Research on Mechanism and Measurement Model for the Effects of Path Dependence on Human Error in Space Station Manipulator Tasks

Abstract

Astronauts’ cognitive and operational processes are partly or absolutely influenced by the thinking and operation habits derived from a previous task or some tasks, which results in disturbance to human error—the disturbance may promote human error or inhibit human error. To explore the mechanism and measurement model of path dependence in human error, this study develops a method for judging the mode of the path dependence symmetric effect, and a mathematical symmetric model for quantifying the degree of the path dependence effect on human error is created. Taking the robotic manipulator teleoperation task as a study object, this study establishes a set of factors that influence the symmetric effect of path dependence, including facilitating or inhibiting human error, and identifies the relationships between these influencing factors. Based on questionnaire analysis, a fuzzy evaluation method for measuring the symmetric degree of the facilitating/inhibiting effect is obtained, by analyzing the simulation data, and the fuzzy method has good convergence, sensitivity and differentiation capabilities.

1. Introduction

From a perspective of psychology, path dependence refers to a fixed mode of thinking; thinking and cognitive behavior are influenced by similar situations in the past, and similar cognitive processing or even automatic processing is used for similar tasks [1]. Path dependence has a certain effect on human error [2,3]. If a task has path dependence, the task will be executed according to the existing thinking pattern and knowledge structure. However, not all executions of the same task with path dependence are completely consistent, resulting in deviation and human error in an execution process [1,2,3]. The theoretical research achievements of path dependence involve many fields, such as economics, physics, biology, management science and psychology. Based on these achievements, this paper extends path dependence to the human-error study field, and discusses whether path dependence promotes human error or inhibits human error under the condition of path dependence in a process to finish a task. Therefore, in this paper, path dependence is viewed as the thinking mode and behavior characteristics of astronauts in a task processing process affected by previous similar tasks, and astronauts more or less complete tasks according to the solidified cognitive characteristics.

Path dependence has two symmetric effects on human error [1,2,3]. On one hand, operators can improve efficiency and inhibit human error effectively if they adopt patterns of thinking and cognitive behavior that are in line with the current task context. On the other hand, operators may make errors if the current task context changes and deviates from previous patterns of thinking and cognitive behavior; the degree of deviation is a variable that affects the severity of human error. The degree of fit between the previous path and the current task determines whether path dependence inhibits or facilitates human error.

To investigate the mechanism of and reduce path-dependent influencing on human error, in the context of manipulator tasks in the space station, this paper explores the factors that influence the effect of path dependence on human error and the corresponding mode of symmetric effect and develops a symmetric model for calculating the degree of effect (DOE), with the aim of providing theoretical support for reducing the negative effect of path dependence on human error and a methodological guidance for measuring the DOE.

The existing studies on space-station manipulator tasks mainly focus on aspects such as the reliability requirements, basic cognitive ability tests, simulated task test operation training indicators, and visual information displays. However, more research needs to be performed on aspects such as human-error prediction.

Targeting the high reliability requirements of the on-orbit operation of space manipulators, Jia et al. [4] developed a multilayer mapping model and carried out sensitivity analysis of the factors influencing the motion reliability to provide a theoretical basis for space manipulator task planning and control decision making. Yang et al. [5] proposed an idea of spatial path dependence, and debated that previous spatial distribution of economic activities and associated factors in a given industrial space affect current and future ones. The findings call for the attention of the existing situation for industrial spatial planning, and new emerging “people-oriented” factors in influencing the spatial layout of information services industries. It was also shown that the spatial ability, motion control ability, and level of continuous attention are closely related to task completion rates as well as the safety and efficiency of operations [6]. To model the mutual dependence between machine degradation and human errors, Che et al. [7] established a Piecewise-deterministic Markov process model framework, which can incorporate machine degradation and human errors to evaluate the system safety. In the model, the machine degradation is described by a multistate model with a Semi-Markov process; a mathematical model is developed to evaluate the human error rate under the effect of fatigue-recovery, where human errors occur according to a nonhomogeneous Poisson process. Visual perception, as the main information channel for human cognition in the environment, plays a vital role in space teleoperation. The prospects of the development of visual information displays for space teleoperations are available in the literature [8]. Through the simulation of manipulator teleoperations, the effects of varying degrees of loss of three-dimensional information on human performance, mental workload, distance perception, and situational awareness of manipulator teleoperations were investigated [9]. In addition, Tang et al. [10] pointed out that the mental workload is a major factor affecting the performance of manipulator teleoperation and that reducing the mental workload of astronauts during various stages is important for the completion of teleoperations. Regarding path dependence, two extreme directions were identified according to the factors influencing the institutional changes [11]. The first type of evolution of path dependence refers to the fact that when a system develops and changes along a specific route, a subjective model will be induced under the joint action of multiple factors such as system externality and learning effects, which will further strengthen this specific route. The second type of evolution of path dependence refers to the fact that when the organization is inefficient and the market is incomplete, the economic activities will stagnate under the influence of the increasing return of the initial institutional arrangement, coupled with the maintenance of the interest groups and organizations bound to it, so that the existing inefficient institutional arrangement will continue to develop under their protection, resulting in low or negative economic growth. It will also make this inefficient system continue to develop and further strengthen itself. Dependence analysis and assessment among human errors are an important hotspot in HRA, which depend heavily on domain experts’ knowledge and experience. Chen et al. [12] develop a dependence assessment model to manage the dependence in HRA, proposing an extended Muirhead mean operator to determine the dependence levels between consecutive operator actions. Research results based on the paths of shock train leading edges [13] show that path-dependent characteristics are apparently embodied by abrupt motions, average velocities of the shock train, structures of the shock train and oscillations. To discuss the progression of occupational careers, which can be conceptualized as a path-dependent process, Dlouhy and Biemann [14] proposed that path dependence leads to a decrease in mobility in occupational careers over time and that occupational turbulence in the earlier career stages is linked to turbulence in the later stages of an occupational career. Path dependence refers to the impact of the path on the outcome of the process. Jia and Vatto [15] developed a model in which past labor market status has effects on present decisions: ① there is habit dependence in the taste for leisure; ② labor market opportunities reflect experiences of the previous period. Simulation results from a tax rate change show that state dependence brought down the short-term (first-year) responses to one-third of the full effect. Zhang et al. [16] identified the marked factors affecting the success of the robotic arm teleoperation task and constructed a dynamic Bayesian network (DBN) model. On this basis, the path dependence was analyzed to revise the model. The revised model can clearly describe the path-dependent effect of human-computer interaction failures and also calculate the reliability of the complex system accurately.

Taking operating task of robot arms for research background, the paper studied the influencing factors, mode of action and evaluation of human–machine interaction for path dependence symmetric effect on human error to provide a theoretical basis for human error based on path dependence, guidance to reduce human error, and a design basis for human–machine systems. The major contributions of this study include: (1) determining the influencing factors of path-dependence symmetric effect on human error; (2) constructing a mode and process of human error based on path dependence; (3) proposing an influencing degree evaluation symmetric model based on path dependence effect on human error.

2. Influencing Factors Analysis of Path Dependence Symmetric Effect on Human Error

The acquisition of influencing factors will be conducted through two processes, including initial influencing factors obtained by literature review and expert consultation and final influencing factors obtained by combining the relative importance calculation and expert judgment.

2.1. Initial Human Error Influencing Factors Based on Path Dependence

The acquisition of initial influencing factors is divided into two steps:

(1)

Based on expert consultation and interviews at the China Astronaut Research and Training Center, four categories of factors that influence path-dependent human error were preliminarily identified, which are task conflict (it is known as similar tasks or cognition results, which can influence path dependence), equipment fault and deterioration, environmental impact and human factors (

Table 1. Factors influencing path-dependent human error.

First-Level Indicator	Symbol	Second-Level Indicator	Symbol	Remark
Task conflict	B1	Safety risk at the initial position	B11	The possibility of a safety risk at a similar initial position, present in some cases (e.g., collision) and not in other cases.
		Degree of delay	B12	Presence/absence of delay in the display of the operational effect
		Similarity of operation mode	B13	Operation action elements, manual or touch-screen operation, etc.
		Information display	B14	Display of the attitude and position information
Equipment fault and deterioration	B2	Joystick	B21	Fault or functional deterioration of the joystick
		Display	B22	Fault or functional deterioration of the display
		Extravehicular camera	B23	Fault or functional deterioration of the extravehicular camera
Environmental impact [17,18]	B3	Noise [17,19,20]	B31	In general, noise is ubiquitous, and moderate noise has little impact on an operator. However, for some task scenarios, excessive ambient noise may have an important impact on the behavioral performance of an operator.
		Illumination	B32	The illumination in the main control room affects, to some extent, the operation of an astronaut. Too much or too little light can cause eye discomfort and distract the astronaut.
		Temperature [17]	B33	Temperature mainly refers to the influence of temperature change in the cabin on the operator.
Human factors	B4	Changes in cognitive and operational abilities [21,22,23,24,25,26]	B41	In ground-based simulations and in-orbit flying missions, astronauts’ operational abilities in terms of perception (visual perception, haptic feedback, and auditory perception), mobility, accessibility, maneuverability, and strength characteristics may differ under the influence of the space environment.
		Level of experience [12,17,18,27,28,29,30,31]	B42	The level of experience represents the extent to which an astronaut understands and is familiar with software and hardware equipment and task operation regulations and procedures, as well as the experience in dealing with equipment anomalies and emergencies. An experienced operator can quickly capture critical information from the system, complete relevant operations, and select the correct coping strategies and methods.
		Physical fatigue [17,30]	B43	Physical fatigue mainly refers to bodily fatigue and is primarily caused by prolonged body load and influenced by factors such as sleep duration and quality. This parameter is typically characterized by the inability to sustain loads with repeated activities. In terms of an operator’s physiological condition, physical fatigue mainly includes individual physiological factors such as physiological fatigue, physiological rhythms, and physical conditions.
		Psychological pressure [27,32,33,34,35,36]	B44	Equipment anomalies can make an astronaut feel nervous or stressed. Psychological pressure is a major factor affecting human behavior and reliability.
		Mental fatigue [12,17,27,29,30]	B45	Primarily refers to central fatigue, which typically stems from a diminished capacity for behavioral activity caused by prolonged engagement in stressful mental work or by abnormal environmental stimuli and is influenced by the environmental atmosphere, pressure, emotions, and mental load. This parameter is typically characterized by unwillingness or inability to perform an activity.
		Mental workload [9,10]	B46	Primarily refers to describe people’s information processing ability at work.

).

(2)

Based on each category of influencing factors, by combining expert interviews with astronauts, domain experts and related researchers and literature reviews, the initial influencing factors were obtained after analyzing the results of interviews and literature reviews (Table 1).

2.2. Determinzing Final Influencing Factors

2.2.1. Calculation Formula of Influencing Factors Relative Importance

Based on preliminary influencing factors (see Table 1), the influencing factors were scored by experts and scholars, and the questionnaires were collected and analyzed to calculate their relative importance. The calculation expression of importance is shown in Formula (1).

$$E_j={\displaystyle \sum _{i=1}^n{x}_i\times }{y}_i$$

(1)

x_i means the ith expert’s proficiency in influencing factors (it is divided into: high, higher, medium, lower, low); y_i indicates the degree that influencing factors affect the cognitive stages (it is divided into five categories: high, higher, medium, lower, low). Five levels are represented by 5, 4, 3, 2 and 1, respectively.

2.2.2. Questionnaire Survey and Statistics

To investigate the influencing factors affect path-dependent human error and their correlation, a questionnaire survey was conducted (35 questionnaires were distributed and 35 were returned, among which 31 were valid). Correlation analysis was conducted using SPSS 22.0 (IBM Corporation, New York, USA). Both Cronbach’s alpha coefficient and the Kaiser–Meyer–Olkin (KMO) value were larger than 0.7, confirming the reliability and validity of the survey.

2.2.3. Result Analysis

Based on Formula (1), the relative importance of questionnaire survey results was calculated. The relative importance of influencing factors at each level was expressed by its average value. The final influencing factors system was determined by combining the expert opinions (experts came from University of South China, Central South University and Hunan Institute of Technology) and relative importance; the expert opinions are listed in

Table 2. Expert judgment statistical results of influencing factors and the descriptions of influencing factors to be eliminated.

Influencing Factor	Initial Influencing Factors	Statistics Results of Expert Opinions (Seven Experts in Total)			Average of Relative Importance	Influencing Factors and Description to be Eliminated
		Agree (Number of Experts)	Disagree (Number of Experts)	Can’t Judge (Number of Experts)
Task conflict	Safety risk at the initial position	6	0	1	18.8	The red indicator indicates the indicator to be eliminated. The reason for elimination is that the average value of relative importance is low and there are great differences in expert opinions.
	Degree of delay	7	0	0	19.2
	Similarity of operation mode	3	3	1	11.3
	Information display	5	1	1	19.1
Equipment fault and deterioration	Joystick	7	0	0	19.8
	Display	4	2	1	12.5
	Extravehicular camera	6	0	1	18.8
Environmental impact	Noise	7	0	0	19.5
	Illumination	7	0	0	19.7
	Temperature	4	3	0	11.7
Human factors	Changes in cognitive and operational abilities	6	0	1	18.6
	Level of experience	7	0	0	20.1
	Physical fatigue	7	0	0	19.6
	Psychological pressure	7	0	0	20.2
	Mental fatigue	7	0	0	20.7
	Mental workload	4	2	1	14.0

. Since the average importance of these four influencing factors is low and the opinions of experts are widely divergent, similarity of operation mode, display, temperature and mental workload are considered to be eliminated. To facilitate analysis, the average relative importance value and influencing factors description were added in Table 2.

Based on the analysis in Table 2, the final influencing factors system obtained is shown in

Table 3. Factors influencing path-dependent human error.

Influencing Factors of “Task Conflict”	Influencing Factors of “Equipment Fault and Deterioration”	Influencing Factors of “Environmental Impact”	Influencing Factors of “Human Factors”
Safety risk at the initial position	Joystick	Noise	Changes in cognitive and operational abilities
Degree of delay	Extravehicular camera	Illumination	Level of experience
Information display			Physical fatigue
			Psychological pressure
			Mental fatigue

.

The findings are summarized as follows.

(1)

Task conflict, equipment fault and deterioration, environmental impact and human factors all significantly influence the effect mode of path dependence on human error. Human factors have the largest influence, followed by task conflict, environmental impact, and equipment fault and deterioration.

(2)

There are significant pairwise correlations between task conflict, equipment fault and deterioration, and environmental impact, as well as between second-level indicators of human error.

3. Mode of the Symmetric Effect of Path Dependence on Human Error in the Context of Space Station Manipulator Operation

The mode of the symmetric effect of path dependence during task execution is not invariable but changes with varying factors such as the task execution process, personnel state, and environmental and equipment states, and these changes may directly lead to the creation of new paths. The changes in the effect mode are closely related to the degree of conflict between the task and the thinking mode (abbreviated as task conflict), the changes in the personnel state and the changes in the environmental and equipment states, the root cause still being the human attitude towards conflicts and changes and the way to solve the problem.

The mode of the symmetric effect on human error is formed by a combination of levels of factors such as task conflict, environmental change, sudden equipment fault and uncertainty in the personnel state. To distinguish the mode and degree of the effects of different factors on human error, we propose that the mode of the symmetric effect on human error be classified into facilitating and inhibiting effects. The following major aspects are considered in the present study:

(1)

Equipment faults, for which the effect of recovery is considered, are studied. If the equipment is recovered, the mode of effect of path dependence will be changed.

(2)

The symmetric effect mode (inhibition or facilitation) of path dependence (as “inertial thinking”) on human error is determined based on the extent to which the task factor matches the mental factor. Influenced by inertial thinking, astronauts tend to habitually migrate the thought process, operation mode and experience of the previous tasks to other similar tasks during execution, thereby forming path dependence. Because of path dependence, an environmental change, a sudden equipment fault and uncertainty in the personnel state may affect the human error to some extent, mainly in the form of either a facilitating or an inhibiting mode. Inertial thinking is the basis of the emergence of “path dependence”, while the mode of the symmetric effect on human error, either “inhabitation” or “facilitation”, is the result of the manifestation of “path dependence”.

(3)

The change in the effect mode due to behavioral recovery (corrective action) is considered.

The model for describing the facilitating and inhibiting symmetric effects of the influencing factors and path dependence on human error based on the above description is shown in Figure 1.

In Figure 1, the inertial thinking is used to determine whether path dependence exists and, if so, controls the effect mode of the corresponding path on human error.

Facilitation and inhibition, the two modes of the symmetric effect of path dependence on human error, are considered in the study. Accordingly, there are two state grades (“good” and “poor”) of the influencing factors. A factor at a “good” (or “poor”) level is considered to have an inhibiting (or facilitating) effect on human error.

In Figure 1, if an error-inducing factor is at a moderate level, path dependence is considered to have no facilitating or inhibiting effect on human error, and therefore, this case is not considered. By the same token, this case is not considered in the calculation of the degree of facilitation or inhibition.

4. A Calculating Model of Path Dependence Symmetric Effect on Human–Machine Interactions

4.1. Calculating Symmetric Model of Human Error Effect Degree

A fault-tree model is used in the present study to describe the sequence of an operator performing a task, where the fault tree is branched into the symmetric modes of inhibiting and facilitating effects while the recovery process due to the effect of facilitation on human error is considered. If the recovery is successful, the effect mode at this node is changed from “facilitation” to “inhibition”, and the degree of inhibition at this node is defined as 100. Figure 2 illustrates a task decomposition process.

The definitions and notations are listed as follows.

Definition 1.

Degree of inhibition (DOI): this parameter has a value in the range of [−100, 0], with a larger absolute value indicating a higher level of inhibition and a value of −100 meaning complete inhibition of human error and human–machine interaction fault.

Degree of facilitation (DOF): this parameter has a value in the range of [0, 100], with a larger value indicating a higher level of facilitation. In terms of calculation, DOF = 100 − |DOI|.

Definition 2.

If the degree of match between the factors of a task and inertial thinking is 100, the task is generally successfully executed. In this case, the influence of the factors is not considered when calculating the DOI for the task. This is because their DOI for the task is 100, indicating complete inhibition of human error in the absence of other factors.

Notations declaration:

• task_i: ith task.
• a_{i_n}: inhibition effect of the nth subtask of the ith task.
• A_{i_n}: facilitation effect of the path dependence of the nth subtask of the ith task on human error.
• R_S: successful recovery for the operation failure.
• d(task_i)_fac: DOF of the path dependence of the ith task on human error.
• d(A_{i_n}): DOF of the nth subtask of the ith task.
• d(task_i)_inh: DOI of the path dependence of the ith task on human error.
• d(a_{i_n}): DOI of the nth subtask of the ith task.
• d(A_{i_j}): DOF of the jth subtask of the ith task.
• d(a_{i_j}): DOI of the jth subtask of the ith task.
• w_{i_n}: weight of the nth subtask of the ith task, and w_{i_1} + w_{i_2} +... w_{i_n} = 1.
• F_ij(x,w): function for calculating the DOF or DOI of the jth subtask of the ith task.

According to the decomposition, the effective mode (facilitating or inhibiting) and the characteristics of a task, the framework to calculate the symmetric effective degree of a task on human error and human–machine interaction fault is defined as follows:

$$d{(task)}_{fac}=\{\begin{array}{l}100,if the DOF of any subtask is 100\\ w_{i-1}\times d(A_{i-1})+w_{i-2}\times d(A_{i-2})+\cdots \cdots +w_{i-n}\times d(A_{i-n}),otherwise\end{array}$$

(2)

d(task_i)_inh = w_{i_1} × d(a_i_1) + w_{i_2} × d(a_i_2) +…+ w_{i_n} × d(a_i_n)

(3)

A task is considered to have a facilitating effect on human error as long as at least one of its subtasks has a facilitating effect. The DOF of the task is calculated using Equation (2). Note that in the calculation, if one or several subtasks has an inhibiting effect, the DOF of each inhibiting subtask is 100 − |DOI|, that is, d(A_i_n) = 100 − | d(a_i_n)|. Similarly, only when each subtask of a task has an inhibiting effect can the task be considered to have an inhibiting effect on human error, and the DOI of the task is calculated using Equation (3).

Based on the findings of relevant studies [37,38] and according to their magnitudes, the DOF and DOI are divided into three grades (high, medium and low) using the non-equidistant method [37,39,40,41] to clearly characterize the level of human-induced fault interactive operation results, as shown in

Table 4. Degree of facilitation (DOF) levels.

Value Range of d(taski)fac	Grade
(0, 40]	Low
(40, 80]	Medium
(80, 100]	High

and

Table 5. Degree of inhibition (DOI) levels.

Value Range of |d(taski)inh|	Grade
(0, 40]	Low
(40, 80]	Medium
(80, 100]	High

.

4.2. Methods for Calculating the DOE of Subtasks

According to the definitions given above and the descriptions in Figure 1 and Figure 2, the facilitating or inhibiting symmetric effective expression of a subtask on human error is as follows:

$$d(A_{ij}) or d(a_{ij})=F_{ij}(x,w)$$

(4)

$$d(a_{ij})=d(A_{ij})-100$$

(5)

In an execution process of a subtask, $F_{ij}(x,w)>0$ indicates that a subtask has a facilitating effect, so $d(A_{ij})=F_{ij}(x,w)$, and $d(a_{ij})=d(A_{ij})-100$, while $F_{ij}(x,w)<0$ means that a subtask has an inhibiting effect, so $d(a_{ij})=F_{ij}(x,w)$,and $d(A_{ij})=100-\left|d(a_{ij})\right|$.

4.3. F_ij(x,w) Evaluation Methods

4.3.1. Selection of Methods for Evaluating the DOE of Human Error

The general evaluation methods based on a review of the relevant literature [39,40,41,42,43,44] are summarized in

Table 6. Commonly used evaluation methods.

Method	Description	Advantages	Disadvantages
Balanced score card	The performance is evaluated in four dimensions: finance, customer, internal process, and learning and growth.	The method is in line with the principle of combining financial and nonfinancial evaluations and is capable of avoiding the short-term behavior of an enterprise.	A relatively large number of indicators are required, so it is difficult to assign weights to the indicators.
Neural network model	A function describing the influence of the evaluation indicators on the evaluation object is fitted through self-learning with a certain number of reliable samples, stabilized through training with multiple samples, and finally used to evaluate the selected evaluation object.	There is no need to assign weights to indicators. The system automatically stabilizes through sample data analysis.	A sufficiently large number of samples is needed to obtain an influence function with a satisfactory goodness of fit. The method is applicable to problems with extensive sample data.
Fuzzy comprehensive evaluation	Factors with unclear boundaries that are difficult to quantity are quantified by applying the principle of fuzzy relation synthesis based on fuzzy mathematics. The grade of the membership of the evaluated object is comprehensively evaluated using multiple factors.	The evaluated object has a unique evaluation value that is not affected by the object set in which the evaluated object is located.	The assignment of weights to indicators is highly subjective. This method is suitable for an evaluation system that is highly subjective with many uncertain factors.
Critical incident method	The most and least important task behaviors are documented, and their most positive and most negative effects on departmental performance are categorized, documented, and evaluated.	The evaluation can be carried out throughout the whole process and is convenient and easy to implement.	Documentation and observation of critical incidents are time- and energy-consuming. This method does not allow quantitative analysis, is unable to specifically differentiate the level of importance of work behaviors, and cannot compare employees well.
Linear weighting method	This is an evaluation function method that assigns weight coefficients to objectives according to their importance and then linearly combines these coefficients to obtain the evaluation value.	The method involves only simple calculations that are easy to understand, and includes all the indicator variables of raw data, making it especially suitable for problems with numerical variables.	This method is unable to reflect the prominent influence of some evaluation indicators.
Operation standard method	The performance of employees is evaluated according to preset standards and indicators.	This method is mainly suitable for intensive production work and has clear standards.	There is uncertainty in the reasonableness of the standards.

.

After comparing a few methods commonly used in Table 6, the fuzzy comprehensive evaluation method (FUZZY method) is chosen to evaluate the (facilitating/inhibiting) symmetric effect of path dependence on human error, considering that all indicators related to the results of the symmetric effect on human error are qualitative and hence the values of these indicators cannot be directly obtained. In the FUZZY method, factors with unclear boundaries that are difficult to quantify are quantified by applying the principle of fuzzy relation synthesis based on fuzzy mathematics, and the grade of membership of the evaluated object is comprehensively evaluated using multiple factors.

4.3.2. FUZZY Method F_ij(x,w) Description to Evaluate the DOE

The main FUZZY method has four steps: (1) Determination of impact factors set; (2) Determination of the comment set; (3) Determination of the membership matrix; (4) Calculation formula for the fuzzy comprehensive evaluation.

(1)

Determination of impact factors set

The factor set contains the influencing factors to be evaluated. According to the path-dependent human error indicator system shown in Table 1, the factor set of the evaluation object is:

B11, B12, B14, B21, B23, B31, B32, B41, B42, B43, B44, B45.

(2)

Determination of the comment set

Let V = {V₁,V₂,V₃, …V_p}, where V is the comment set for the evaluation object and reflects the various overall evaluation results that the evaluator may collect about the evaluation object. V_j (j = 1,2,3, …p) is the jth evaluation result, where p is the total number of evaluation results. Based on a review of the relevant literature [34,36,37], the influencing factors in the present study are defined by three possible grades of effect: good, fair and poor, as shown in

Table 7. Levels of the effect of factors influencing human error.

First-Level Indicator	Second-Level Indicator	Level of Effect
Task conflict (B1)	Safety risk at the initial position (B11)	No risk, low risk, medium-to-high risk
	Delay (B12)	No delay, normal delay, severe delay
	Information display (B14)	Clear and reasonable, basically clear and reasonable, no display
Equipment fault and deterioration (B2)	Joystick (B21)	No fault or deterioration, slight fault or deterioration, severe fault or deterioration
	Extravehicular camera (B23)	No fault or deterioration, slight fault or deterioration, severe fault or deterioration
Environmental impact (B3)	Noise (B31)	No noise, soft noise, loud noise
	Illumination (B32)	Comfortable, slightly uncomfortable, uncomfortable
Human factors (B4)	Changes in cognitive and operational abilities (B41)	Large, medium, small
	Level of experience (B42)	High, medium, low
	Physical fatigue (B43)	Very fatigued, fair, not fatigued
	Psychological pressure (B44)	High, medium, low
	Mental fatigue (B45)	Very fatigued, fair, not fatigued

.

Without loss of generalizability, the standard membership of the comment set is defined specifically for the present study as follows: (1) for DOF, V = {good, fair, poor} = {20, 60, 100}; and (2) for DOI, V = {good, fair, poor} = {100, 60, 20}.

(3)

Determination of the membership matrix

During the comprehensive evaluation of the DOE on human error, the membership of the indicators is determined with the graded ratio method [45]. That is, membership is determined by directly using the questionnaire survey results to count the frequencies of “good, fair, and poor” of each factor. Membership under the facilitating effect is calculated using the following equation:

$$r_{ij,c}=\frac{Q_{ij}}{Q}$$

(6)

Similarly, membership under the inhibiting effect is calculated using the following equation:

$$r_{ij,c}=-\frac{Q_{ij}}{Q}$$

(7)

In Equations (5) and (6), r_ij,c is the membership of the influencing factor x at the cth grade, in which r_ij,c > 0 and r_ij,c < 0 indicate the membership of the factor x at the cth grade with the facilitating and the inhibiting effects, respectively; Q_ij is the number of valid questionnaires for the shadow factor X at the cth grade; and Q is the total number of valid questionnaires.

(4)

Calculation formula for the fuzzy comprehensive evaluation

The vector of the fuzzy comprehensive evaluation results is denoted as S. The comprehensive evaluation model is defined as follows:

$$S=W\ast R=(w_1,w_2,\cdots \cdots ,w_d)\ast \left(\begin{array}{ccc}{r}_{11}& \cdots & r_{1p}\\ ⋮& \ddots & ⋮\\ r_{d1}& \cdots & r_{dp}\end{array}\right)=(s_1,s_2,\cdots \cdots ,s_d)$$

(8)

where S is the fuzzy subset of V, s_j (j = 1,2,…, p) is the membership of the result of the evaluation set, V_j, to S, and w_d is the weight of the dth indicator.

The comprehensive membership of the evaluation object is obtained by combining the fuzzy comprehensive evaluation set S and the standard membership V of the comment set:

$$F_{ij}(x,w)=S\ast V^T$$

(9)

where V^T is the transpose of V.

The concept of Fuzzy sets is different in different application fields and backgrounds. The fuzzy sets in this paper can be viewed as the standard membership of the comment set. In general, a fuzzy rule has the form: if x is A then y is B. But in this paper, it main focuses on the fuzzy calculation process and formulas.

4.3.3. Weights of Influencing Factors

To improve the rationality of weights, the weights of influencing factors in this paper are obtained by combination weighting method based on game theory. Main processes of this method are as follows:

(1)

Random linear combination of k weight vectors:

$$w_c={\displaystyle \sum _{i=1}^k{m}_i}{w}_i^T$$

(10)

w_c is a combination weight based on basic weight sets; m_i denotes combination coefficient; w_i is the weight of each weight method; k is number of weight methods.

(2)

According to the differential properties of matrix, the linear equation of optimal first-order derivative about Equation (11) is:

$$\left[\begin{array}{cccc}{w}_1\cdot w_1^T& w_1\cdot w_2^T& \cdots & w_1\cdot w_K^T\\ w_2\cdot w_1^T& w_2\cdot w_2^T& \cdots & w_2\cdot w_K^T\\ \cdots & \cdots & \cdots & \cdots \\ w_k\cdot w_1^T& w_k\cdot w_2^T& \cdots & w_k\cdot w_K^T\end{array}\right]\ast \left[\begin{array}{c}{m}_1\\ m_2\\ \cdots \\ m_k\end{array}\right]=\left[\begin{array}{c}{w}_1\cdot w_1^T\\ w_2\cdot w_2^T\\ \cdots \\ w_k\cdot w_K^T\end{array}\right]$$

(11)

(3)

m_k can be obtained based on Formula (11). The normalization expression of m_k is as follows:

$$m_k^{normal}=(\left|m_k\right|)/{\displaystyle \sum _{i=1}^k\left|m_i\right|}$$

(12)

(4)

The optimal comprehensive weight calculation method for the evaluation factors is written as:

$$w_c^{optimal}={\displaystyle \sum _{i=1}^k{m}_i^{normal}}\ast w_i^T$$

(13)

To obtain optimal comprehensive weights, initial weights should be obtained by different methods including AHP (analysis hierarchy process) and improved G2 methods in this paper. The AHP [46] and G2 [47] methods are not described here.

Initial data was obtained by questionnaire. Respondents in this paper included relevant experts from the astronaut training center, human reliability analysis experts, and experts and scholars in the field of human factor engineering. A total of 35 questionnaires were distributed, and 35 were returned, among which 31 were actually valid

Based on Formulas (10)–(13), the optimal comprehensive weights of influencing factors were obtained by analyzing two different weight vectors obtained by AHP and improved G2 methods. The weights obtained by different methods including combination weighting method based on game theory, AHP method and G2 method were shown in

Table 8. Weights of second-level indicators influencing the path-dependent human error.

Second-Level Indicator	Weight
	AHP Method	G2 Method	Combination Weighting Method Based on Game Theory.
Safety risk at the initial position (B11)	0.0925	0.0856	0.0875
Delay (B12)	0.0939	0.0957	0.0952
Information display (B14)	0.1008	0.0783	0.0813
Joystick (B21)	0.1001	0.0827	0.0876
Extravehicular camera (B23)	0.0873	0.0931	0.0915
Noise (B31)	0.0523	0.0898	0.0793
Illumination (B32)	0.0523	0.0415	0.0446
Changes in cognitive and operational abilities (B41)	0.1092	0.0943	0.0985
Level of experience (B42)	0.1186	0.1474	0.1393
Physical fatigue (B43)	0.0525	0.0632	0.0602
Psychological pressure (B44)	0.0723	0.0629	0.0655
Mental fatigue (B45)	0.0680	0.0653	0.0661

.

The distributions of weights (see Figure 3 based on Table 6).

Please note: serial number of x-axis in Figure 3 shows a corresponding sequence of influencing factors.

It is shown in Figure 3 that the weight curve obtained by combination weighting method is between the curve obtained by G2 method and the curve obtained by AHP method, which indicates that the weight obtained by combination weighting method considers two different weight values respectively obtained by AHP and G2 methods, then the weight values are balanced. To a certain extent, the subjectivity of experts is eliminated. Obviously, the weights obtained by combination weighting method are more reasonable.

5. Results and Discussion

5.1. Influencing Factors

The influencing factors were obtained by two processes. Firstly, initial influencing factors were collected by expert consultation and literature reviews. Secondly, based on relative importance and expert judgment, a few initial influencing factors were eliminated. Obviously, the analysis process is reasonable and the obtained influencing factors are convincing.

The Cronbach’s alpha coefficient and the Kaiser–Meyer–Olkin (KMO) value were larger than 0.7, which shows that the reliability and validity of the questionnaire survey about relative importance can be accepted. The factors eliminated from initial influencing factors combined the relative importance and expert judgment. Although the questionnaire survey and expert judgment are somewhat subjective, the process of eliminating influencing factors shows that the subjectivity has been minimized.

5.2. Weights of Influencing Factors

In general, the acquisition of influencing factor weights requires a related questionnaire. Given the uncertainty of human beings, the data of the questionnaire survey are somewhat subjective. To decrease the subjectivity, the weights of influencing factors in this paper were obtained by combining two different weights that were obtained by AHP method and G2 method, respectively. It is shown in Figure 3 that the weight values are between the values obtained by AHP method and the values obtained by G2 method. To a certain extent, the subjectivity of experts was reduced. Obviously, in comparison to the single weight obtained by a method, the weights obtained by the combination weighting method had less subjectivity.

5.3. Performance Discussion of the Fuzzy Evaluation Method of F_ij(x,w)

The performance analysis simulation process is as follows: (1) The convergence analysis focuses on the inherent characteristics of the fuzzy evaluation method and determines the condition under which the maximum or minimum value is obtained. While the weights remain fixed, the evaluation function yields the maximum or minimum value only when all influencing factors are within the range of values and their grades are simultaneously “good” or “poor”. Then, the maximum and minimum values of the path dependence can be obtained based on evaluation methods of F_ij(x,w), namely, Formulas (6)–(9). The calculation process about maximum and minimum values used a programming language called C.; (2) Analysis of the consistency/effectiveness of evaluation results is carried out mainly to investigate whether the value grades of the influencing factors are consistent with the evaluation results. With the influencing factors simultaneously taking the same grades (good, fair or poor), simulation calculation was conducted using a program written in C language to obtain the evaluation results. (3) The performance analysis of the variation trend of the measurement results is conducted mainly to investigate whether there are any differences in the evaluation results when the grade values of the influencing factors differ (i.e., there is a difference in the membership matrix); due to the diversity of the membership matrix, a part of the membership matrix was intentionally selected in the performance analysis, and then simulation calculation was carried out using a program written in C language to obtain the evaluation results.

(1)

Convergence Analysis

To maximize or minimize the value of the DOF, the input grades of all the influencing factors in the membership matrix should simultaneously be “good” or “poor”. From Equations (6)–(9) and Table 5, we have

d(A_i_j)_max = 100; d(A_i_j)_min = 20.

d(a_i_j)_max = −20; d(a_i_j)_min = −100.

Obviously, 0 < d(A_i_j) ≤ 100, and −100 ≤ d(a_i_j) ≤ 0. Therefore, the fuzzy evaluation method can converge completely in the range of the evaluation of the effect on human error.

(2)

Analysis of the Consistency/Effectiveness of the Evaluation Results

(1) Analysis of the Consistency/Effectiveness of the DOF Evaluation Results for Path-Dependent Human Error

To investigate whether the measurement results were consistent with or effective for the variation trend of the factor input values when the influencing factors in the membership matrix took values at the three different grades, we proposed that all the influencing factors take the same values at several special points. Equations (6)–(9) and Table 7 and Table 8 are used to obtain the DOF evaluation results for human error, as shown in Figure 4.

Figure 4 shows that when all the influencing factors are at grades of poor, fair and good, the DOF evaluation values are 100, 60 and 20, respectively. This means that: ① When the evaluation values of the influencing factors are poor, fair and good, the evaluation result falls into the high, fair and low intervals, respectively, indicating that the input values of the human error factors are fully consistent with the evaluation results, an effectiveness of 100. ② The better the grade of the influencing factors is, the higher is the level at which the influencing factors are located, and the smaller the evaluation result is. Therefore, the DOF evaluation results are consistent with the variation in the grade of the influencing factors, and the “fuzzy evaluation method + combination weighting method” is fully effective.

(2) Analysis of the consistency/effectiveness of the DOI evaluation results for path-dependent human error

The DOI is calculated similarly to the DOF but has a negative value, with the negative sign indicating the inhibition but not the magnitude. Likewise, Equations (5)–(8) and Table 7 and Table 8 are used to obtain the DOI evaluation result for the human error and human–machine interaction fault. The results are shown in Figure 5.

Similarly, as seen from Figure 5, when all the influencing factors are at grades of poor, fair and good, the DOI evaluation values for human error are −20, −60 and −100, respectively, which are similar to the DOF evaluation values for human error. This shows that: ① When the levels of influencing factors are poor, fair and good, the corresponding evaluation results fall into the poor, fair and good intervals, respectively, indicating that, for the mode of the inhibiting effect on human error, the level of the influencing factors is completely consistent with the evaluation result, an effectiveness of 100. ② The higher the grade of a certain category of influencing factors is, the higher is the level at which the influencing factors are located, and the larger the DOI evaluation result is for human error. Therefore, the DOI evaluation results for human error are consistent with the variation in the grade of the influencing factors, and the “fuzzy evaluation method + combination weighting method for calculating the effect on human error” is fully effective.

(3)

Variation trend of the calculation results

(1)

Analysis of the variation trend of the DOF evaluation results for human error

To reflect the changes in the DOF evaluation results when the influencing factors take different grade values, some special values are simulated for the factor grades. Consistent values are taken for all factors at the same grade. To simplify the discussion,

Table 9. Values of the first row in each membership matrix and the comprehensive evaluation results.

Serial Number of the Grade Values of the Influencing Factors	The First Row of Each Membership Matrix (of the Levels of Impact Factors Are Good, Fair and Poor, Respectively)	DOF Evaluation Value
1	1, 0, 0	20
2	0.8, 0.2, 0	28
3	0.8, 0.1, 0.1	32
4	0.8, 0, 0.2	36
5	0.5, 0.5, 0	40
6	0.5, 0.4, 0.1	44
7	0.5, 0.3, 0.2	48
8	0.5, 0.2, 0.3	52
9	0.5, 0.1, 0.4	56
10	0.5, 0, 0.5	60
11	0.3, 0.3, 0.4	64
12	0.3, 0.2, 0.5	68
13	0.2, 0.3, 0.5	72
14	0.2, 0.2, 0.6	76
15	0.1, 0.3, 0.6	80
16	0.1, 0.2, 0.7	84
17	0, 0.3, 0.7	88
18	0, 0.2, 0.8	92
19	0, 0.1, 0.9	96
20	0, 0, 1	100

presents only the first row of the membership matrix and the DOF evaluation results of the human–machine interaction when some special values are simulated.

The evaluation results in Table 9 are illustrated in Figure 6.

Please note: serial number of x-axis in Figure 6 is consistent with the serial number in Table 9.

Figure 6 shows that similar to the path dependence, the evaluation values are different when the grades of the influencing factors take different values. This indicates that the evaluation method can differentiate between the evaluation results for different input grade values. In other words, there will not be a situation in which the input values are different but the calculation results are the same, or a situation in which the input values are the same while the calculation results are different. On the other hand, Figure 6 shows that when the input grade values are different, there is a difference between the calculation results, and this difference has a certain range, indicating that the calculation method has a certain sensitivity.

(2) Analysis of the variation trend of the DOI evaluation result for human error

Similar to the DOF, some special values are assigned to the influencing factor grades (same as those in Table 9) to reflect the changes in the DOI evaluation results when the influencing factors are assigned different grade values. Based on Equations (6)–(9) and Table 6 and Table 7, the DOI evaluation results for human error are obtained, as shown in Figure 7.

Figure 7 shows that similar to the case of DOF variation, the DOI values are different when the grades of the influencing factors are different. This indicates that the fuzzy evaluation method is able to differentiate between the evaluation results for different input grade values. In other words, there will not be a situation in which the input values are different but the calculation results are the same, or a situation in which the input values are the same while the calculation results are different. On the other hand, Figure 7 shows that when the input grade values are different, there is a difference between the calculation results, and this difference has a certain range, showing that the calculation method has a certain sensitivity.

However, the methods also have limitations. For example: (1) due to the relative scarcity of path-dependence research, the influencing factors of the effect of path dependence on human error, which were obtained in the present study based on a literature survey, may not be complete. Further investigation and literature tracking are necessary to obtain more influencing factors for the effect of path dependence on human errors; (2) the relative importance of influencing factors is based on the questionnaire survey. Its values of relative importance could be biased, and therefore the eliminated influencing factors may be biased; (3) the divisions of DOF and DOI levels were based on relevant studies, which may be subjective.

6. Example Analysis

The following is an example that illustrates the procedure for calculating the DOE of the path dependence on human–machine interaction in the context of a space robotic manipulator task.

Suppose that task A is divided into subtasks A1–A3. The DOI and DOF of each subtask are first successively calculated, and then the DOI and DOF of the task are obtained according to the overall calculation method.

(1)

Subtask A1

Step 1: The second-level indicator evaluation matrix R for the effect of the path dependence on human error is obtained using Equations (6) and (7). The different rows in R reflect the membership of the evaluated object to the fuzzy subset at each grade from different single factors. Assume the membership matrix R₁ of the subtask A1 is as follows:

$$R_1=\left(\begin{array}{ccc}-0.8& 0.2& 0\\ -0.2& 0.3& 0.5\\ -0.5& 0.4& 0.1\\ -0.6& 0.3& 0.1\\ -0.6& 0.3& 0.1\\ -0.8& 0.2& 0\\ -0.9& 0.1& 0\\ -0.4& 0.3& 0.3\\ -0.3& 0.5& 0.2\\ -0.3& 0.4& 0.3\\ -0.2& 0.5& 0.3\\ -0.2& 0.6& 0.2\end{array}\right)$$

Step 2: Using Table 8, the weight W of the second-level indicators for the effect of the path dependence on human error is obtained as follows:

W = (0.0875, 0.0952, 0.0813, 0.0876, 0.0915, 0.0793, 0.0446, 0.0985, 0.1393, 0.0602, 0.0655, 0.0661)

Step 3: According to Equation (8), the fuzzy comprehensive evaluation result vector S1 for the effect of path dependence on human error is obtained as follows:

$$S_1=W\ast R_1=\left(\begin{array}{ccc}-0.4663& 0.3483& 0.1820\end{array}\right)$$

Step 4: According to Equation (9), the comprehensive membership $F_{A1}(x,w)$ of the path dependence of subtask A1 to the fuzzy evaluation object of the human error is obtained as follows:

$$F_{A1}(x,w)=S\ast V^T=\left(\begin{array}{ccc}-0.4663& 0.3483& 0.1820\end{array}\right)\ast \left(\begin{array}{c}100\\ 60\\ 20\end{array}\right)=-22.0920$$

Similarly, the membership matrices R₂ and R₃ of subtasks A2 and A3 are assumed to be as follows:

$$\begin{array}{ccc}{R}_2=\left(\begin{array}{ccc}-0.5& 0.5& 0\\ -0.2& 0.5& 0.3\\ -0.5& 0.4& 0.1\\ 0& 0.7& 0.3\\ -0.6& 0.3& 0.1\\ -0.8& 0.2& 0\\ -0.5& 0.5& 0\\ -0.6& 0.3& 0.1\\ 0& 0.5& 0.5\\ -0.3& 0.4& 0.3\\ 0& 0.7& 0.3\\ -0.2& 0.6& 0.2\end{array}\right)& \hspace{1em}& R_3=\left(\begin{array}{ccc}0& 0.5& 0.5\\ -0.1& 0.5& 0.4\\ -0.5& 0.4& 0.1\\ 0& 0.7& 0.3\\ -0.2& 0.3& 0.5\\ -0.5& 0.5& 0\\ -0.5& 0.5& 0\\ -0.5& 0.3& 0.2\\ 0& 0.5& 0.5\\ -0.3& 0.4& 0.3\\ 0& 0.8& 0.2\\ -0.2& 0.6& 0.2\end{array}\right)\end{array}$$

Similarly, the fuzzy comprehensive evaluation result vectors S₂ and S₃ of subtasks A2 and A3 for the effect of path dependence on human error, respectively, are obtained as follows:

$$\begin{gathered} S_2=W\ast R_2=\left(\begin{array}{ccc}-0.3345& 0.4596& 0.2026\end{array}\right) \\ {S}_3=W\ast R_3=\left(\begin{array}{ccc}-0.2110& 0.4899& 0.2957\end{array}\right) \end{gathered}$$

Finally, the DOF and DOI of subtasks A2 and A3 are as follows:

F_A2 (x, w) = −1.8196, F_A3 (x, w) = 14.2152

(2)

Analysis of the DOF/DOI consistency of task A

According to the definition, task A has a facilitating effect as long as it has at least one facilitating subtask. Its DOF is calculated using Equation (2) (noting that only when all the subtasks are inhibiting is the effect mode of the task inhibiting), and in this case the DOI of the task is calculated using Equation (3). Assuming that the weights of the subtasks A1, A2, and A3 are $W_A=(w_1,w_2,w_3)=(0.2,0.3,0.5)$, the DOF of task A is calculated using Equation (2) as follows:

d (A)fac = w1 * ×FA1 (x, w) + w2 × FA2 (x, w) + w3 × FA3 (x, w)

= 0.2 × (100 − |−22.0920|) + 0.3 × (100 − |−1.8196|) + 0.5 ×14.2152

= 52.1433

According to the grade standard of DOF levels for human–machine interaction in Table 4, because the DOF of task A, d (A)_fac, is between 40 and 80, so the DOF of task A for human error is at a “Medium” level under path dependence.

7. Conclusions

Path dependence influences human error by inhibiting or facilitating the possible occurrence of an accident. To investigate the underlying mechanism, the present study explored the symmetric effect of path dependence on human error; obtained the influencing factor system for the effect of path dependence on human error as well as the relations between these influencing factors; developed the process diagram, judgment criteria and state transition process for the symmetric mode of the path-dependence effect; established a task-based symmetric model for calculating the DOE of path dependence on human error; and obtained a fuzzy evaluation method for measuring the DOE of subtasks.