15,1.69)

(0.78,1.12,1.92) (0.86,1.43,2.04) (0.73,1.06,1.63) (1,1,1) (0.85,1.41,2.13) (0.79,1.19,1.72) (0.79,1.19,1.72) (0.84,1.42,2.05) (0.72,1.07,1.65) (1,1,1) (0.85,1.45,2.13) (0.78,1.16,1.75) (0.78,1.16,1.75)

(0.65,0.81,1.14) (0.82,1.19,1.74) (0.52,0.71,1.23) (0.47,0.71,1.17) (1,1,1) (0.64,0.80,1.10) (0.64,0.80,1.10) (0.77,1.15,1.72) (0.51,0.72,1.21) (0.47,0.69,1.17) (1,1,1) (0.65,0.82,1.14) (0.65,0.79,1.14)

(0.58,0.86,1.32) (0.91,1.26,1.55) (0.57,0.89,1.39) (0.58,0.84,1.26) (0.91,1.25,1.56) (1,1,1) (0.57,0.85,1.28) (0.87,1.22,1.56) (0.59,0.93,1.36) (0.57,0.86,1.29) (0.88,1.22,1.54) (1,1,1) (0.57,0.85,1.30)

(1,1,1) (0.91,1.26,1.55) (0.57,0.89,1.39) (0.58,0.84,1.26) (0.91,1.25,1.56) (0.78,1.17,1.76) (1,1,1) (0.87,1.21,1.56) (0.59,0.87,1.36) (0.57,0.86,1.29) (0.88,1.26,1.54) (0.77,1.18,1.75) (1,1,1)

Table A.3 Importance assessment of interdependence relationship with respect to “A” of eight experts Experts

Controlled factor:A

A

B

C

D

E

Expert 1

A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E A B C D E

(1,1,1) (0.64,0.98,1.41) (0.34,0.51,0.82) (0.33,0.54,0.83) (1.14,1.49,2.44) (1,1,1) (0.66,0.93,1.33) (0.35,0.50,0.84) (0.32,0.50,0.84) (1.08,1.56,2.63) (1,1,1) (0.65,0.95,1.45) (0.35,0.49,0.85) (0.33,0.51,0.81) (1.10,1.64,2.70) (1,1,1) (0.65,0.90,1.39) (0.35,0.49,0.84) (0.34,0.49,0.85) (1.12,1.56,2.38) (1,1,1) (0.64,0.93,1.37) (0.34,0.49,0.81) (0.33,0.50,0.83) (1.10,1.54,2.44) (1,1,1) (0.63,0.92,1.35) (0.35,0.50,0.86) (0.34,0.50,0.81) (1.09,1.64,2.33) (1,1,1) (0.66,0.90,1.39) (0.35,0.50,0.83) (0.32,0.49,0.85) (1.06,1.61,2.56) (1,1,1) (0.65,0.92,1.35) (0.35,0.51,0.85) (0.32,0.49,0.82) (1.12,1.54,2.33)

(0.71,1.02,1.56,0.64) (1,1,1) (0.35,0.50,1.05) (0.34,0.50,0.99) (1.45,1.96,2.86) (0.75,1.08,1.51) (1,1,1) (0.34,0.51,1.03) (0.33,0.50,0.97) (1.59,1.85,2.70) (0.69,1.05,1.54) (1,1,1) (0.34,0.49,1.01) (0.33,0.51,1.01) (1.41,1.75,2.63) (0.72,1.11,1.53) (1,1,1) (0.34,0.50,1.04) (0.33,0.51,0.96) (1.56,1.92,2.56) (0.73,1.08,1.57) (1,1,1) (0.35,0.49,0.99) (0.34,0.50,0.99) (1.49,1.85,2.56) (0.74,1.09,1.58) (1,1,1) (0.34,0.51,1.01) (0.33,0.49,0.97) (1.52,1.96,2.44) (0.72,1.11,1.52) (1,1,1) (0.35,0.50,0.97) (0.33,0.51,0.96) (1.49,1.82,2.38) (0.74,1.09,1.54) (1,1,1) (0.34,0.51,1.02) (0.33,0.50,1.04) (1.47,1.85,2.63)

(1.22,1.98,2.91) (0.95,1.99,2.88) (1,1,1) (0.76,1.10,1.47) (2.70,4.17,4.76) (1.19,2.01,2.85) (0.97,1.96,2.92) (1,1,1) (0.78,1.14,1.59) (2.56,3.85,5.26) (1.17,2.05,2.88) (0.99,2.03,2.91) (1,1,1) (0.80,1.08,1.52) (2.38,4.76,6.25) (1.19,2.03,2.86) (0.96,1.99,2.90) (1,1,1) (0.79,1.12,1.49) (2.33,4.00,7.69) (1.23,2.06,2.93) (1.01,2.03,2.85) (1,1,1) (0.78,1.10,1.45) (2.70,4.55,6.67) (1.16,2.01,2.87) (0.99,1.97,2.91) (1,1,1) (0.76,1.06,1.52) (2.63,4.17,5.56) (1.21,1.99,2.88) (1.03,2.02,2.86) (1,1,1) (0.79,1.09,1.59) (2.44,3.57,5.26) (1.17,1.98,2.86) (0.98,1.95,2.93) (1,1,1) (0.78,1.12,1.54) (2.70,4.35,4.76)

(1.21,1.85,3.05) (1.01,2.02,2.97) (0.68,0.91,1.31) (1,1,1) (2.44,3.70,5.88) (1.19,1.99,3.08) (1.03,1.99,3.05) (0.63,0.88,1.28) (1,1,1) (2.33,3.45,5.26) (1.24,1.95,3.03) (0.99,2.03,2.91) (0.66,0.93,1.25) (1,1,1) (2.22,3.85,5.56) (1.17,2.03,2.95) (1.04,1.95,3.05) (0.67,0.89,1.27) (1,1,1) (2.38,3.57,4.76) (1.21,2.01,3.03) (1.01,1.99,2.98) (0.69,0.91,1.28) (1,1,1) (2.13,4.17,4.55) (1.23,1.99,2.91) (1.03,2.03,3.01) (0.66,0.94,1.32) (1,1,1) (2.33,3.45,6.25) (1.18,2.03,3.09) (1.04,1.97,3.05) (0.63,0.92,1.27) (1,1,1) (2.22,3.57,5.26) (1.22,2.03,3.09) (0.96,1.99,2.99) (0.65,0.89,1.29) (1,1,1) (2.44,3.85,5.56)

(0.41,0.67,0.88) (0.35,0.51,0.69) (0.21,0.24,0.37) (0.17,0.27,0.41) (1,1,1) (0.38,0.64,0.93) (0.37,0.54,0.63) (0.19,0.26,0.39) (0.19,0.29,0.43) (1,1,1) (0.37,0.61,0.91) (0.38,0.57,0.71) (0.16,0.21,0.42) (0.18,0.26,0.45) (1,1,1) (0.42,0.64,0.89) (0.39,0.52,0.64) (0.13,0.25,0.43) (0.21,0.28,0.42) (1,1,1) (0.41,0.65,0.91) (0.39,0.54,0.67) (0.15,0.22,0.37) (0.22,0.24,0.47) (1,1,1) (0.43,0.61,0.92) (0.41,0.51,0.66) (0.18,0.24,0.38) (0.16,0.29,0.43) (1,1,1) (0.39,0.62,0.94) (0.42,0.55,0.67) (0.19,0.28,0.41) (0.19,0.28,0.45) (1,1,1) (0.43,0.65,0.89) (0.38,0.54,0.68) (0.21,0.23,0.37) (0.18,0.26,0.41) (1,1,1)

Expert 2

Expert 3

Expert 4

Expert 5

Expert 6

Expert 7

Expert 8

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Table A.4 Importance assessment of inner dependence relationship with controlled factor “B6” of eight experts Experts

Controlled factor: B6

B1

B3

B4

B7

Expert 1

B1 B3 B4 B7 B1 B3 B4 B7 B1 B3 B4 B7 B1 B3 B4 B7 B1 B3 B4 B7 B1 B3 B4 B7 B1 B3 B4 B7 B1 B3 B4 B7

(1,1,1) (0.65,0.81,1.27) (0.64,0.84,1.12) (0.58,0.76,1.09) (1,1,1) (0.63,0.79,1.20) (0.62,0.83,1.18) (0.61,0.73,1.10) (1,1,1) (0.63,0.85,1.22) (0.63,0.87,1.14) (0.62,0.75,1.14) (1,1,1) (0.62,0.79,1.28) (0.64,0.85,1.16) (0.61,0.78,1.10) (1,1,1) (0.62,0.83,1.20) (0.62,0.82,1.11) (0.59,0.74,1.08) (1,1,1) (0.63,0.81,1.22) (0.63,0.86,1.14) (0.62,0.75,1.09) (1,1,1) (0.62,0.80,1.19) (0.62,0.85,1.15) (0.60,0.72,1.12) (1,1,1) (0.63,0.81,1.23) (0.63,0.83,1.12) (0.61,0.75,1.09)

(0.79,1.24,1.53) (1,1,1) (0.72,1.22,1.79) (0.59,0.82,1.39) (0.83,1.26,1.58) (1,1,1) (0.76,1.19,1.69) (0.61,0.80,1.28) (0.82,1.18,1.59) (1,1,1) (0.74,1.27,1.64) (0.60,0.78,1.33) (0.78,1.26,1.61) (1,1,1) (0.72,1.22,1.75) (0.61,0.85,1.41) (0.83,1.21,1.62) (1,1,1) (0.73,1.18,1.69) (0.60,0.81,1.30) (0.82,1.23,1.58) (1,1,1) (0.76,1.23,1.59) (0.60,0.84,1.28) (0.84,1.25,1.61) (1,1,1) (0.74,1.19,1.72) (0.59,0.81,1.33) (0.81,1.23,1.59) (1,1,1) (0.73,1.22,1.69) (0.60,0.84,1.32)

(0.89,1.19,1.56) (0.56,0.82,1.38) (1,1,1) (0.58,1.03,1.47) (0.85,1.21,1.62) (0.59,0.84,1.32) (1,1,1) (0.59,0.99,1.59) (0.88,1.15,1.59) (0.61,0.79,1.35) (1,1,1) (0.60,0.95,1.54) (0.86,1.17,1.57) (0.57,0.82,1.39) (1,1,1) (0.58,0.97,1.45) (0.90,1.22,1.61) (0.63,0.85,1.37) (1,1,1) (0.61,0.99,1.41) (0.88,1.16,1.59) (0.58,0.84,1.31) (1,1,1) (0.59,1.01,1.49) (0.87,1.17,1.61) (0.59,0.81,1.36) (1,1,1) (0.58,0.98,1.47) (0.89,1.21,1.59) (0.59,0.82,1.37) (1,1,1) (0.60,0.99,1.45)

(0.92,1.32,1.71) (0.72,1.22,1.69) (0.68,0.97,1.71) (1,1,1) (0.91,1.37,1.65) (0.78,1.25,1.63) (0.63,1.01,1.69) (1,1,1) (0.88,1.34,1.61) (0.75,1.28,1.67) (0.65,1.05,1.67) (1,1,1) (0.91,1.29,1.65) (0.71,1.18,1.65) (0.69,1.03,1.72) (1,1,1) (0.93,1.35,1.69) (0.77,1.24,1.67) (0.71,1.01,1.64) (1,1,1) (0.92,1.34,1.62) (0.78,1.19,1.68) (0.67,0.99,1.69) (1,1,1) (0.89,1.39,1.67) (0.75,1.23,1.69) (0.68,1.02,1.71) (1,1,1) (0.92,1.33,1.63) (0.76,1.19,1.67) (0.69,1.01,1.68) (1,1,1)

Expert 2

Expert 3

Expert 4

Expert 5

Expert 6

Expert 7

Expert 8

Chou, W.-C., Cheng, Y.-P., 2012. A hybrid fuzzy MCDM approach for evaluating website quality of professional accounting firms. Expert Syst. Appl. 39, 2783–2793. Deacon, T., Amyotte, P.R., Khan, F.I., MacKinnon, S., 2013. A framework for human error analysis of offshore evacuations. Saf. Sci. 51, 319–327. Dsouza, N., Lu, L., 2017. A literature review on human reliability analysis techniques applied for probabilistic risk assessment in the nuclear industry. In: Cetiner, S.M., Fechtelkotter, P., Legatt, M. (Eds.), Advances in Human Factors in Energy: Oil, Gas, Nuclear and Electric Power Industries: Proceedings of the AHFE 2016 International Conference on Human Factors in Energy: Oil, Gas, Nuclear and Electric Power Industries, July 27-31, 2016, Walt Disney World®, Florida, USA. Springer International Publishing, Cham, pp. 41–54. Gibson, W.H., Mills, A.M., Smith, S., Kirwan, B.K., 2013. Railway Action Reliability Assessment, a Railway-specific Approach to Human Error Quantification, Rail Human Factors. Taylor & Francis, pp. 671–676. Kirwan, B., Gibson, H., Kennedy, R., Edmunds, J., Cooksley, G., Umbers, I., 2004. Nuclear action reliability assessment (NARA): a data-based HRA tool. In: In: Spitzer, C., Schmocker, U., Dang, V.N. (Eds.), Probabilistic Safety Assessment and Management: PSAM 7 — ESREL ’04 June 14–18, 2004, Berlin, Germany, vol. 6. Springer London, London, pp. 1206–1211. Kyriakidis, M., Majumdar, A., Ochieng, W.Y., 2018. The human performance railway operational index—a novel approach to assess human performance for railway operations. Reliab. Eng. Syst. Saf. 170, 226–243. Liu, P., Yang, L., Gao, Z., Li, S., Gao, Y., 2015. Fault tree analysis combined with quantitative analysis for high-speed railway accidents. Saf. Sci. 79, 344–357. Maniram Kumar, A., Rajakarunakaran, S., Arumuga Prabhu, V., 2017. Application of Fuzzy HEART and expert elicitation for quantifying human error probabilities in LPG refuelling station. J. Loss Prev. Process. Ind. 48, 186–198. Pan, X., Lin, Y., He, C., 2016. A Review of Cognitive Models in Human Reliability Analysis. Quality and Reliability Engineering International. Pasquale, V.D., Iannone, R., Miranda, S., Riemma, S., 2013. An Overview of Human Reliability Analysis Techniques in Manufacturing Operations. Petrillo, A., Falcone, D., De Felice, F., De Zomparelli, F., 2017. Development of a risk analysis model to evaluate human error in industrial plants and in critical infrastructures. International Journal of Disaster Risk Reduction 23, 15–24.

References Akyuz, E., 2017. A marine accident analysing model to evaluate potential operational causes in cargo ships. Saf. Sci. 92, 17–25. Akyuz, E., Celik, E., 2016a. A modified human reliability analysis for cargo operation in single point mooring (SPM) off-shore units. Appl. Ocean Res. 58, 11–20. Akyuz, E., Celik, M., 2015. A methodological extension to human reliability analysis for cargo tank cleaning operation on board chemical tanker ships. Saf. Sci. 75, 146–155. Akyuz, E., Celik, M., 2016b. A hybrid human error probability determination approach: the case of cargo loading operation in oil/chemical tanker ship. J. Loss Prev. Process. Ind. 43, 424–431. Akyuz, E., Celik, M., Cebi, S., 2016. A phase of comprehensive research to determine marine-specific EPC values in human error assessment and reduction technique. Saf. Sci. 87, 63–75. Cagri Tolga, A., Tuysuz, F., Kahraman, C., 2013. A fuzzy multi-criteria decision analysis approach for retail location selection. Int. J. Inf. Technol. Decis. Making 12, 729–755. Casamirra, M., Castiglia, F., Giardina, M., Tomarchio, E., 2009. Fuzzy modelling of HEART methodology: application in safety analyses of accidental exposure in irradiation plants. Radiat. Eff. Defect Solid 164, 291–296. Castiglia, F., Giardina, M., 2011. Fuzzy risk analysis of a modern gamma-ray industrial irradiator. Health Phys. 100, 622–631. Castiglia, F., Giardina, M., 2013. Analysis of operator human errors in hydrogen refuelling stations: comparison between human rate assessment techniques. Int. J. Hydrogen Energy 38, 1166–1176. Castiglia, F., Giardina, M., Tomarchio, E., 2015. THERP and HEART integrated methodology for human error assessment. Radiat. Phys. Chem. 116, 262–266. Castillo, E., Calviño, A., Grande, Z., Sánchez-Cambronero, S., Gallego, I., Rivas, A., Menéndez, J.M., 2016. A markovian-bayesian network for risk analysis of high speed and conventional railway lines integrating human errors. Comput. Aided Civ. Infrastruct. Eng. 31, 193–218. Chadwick, L., Fallon, E.F., 2012. Human reliability assessment of a critical nursing task in a radiotherapy treatment process. Appl. Ergon. 43, 89–97. Chen, C.-T., 2001. A fuzzy approach to select the location of the distribution center. Fuzzy Set Syst. 118, 65–73.

257

International Journal of Industrial Ergonomics 67 (2018) 242–258

W. Wang et al.

Xu, P., Chan, E.H.W., Visscher, H.J., Zhang, X., Wu, Z., 2015. Sustainable building energy efficiency retrofit for hotel buildings using EPC mechanism in China: analytic Network Process (ANP) approach. J. Clean. Prod. 107, 378–388. Zhan, Q., Zheng, W., Zhao, B., 2017. A hybrid human and organizational analysis method for railway accidents based on HFACS-Railway Accidents (HFACS-RAs). Saf. Sci. 91, 232–250. Zhong, L., Yao, L., 2017. An ELECTRE I-based multi-criteria group decision making method with interval type-2 fuzzy numbers and its application to supplier selection. Appl. Soft Comput. 57, 556–576. Zhu, K.-J., Jing, Y., Chang, D.-Y., 1999. A discussion on Extent Analysis Method and applications of fuzzy AHP. Eur. J. Oper. Res. 116, 450–456.

Preischl, W., Hellmich, M., 2013. Human error probabilities from operational experience of German nuclear power plants. Reliab. Eng. Syst. Saf. 109, 150–159. Reer, B., 2008. Review of advances in human reliability analysis of errors of commission—Part 2: EOC quantification. Reliab. Eng. Syst. Saf. 93, 1105–1122. Saaty, T.L., 1996. Decision Making with Dependence and Feedback: the Analytic Network Process. RWS Publications, Pittsburgh. Wang, J., Fang, W., 2014. A structured method for the traffic dispatcher error behavior analysis in metro accident investigation. Saf. Sci. 70, 339–347. Williams, J.C., 1988. A data-based method for assessing and reducing human error to improve operational performance, human factors and power plants, 1988. In: Conference Record for 1988 IEEE Fourth Conference, pp. 436–450.

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