Identification and Correlation Analysis of Multi-Dimensional Risk Factors for Bus Accidents

Abstract

Public transport accidents pose a significant threat to public safety, so it is necessary to conduct an in-depth exploration of their risk mechanisms. In this study, risk factors were first identified through statistical analysis of the time, road section, type, and cause of accidents. Subsequently, the N-K model was applied to analyze the coupling effect among human, vehicle, road, environment, and management factors, and the Decision-Making Trial and Evaluation Laboratory (DEMATEL) model was adopted to evaluate the centrality and causal relationship of these factors. The DEMATEL results were corrected using the coupling values obtained from the N-K model, through which the key factors affecting public transport accidents were identified. Finally, conclusions were drawn as follows: Human factors are the dominant inducement of public transport accidents, accounting for 70.86%, among which driver fatigue and weak safety awareness are the main sub-factors. The “human-vehicle-environment” triple coupling factor presents the highest risk, with a coupling value of 0.62, which is 1.77 times the average level of single-factor coupling. Seven key risk factors were identified, and their ranking by centrality from highest to lowest is: as follows driver fatigue, driver physical health, brake failure, unchannelized intersections, rainy weather, following too closely, and insufficient safety training. Among these factors, insufficient safety training exerts the strongest driving effect on other factors.

1. Introduction

1.1. Background

With the continuous acceleration of urbanization, buses have become one of the main ways of daily travel for people. However, during the operation of buses, public transport vehicles often encounter a variety of traffic safety risks, which often lead to traffic accidents and have a significant impact on public safety, urban transportation systems, and social resources. Therefore, studying the risk factors and key factors that affect bus traffic accidents is of great significance to improve the safety of bus operation and reduce the occurrence of traffic accidents.

1.2. Literature Review

Public transport accidents pose a significant threat to public safety, and in-depth exploration of the risk factors contributing to such accidents has become crucial for safeguarding the operational safety of public transport. From the perspective of existing studies, scholars have conducted multi-dimensional investigations into the risk factors of public transport accidents and achieved relatively abundant research results. At the research level of the correlation between single factors and public transport accidents, numerous scholars have identified the key influencing factors of public transport accidents through quantitative analysis methods. Based on survey data from 2023 public transport drivers in Taiwan, Tseng confirmed via the Logistic regression model that there is a “U-shaped” correlation between driving experience and the risk of liability accidents, with drivers having 6 to 8 years of driving experience facing the lowest driving risk [1]. Han conducted a questionnaire survey on the driving behaviors of 320 public transport drivers in Tehran, Iran, and identified through multiple Logistic regression that behaviors such as signal violations and speeding by Iranian public transport drivers are important inducements for high-risk accidents [2]. Miyama’s study on Japanese bus drivers showed that driving while ill and insufficient sleep are key risk factors leading to public transport accidents caused by fatigued driving [3]. By comparing and analyzing using the decision tree and ordered Logit model, Bhin found that there are significant differences in the factors affecting the severity of accidents between drivers of different genders [4]. Zhang sorted out the causal chain of “insufficient safety management–inadequate training–situational misjudgment–speeding” in Chinese passenger and freight vehicle accidents through the improved DREAM model and social network analysis [5]. Through a questionnaire survey, Mokarami found a negative correlation between bus accidents and safety culture as well as the unsafe behaviors of drivers [6]. The Bayesian network model constructed by Khoo indicated that drivers with 6 to 10 years of driving experience on specific routes are more likely to enhance passengers’ sense of safety [7]. Nævestad’s comparative study on public transport drivers in Norway and Greece revealed that safety norms and personal freedom values in the safety culture of different countries significantly affect the dangerous driving behaviors of drivers [8]. In addition, studies on the difference in accident risks between roadside bus stops and roadside parking zone bus stops [9], the prediction of public transport accidents based on historical traffic violation data [10], and the connection between drivers’ mental health assessment and public transport accidents [11] have all verified through statistical models the significant impact of specific types of violation behaviors on accident risks.

Existing single-factor analyses of public transport accidents mostly focus on the independent impact of a single category of factors such as humans, vehicles, and roads. Although they can identify specific risk factors, they ignore the interaction and correlation effects between different factors, fail to fully present the complex causal logic of accident occurrence, and thus struggle to support the comprehensive prediction and precise control of accident risks. Therefore, scholars have shifted to systematic analysis research on “multi-factor coupling” to reveal the accident risk mechanism. Kim analyzed intercity bus accidents on South Korean highways using the Probit model and found that factors such as driver fatigue and slippery roads have heterogeneous impacts on the severity of accidents [12]. By conducting a detailed analysis of the General Estimates System (GES) accident database from 2005 to 2009, Kaplan found that factors such as drivers’ personal characteristics, driving behaviors, and road environment are important factors affecting the severity of public bus accidents in the United States [13]. Samerei discovered in the study of Australian bus accident datasets that the causes of bus accidents involve multiple aspects, including driver characteristics, road environment, and the behaviors of traffic participants [14]. Based on the investigation reports of 56 Chinese passenger and freight vehicle accidents that caused more than 10 deaths, Sha found that pedestrians crossing the road and drivers’ behaviors are the core factors leading to accidents [15]. Huang proposed the Tropos target risk accident framework and, combined with typical cases such as the Chongqing Wanzhou bus falling into the river, clearly presented the risk transmission path of “target layer–event layer–processing layer” [16]. Suwandi’s bibliometric analysis revealed that since 2018, research attention on the role of human factors in bus accidents has increased significantly, with fatigue and distraction becoming core research topics [17]. After conducting a qualitative analysis of the reports on traffic injury accidents in the Boulogne-Billancourt community in France, Brenac found that in public transport accidents, the proportion of indirect involvement accidents of buses is higher than that of direct involvement accidents, and the main causes of accidents are drivers’ blocked vision and pedestrians crossing the road [18]. In the analysis of 117,859 actual operation data of the No. 851 bus route in Nanjing, Liu found that the reduction in driving speed is a key factor leading to drivers’ distracted driving [19]. Suraji applied Principal Component Analysis (PCA) technology to identify the causes of traffic accidents related to vehicle conditions, and the research results showed that intercity bus accidents are mainly caused by four key factors, namely the braking system, tire condition, vehicle stability, and applicability [20]. Wang’s study found that the factors affecting the traffic safety attitude of bus drivers and their dangerous driving behaviors are mainly enterprise management and external environment factors [21].

A summary of the above literature shows that existing studies have obvious limitations. Firstly, single-factor analysis cannot capture the risks arising from the interaction of multiple elements within the system, and it is easy to mistake surface phenomena for risk sources. Static and single-dimensional studies are difficult to adapt to dynamic scenarios, ultimately leading to a one-sided understanding of risks. Secondly, the research depth on the multi-factor coupling effect is insufficient. Although some studies mention the correlation among multiple factors such as drivers, vehicles, roads, environment, and management, most of them only stay at the level of listing factors or sorting out simple transmission relationships, and fail to deeply reveal the coupling mechanism of the interaction between various factors. As a result, they cannot accurately reflect the complex causal chain of accident occurrence. Existing studies have not clarified the degree of risk superposition under different factor combinations, nor can they judge the differences in the accident-inducing intensity of combined scenarios, which makes the prediction of accident risks lack accuracy. Finally, the integration of methods for risk factor assessment is insufficient. Most existing studies rely on a single model for analysis or only construct a system framework through structural equation models, lacking complementarity and correction between different models. A single model has inherent limitations and cannot fully reflect the causal logic between factors, while framework models lack accurate numerical support. This leads to insufficient accuracy and reliability in the identification of key risk factors, and fails to provide a scientific and practical basis for safety management.

Based on the limitations of current research, this study proposes a research approach that integrates multiple methods: Firstly, through statistical analysis of the time, road section, type, and cause of accidents, the potential risk factors of public transport accidents are systematically sorted out and initially identified, so as to make up for the lack of systematicness in risk factor screening in existing studies. Secondly, the N-K model is used to focus on analyzing the coupling effect among human, vehicle, road, environment, and management factors, and quantify the risk superposition degree of different factor combinations, so as to solve the insufficient research on the multi-factor coupling mechanism. At the same time, the Decision-Making Trial and Evaluation Laboratory (DEMATEL) model is used to evaluate the centrality and causal relationship of each factor, and the coupling values obtained by the N-K model are used to correct the DEMATEL results, so as to realize the complementary advantages of the quantitative model and the causal analysis model and improve the accuracy of key risk factor identification. Finally, through the research, the core influencing factors are clarified, which provides a more scientific and accurate decision-making basis for the safety management of public transport and further improves the research on the risk mechanism of public transport accidents.

1.3. N-K Model and DEMATEL Model

Currently, the N-K model has been applied in multiple fields such as warehouse management safety, airport ground control, mining operations, and ship navigation safety [22,23,24,25]. Compared with traditional methods like fault tree analysis and statistical analysis, the N-K model conducts analysis based on actual data, incorporates the interactions of multiple factors into consideration, and analyzes the role of each factor in complex systems as well as the complex relationships among them, thus making it suitable for the research on multi-factor coupling in bus traffic accidents. The Decision-Making Trial and Evaluation Laboratory (DEMATEL) model has been widely used in fields including environmental protection, supply chain management, and product design [26,27,28,29,30]. By constructing the mutual influence relationships among factors, the DEMATEL model can systematically analyze the causal relationships of complex problems and reveal the interactive influences between factors. For the analysis of risk factors in bus traffic accidents, the DEMATEL model is conducive to identifying key factors and their mutual influences, effectively improving the accuracy of risk assessment and the ability to support decisions.

The remaining parts of this paper are organized as follows: Section 2 explains the sources and selection and exclusion criteria of bus accident data, identifies the attribution of core category factors of bus accidents, and puts forward preliminary preventive suggestions; Section 3 constructs risk factor analysis models including the N-K model, the DEMATEL model, and their integrated model after comparing traditional methods; Section 4 calculates coupling values and factor importance using the N-K model and the DEMATEL model, and identifies seven key risk factors; Section 5 summarizes the research results, limitations, and future research directions.

2. Acquisition and Processing of Bus Accident Data

2.1. Sources and Screening of Bus Accident Data

This study mainly obtains bus accident data from accident investigation reports released by transportation departments and the literature related to bus accidents. Prior to conducting specific coupling analysis of bus accidents, detailed explanations are provided regarding the data sources and selection and exclusion criteria.

The sources of bus accident data are mainly publicly reported bus accidents, and accident cases are selected as samples from publicly available online channels such as news websites and government department websites (e.g., the Ministry of Transport, traffic police detachments in various regions). This method enables convenient and efficient data acquisition, allowing accident data to be collected within a relatively wide scope, which provides a sample basis for subsequent coupling analysis of risk factors. In the process of integrating the acquired bus accident data, a unified accident information framework is used as the basis to extract key information from accident reports, including accident time, location, cause, number of casualties, and accident level. This integration method ensures the standardization and systematicness of the data, enabling data from different sources to be presented in a unified format, which facilitates subsequent screening and comparative analysis. To ensure the validity and reliability of bus accident data, the collected bus accident reports need to be screened in accordance with specific criteria, and then further data exclusion work is carried out on the screened dataset. The specific selection and exclusion criteria are as follows:

The selection criteria for bus accident data are as follows: Bus accidents with public reports and in which buses are the core participants are selected, regardless of accident type and accident level. Accident reports must contain key field information, covering at least the accident occurrence time, road section type, accident cause, number of casualties, etc. Core influencing factors (human, vehicle, road, environment, management) are summarized based on literature analysis and existing methods, and accident reports are screened from the perspective of these five factors, with accident reports required to include at least one type of core influencing factor in their descriptions.

The exclusion criteria for bus accident data are as follows: Accidents involving buses in non-road operation status are excluded, and only accidents occurring during normal road operation are retained. If the same accident is published by multiple websites, duplicates are identified through matching the three elements of “accident time, location, and number of casualties”, and only one valid entry is retained. If the same accident is repeatedly published by the same website, the earliest published version is retained. Abnormal cases are identified and eliminated through data cleaning, such as accidents with overly old occurrence time or contradictions between the number of casualties and accident level. Accident reports with vague descriptions of accident causes and unclassifiable influencing factors are excluded if it is determined that the information cannot be supplemented after verification.

After screening and excluding bus traffic accident cases, a total of 178 bus traffic accident data records from 2004 to 2024 were obtained.

2.2. Identification of Risk Factors and Binarization Standards

Through in-depth analysis and research on 178 bus traffic accidents, the risk factors affecting bus accidents in this study are divided into core category factors and specific factor nodes. The core category factors include human factors, vehicle factors, road factors, environmental factors, and management factors. Each core category factor is further subdivided into 26 risk factor nodes, thereby forming a set of risk factors for bus traffic accidents.

To realize the conversion of risk factor nodes into the five core category factors (human factor H, vehicle factor V, road factor R, environmental factor E, management factor M) of the N-K model, this study constructed an “attribution” mapping rule and clarified the definitions of core category factors and the mapping logic of each risk factor node. The definitions of the five core category factors are as follows: the human factor (H) refers to the set of risk factors related to the behavioral characteristics, physiological status, and safety awareness of personnel involved in bus operation, and is the factor related to the direct triggering subject of accidents; the vehicle factor (V) refers to the set of risk factors related to the technical performance, equipment status, and maintenance management of buses, which directly affects the driving safety and controllability of vehicles; the road factor (R) refers to the set of risk factors related to road infrastructure, traffic facilities, and road section geometric characteristics, which determines the safety of the road environment for vehicle driving; the environmental factor (E) refers to the set of risk factors related to the natural environment and traffic flow environment, which indirectly affects the occurrence of accidents by influencing the functional performance of humans, vehicles, and roads; the management factor (M) refers to the set of risk factors related to the safety management mechanism of bus companies and industry supervision, and is a systematic factor that ensures the controllability of risks from humans, vehicles, roads, and the environment. “Attribution” mapping determines the core category factor to which a factor node primarily belongs based on the core attribute of the factor node, i.e., the category most directly associated with the factor node. Each risk factor node corresponds to only one core attribution category, and the specific attribution relationship is shown in

Table 1. Risk factors for bus traffic accidents.

Core Category Factors	Factor Node	Factor Node Code
Human factors	Physical health condition	X1
	Fatigued driving	X2
	The following distance is too close	X3
	Speeding driving	X4
	Judgment error or operational error	X5
	Dangerous passenger behaviors	X6
	Improper behaviors when getting on and off the vehicle	X7
	The activities of traffic participants interfere with the bus	X8
Vehicle factors	Brake system failure	X9
	Tire wear or flat tire	X10
	Failure to conduct regular inspections and maintenance on time	X11
	The maintenance quality of the vehicle is unqualified	X12
	Incomplete or damaged safety equipment	X13
Road factors	Road surface unevenness, potholes, etc.	X14
	Road surface adhesion	X15
	The signal light is set unreasonably or malfunctioning	X16
	The traffic flow is too heavy and a traffic jam has occurred	X17
	There are blind spots or poor sight distances on the road section	X18
Environmental factors	The weather has reduced the visibility of the road surface	X19
	Strong light irradiation affects the driver’s vision	X20
	Weather impacts such as road icing and snow accumulation	X21
Management factors	The safety management system is not perfect	X22
	Insufficient safety education and training	X23
	The vehicle scheduling is unreasonable	X24
	Failure to effectively supervise drivers to comply with traffic regulations	X25
	The investigation and handling after the accident are not timely or professional	X26

.

To identify the core category factors involved in each bus accident, the 26 risk factor nodes (X1–X26) were subjected to binarization processing, and uniform criteria for judging a “risk-free state (assigned a value of 0)” and “risky state (assigned a value of 1)” were defined. The core category factors involved in a bus accident are expressed as a vector $[H,V,R,E,M]$ (where 1 indicates relevance and 0 indicates no relevance). Combining the Provisions on the Procedures for Handling Road Traffic Accidents, Provisions on the Administration of Urban Bus and Tram Passenger Transport, and the practical experience of on-site bus accident investigations, this study formulated binarization standards for each risk factor node. The objectivity of the results was ensured through a mechanism of “independent assignment by two researchers and verification against original materials”. The specific standards are as follows:

If an accident report contains the following risk factors, the accident is classified under human factors (X1–X8): When X1 (driver’s physical health status) is assigned a value of 1, the accident investigation report must clearly record that the driver had health abnormalities such as sudden syncope or heart attack, and secondary health problems after the accident must be excluded; when assigned a value of 0, the driver’s physical condition was normal or there were no records of relevant abnormalities. When X2 (fatigued driving) is assigned a value of 1, it must meet the conditions of “continuous driving for more than 4 h without effective rest” or “post-accident tests showing the driver had physiological signs of fatigue”; when assigned a value of 0, the driving duration was in compliance with regulations and there were no records of fatigue signs. When X3 (following too closely) is assigned a value of 1, the safe distance between the two vehicles at the time of the accident, calculated based on the brake marks at the accident scene, was less than 80% of the minimum safe distance specified in the specification for the setting of highway traffic signs and markings; when assigned a value of 0, the safe distance met the regulatory requirements. When X4 (speeding) is assigned a value of 1, it was confirmed through tachograph data or road speed measurement equipment that the vehicle speed at the time of the accident exceeded the speed limit of the road section by 10% or more; when assigned a value of 0, the vehicle speed was within the speed limit range. When X5 (judgment or operation error) is assigned a value of 1, the accident investigation conclusion clearly pointed out that the driver had judgment or operation deviations that directly led to the accident, such as “failure to observe pedestrians at the intersection” or “wrong gear operation”; when assigned a value of 0, the driver’s judgment and operation complied with safe driving standards. When X6 (weak safety awareness of the driver) is assigned a value of 1, there were records of the driver’s violating behaviors such as “not wearing a seat belt” or “using a handheld phone while driving”; when assigned a value of 0, there were no such violating behaviors. When X7 (violations by other road users) is assigned a value of 1, pedestrians or non-motor vehicle users had violating behaviors such as “running red lights” or “crossing motor vehicle lanes”, and such behaviors were one of the inducing factors of the accident; when assigned a value of 0, the behaviors of other road users were in compliance with regulations. When X8 (dangerous behaviors of passengers) is assigned a value of 1, there were passenger behaviors such as “grabbing the steering wheel”, “arson”, or “unauthorized operation of vehicle equipment”; when assigned a value of 0, there were no records of such behaviors.

If an accident report contains the following risk factors, the accident is classified under vehicle factors (X9–X13): When X9 (vehicle braking system failure) is assigned a value of 1, the vehicle technical appraisal report showed failures such as excessive brake pedal travel, brake fluid leakage, or excessive brake pad wear, and the failures occurred before the accident; when assigned a value of 0, the braking system passed the inspection. When X10 (steering system failure) is assigned a value of 1, there were failures such as the steering wheel’s free travel exceeding 15 degrees or loose steering tie rods; when assigned a value of 0, the steering system performed normally. When X11 (lighting failure) is assigned a value of 1, key lights of the vehicle (such as low-beam lights, turn signals, or brake lights) could not work normally at the time of the accident; when assigned a value of 0, the lighting system was fully functional. When X12 (tire failure) is assigned a value of 1, the tires had problems such as blowouts, abnormal tire pressure, or tread depth less than 1.6 mm; when assigned a value of 0, the tire condition met safety standards. When X13 (insufficient vehicle maintenance) is assigned a value of 1, the maintenance records of the bus company showed that the accident vehicle failed to complete Level 2 or above maintenance within the specified cycle; when assigned a value of 0, the maintenance records were complete and in compliance with regulations.

If an accident report contains the following risk factors, the accident is classified under road factors (X14–X18): When X14 (road design defects) is assigned a value of 1, the road had design problems that did not conform to the code for design of urban road engineering, such as “no warning signs for sharp bends” or “lane width less than 3.5 m”, and such problems were directly related to the occurrence of the accident; when assigned a value of 0, the road design complied with the code. When X15 (road surface adhesion) is assigned a value of 1, based on meteorological records and road surface surveys, the road surface had ice, snow, water accumulation, or oil stains, with an adhesion coefficient less than 0.6; when assigned a value of 0, the road surface was dry, with an adhesion coefficient not less than 0.6. When X16 (lack of traffic facilities) is assigned a value of 1, the road section where the accident occurred lacked key facilities such as traffic signals, crosswalk signs, or speed bumps; when assigned a value of 0, the traffic facilities were complete and fully functional. When X17 (traffic congestion) is assigned a value of 1, the queue length of vehicles on the road section at the time of the accident exceeded 50 m or the traffic speed was less than 10 km/h; when assigned a value of 0, the traffic was smooth and without congestion. When X18 (road section blind spots or poor sight distance) is assigned a value of 1, the accident site had problems such as obstruction by buildings or a curve sight distance of less than 50 m; when assigned a value of 0, the sight distance met the regulatory requirements.

If an accident report contains the following risk factors, the accident is classified under environmental factors (X19–X21): When X19 (low visibility due to smog/haze) is assigned a value of 1, meteorological data showed that the visibility at the time of the accident was less than 200 m; when assigned a value of 0, the visibility was greater than 200 m. When X20 (heavy rain/ice–snow weather) is assigned a value of 1, the accident occurred during heavy rain, heavy snow, or road icing weather; when assigned a value of 0, the weather was clear, or it was light rain or light snow without road icing. When X21 (insufficient lighting at night) is assigned a value of 1, the accident occurred between 19:00 and 6:00 the next day, and the road section lighting brightness was less than 20 lux; when assigned a value of 0, the lighting brightness was not less than 20 lux or the accident occurred during daytime.

If an accident report contains the following risk factors, the accident is classified under management factors (X22–X26): When X22 (imperfect safety management system) is assigned a value of 1, the bus company had not established core management systems such as safety training or accident emergency response plans; when assigned a value of 0, the management systems were complete and filed. When X23 (insufficient safety training) is assigned a value of 1, the annual safety training duration for the involved driver was less than 24 h or the driver failed the training assessment; when assigned a value of 0, the training duration was in compliance with regulations and the driver passed the assessment. When X24 (unreasonable scheduling) is assigned a value of 1, the daily schedule of the involved driver had problems such as “continuous driving for more than 6 h” or “interval rest less than 0.5 h”; when assigned a value of 0, the scheduling complied with the requirements of the safety management specifications for road passenger transport enterprises. When X25 (lack of emergency response plans) is assigned a value of 1, the bus company had not formulated special emergency response plans for sudden accidents such as fires or vehicle loss of control; when assigned a value of 0, the emergency response plans were complete and drills had been conducted. When X26 (inadequate industry supervision) is assigned a value of 1, the supervision department had records of two or more failed safety inspections for the involved enterprise within the past year; when assigned a value of 0, all inspection results were qualified.

Two researchers with more than 5 years of experience in bus accident investigation were invited to independently complete the binarization assignment of the 26 factor nodes in accordance with the above standards. For cases with inconsistent assignments, a joint consultation was conducted by reviewing original materials such as accident investigation reports and vehicle technical appraisal reports. The final assignment consistency rate reached 98%, ensuring the reliability of the binarization results. To verify the rationality of the mapping rule, 20 typical bus accident cases (including types such as collisions, vehicle loss of control, and passenger dangerous behaviors) were selected. Three experts in the field of traffic engineering (with no less than 10 years of work experience) independently completed the mapping in accordance with the above rules. The consistency rate between their results and the mapping results of this study reached 95%, indicating that the mapping rule has good operability and accuracy.

2.3. Analysis of Accident Causes

The core category factors involved in the 178 bus accidents were identified in accordance with the above rules, and a preliminary analysis of the results is presented below. The proportion of causes of bus accidents is shown in Figure 1:

(1) Human factors are found to occupy a dominant position.

In the analysis of bus accident causes, human factors occupy a dominant position, accounting for as high as 70.85%. This conclusion is consistent with Han’s study on urban bus drivers in China [2] (human factors accounting for 68.2%) and Kaplan’s study on bus accidents in the United States [13] (human factors accounting for 65.3%), indicating that human factors are the core inducement of bus accidents worldwide. It highlights that during bus operations, drivers’ behaviors and decisions play a crucial role in ensuring driving safety. Human factors encompass drivers, passengers, and other external factors. Drivers’ behaviors such as fatigue, lack of skills, poor health conditions, speeding, and violation of traffic rules may lead to operational errors or judgment mistakes, thereby increasing the risk of accidents. According to statistical data (Figure 2), among bus accidents caused by human factors, the proportion of cases attributed to drivers’ weak safety awareness stands at 32.26%, while that resulting from improper operation by drivers is 25.81%, and the proportion of accidents caused by drivers’ sudden syncope reaches 12.90%. Of course, passengers’ dangerous behaviors, improper operations when getting on or off the vehicle, and failure to use safety devices in accordance with regulations may all have an impact on the order and safety inside the vehicle. In modern society, due to enormous work pressure, incidents such as bus arson, knife attacks, and interference with drivers’ driving occur frequently. Among bus accidents caused by human factors, the proportion of accidents triggered by passengers’ retaliation against society or dangerous behaviors is as high as 29.03%. In addition, violations by other road users and errors by traffic controllers, such as improper control of traffic signals, delayed traffic guidance, lane-cutting behaviors, and pedestrians crossing the road at will, will all interfere with the normal operation of buses and increase the possibility of accidents.

(2) Vehicle factors should not be overlooked.

In the analysis of the causes of bus accidents, it has been identified that accidents triggered by vehicle factors account for 6.86%; although this proportion is relatively low, the performance and condition of the vehicle itself are closely associated with the operational safety of buses. The safety of buses is comprehensively influenced by a variety of factors, which include technical defects, maintenance status, and equipment configuration. Problems with components such as the braking system, tires, and engine may lead to vehicle loss of control. In Suraji’s related research, it was found that braking, wheels, stability, and airworthiness are the four main vehicle factors causing bus accidents, among which accidents caused by poor wheel conditions are often accompanied by braking system failures [20]. In addition, untimely maintenance and repairs may cause aging or damage to components, thereby increasing the possibility of accidents. Imperfect or faulty equipment, such as the lack of safety equipment or unstable monitoring systems, will also have a negative impact on emergency response capabilities and passenger safety.

(3) Road factors exert a certain degree of influence.

In the process of exploring the causes of bus accidents, it has been found that the proportion of accidents attributed to road factors stands at 4.00%. The complexity and diversity of urban road environments, which include the irrationality of road design and the unsatisfactory condition of road surfaces, may all pose potential threats to the driving safety of buses. Road indicators such as lane width, design speed, and urban form are closely related to accident risks. Studies have pointed out that urban form can indirectly affect the probability of collisions by changing vehicle operating speeds, while unreasonable road design indicators such as insufficient lane width will increase the difficulty of vehicle operation, thereby increasing accident risks [31]. At the same time, as an important part of road facilities, the design of bus stops also has a significant impact on traffic safety. Analysis shows that unreasonable setting of bus stops may increase the risk of conflicts between vehicle parking and traffic, thereby becoming a hidden danger of bus accidents [9]. In addition, deterioration in road surface conditions, ambiguity in traffic signs and signals, complexity of road conditions, and inadequacy in traffic management can all elevate driving risks, thereby inducing the occurrence of accidents. Road condition issues such as sharp turns, steep slopes, traffic congestion, and sight blind spots, as well as frequent violations of traffic rules and inappropriate control of intersections, not only require drivers to adopt more cautious driving measures but also necessitate that relevant management departments strengthen the maintenance and optimization of traffic facilities.

(4) Environmental factors pose potential risks.

In the process of exploring the causes of bus accidents, environmental factors have been identified to account for 7.43% of the total accident causes. Among them, as a key environmental risk factor, the impact of temperature on road safety has been confirmed by numerous studies. The relevant literature points out that abnormal temperatures can change drivers’ physiological states and road surface conditions, thereby increasing the probability of accidents. The impact of temperature on road safety has multi-dimensional characteristics; in addition to high daytime temperatures, the risk effect of high nighttime temperatures cannot be ignored. Hsu analyzed the association between high nighttime temperatures and the risk of road traffic deaths, and the results showed that exposure to high nighttime temperatures significantly increases the risk of road traffic deaths [32]. The potential mechanisms may be related to the decrease in drivers’ sleep quality, the increase in daytime fatigue caused by high nighttime temperatures, as well as the reduced efficiency of vehicle heat dissipation systems when driving at night. In addition, severe weather (such as rain, snow, and fog) reduces visibility and road friction, while extreme temperatures may damage vehicle performance, affecting the working conditions of brakes, engines, and tires. At the same time, strong sunlight or insufficient light at night can obstruct vision and increase the risk of accidents. Furthermore, from the perspective of practical application scenarios, the combined impact of vehicle factors and environmental factors is particularly significant for professional drivers (such as truck drivers and food delivery riders). For example, high-temperature environments not only cause thermal stress on vehicle tires and brake systems, leading to reduced tire grip and delayed brake response, but also affect drivers’ physiological states and operational performance, such as causing distraction and slowing down reaction speed. The superposition of these two aspects may produce risk effects far exceeding those of a single factor. In similar studies, Hsu paid attention to the “multi-factor superimposed risk” faced by professional groups. For instance, a study on food delivery riders in Kaohsiung, Taiwan found that dual exposure to platform incentive mechanisms and high-temperature environments significantly increases riders’ dangerous riding behaviors (such as running red lights and speeding). This conclusion also confirms the importance of multi-factor combined effects in road safety research [33].

(5) Management factors call for further enhancement.

In the causes of bus operation accidents, management factors account for 10.86%. The management of bus operations covers multiple dimensions such as personnel scheduling, safety training, and system implementation, or any oversight which may exert a negative impact on driving safety. Studies have shown that corporate management is not only directly related to bus drivers’ dangerous driving behaviors but also has an indirect impact by influencing drivers’ attitudes towards traffic safety. Among these factors, drivers’ attitudes towards traffic safety have the most significant influence on their dangerous driving behaviors [21]. Specifically, if the safety training for drivers fails to achieve the expected effect, it may result in their insufficient mastery of safety regulations and emergency handling measures; the irrationality of operational scheduling may lead to drivers’ fatigue driving; and the ineffective implementation of safety management systems may cause violations to not be corrected and handled in a timely manner.

3. Construction of Risk Factor Analysis Model for Bus Traffic Accidents

Traditional methods for analyzing the risk factors of bus traffic accidents include accident statistical analysis, expert experience method, safety assessment method, causal analysis method, driver behavior analysis method, and on-site observation method, among others. Accident statistical analysis, which draws on historical data to reveal the regularity of accident occurrences, holds significant practical significance; however, it has limitations in predicting potential risks in the future. The expert experience method, which relies on experts’ knowledge reserves and judgment capabilities, exhibits a relatively strong ability to respond to newly emerging risks, yet its results may be influenced by subjective factors. The safety assessment method conducts risk analysis on various links of the traffic system through a systematic approach, making it suitable for complex traffic systems, although its analysis process is relatively complicated. The causal analysis method, by tracing the root causes of accidents, uncovers the in-depth reasons behind problems and is applicable to complex systems, but this method requires analysts to possess strong analytical capabilities and sufficient data support. The driver behavior analysis method focuses on the analysis of human factors, which is conducive to reducing operational errors, but it needs to rely on detailed data and monitoring technologies. The on-site observation method identifies risk factors through on-the-spot investigations, boasting high practicality, yet it may have an impact on work efficiency, and the stability of its results remains to be improved. In view of the respective advantages and disadvantages of the aforementioned methods, this chapter adopts a combined approach of the N-K model and the DEMATEL model to analyze the risk factors of bus traffic accidents, so as to better reveal the coupling relationships between risk elements. The parameters appearing in the model are shown in

Table 2. Explanation of model parameters.

Variable	Explanation
T	Coupling value
$T_{2n}$	Coupling values of two-factor (in which n denotes the type of multi-factor coupling, the value of n ranges from 1 to 10)
$T_{3n}$	Coupling values of three-factor (in which n denotes the type of multi-factor coupling, the value of n ranges from 1 to 10)
$T_{4n}$	Coupling values of four-factor (in which n denotes the type of multi-factor coupling, the value of n ranges from 1 to 10)
$T_{5n}$	Coupling values of five-factor (in which n denotes the type of multi-factor coupling, the value of n ranges from 1 to 10)
H	Human factors leading to bus accidents
V	Vehicle factors leading to bus accidents
R	Road factors leading to bus accidents
E	Environmental factors leading to bus accidents
M	Management factors leading to bus accidents
$P_{jklos}$	Probability of multi-factor coupling occurrence (when humans are in state j, vehicles in state k, roads in state l, the environment in state o, and management in state s, where the states are denoted by 0 and 1, 0 indicates that the risk factor does not occur, while 1 indicates that it does)
$P_j$	Probability of single-factor coupling occurrence when humans are in state j
$P_k$	Probability of single-factor coupling occurrence when vehicles are in state k
$P_l$	Probability of single-factor coupling occurrence when roads are in state l
$P_o$	Probability of single-factor coupling occurrence when the environment is in state o
$P_s$	Probability of single-factor coupling occurrence when management is in state s
A	Direct influence matrix
B	Coupling matrix
V	Comprehensive influence matrix
$D_i$	Influence degree
$C_i$	Influenced degree
$M_i^{\prime }$	Value of centrality
$R_i$	Cause degree
F	Reachability matrix
Z	Overall influence matrix
$Z_{ij}$	Element of matrix Z
$\lambda$	The critical value that distinguishes whether the influence relationship between risk factors is significant
$\alpha$	The sum of the mean value
$\beta$	The sum of the standard deviation
$f_{ij}$	The core elements of the risk factor reachability matrix F
$M_i^{″}$	The revised centrality of the risk factor
$T_i$	The coupling value corresponding to the potential coupling form of the risk factor
$\sigma$	The correction coefficient

.

3.1. Introduction to the N-K Risk Coupling Model

Risk coupling refers to a phenomenon in which two or more risk factors interact through various forms of mutual influence, ultimately leading to a combined risk effect. As a measuring indicator, the coupling degree directly reflects the intensity of the mutually reinforcing effects between risk factors [22]. The N-K model, which was first proposed by Stuart Kauffman in the 1990s [23], has been widely applied in the exploration of complexity and adaptability. The N-K model is based on two main parameters: N represents the total number of elements involved in interactions within the system, and in this study, it denotes the total number of all factors that may affect the risk of traffic accidents; K, on the other hand, indicates the number of interactions or dependencies between each single element and other elements [24]. In the N-K model, no element exists in isolation; instead, each may interact with others, thereby exerting an impact on the overall risk of the system.

In the research on risk coupling of bus traffic accidents, five categories of elements are involved: human factors, vehicle factors, road factors, environmental factors, and management factors. The degree of interrelation between risk factors is quantified by the coupling value T, where $T_{\mathrm{2}\mathrm{n}}$, $T_{\mathrm{3}\mathrm{n}}$, $T_{\mathrm{4}\mathrm{n}}$, and $T_{\mathrm{5}\mathrm{n}}$ represent the coupling values of two-factor, three-factor, four-factor, and five-factor coupling, respectively (in which n denotes the type of multi-factor coupling; for example, in the case of two-factor coupling, there are 10 modes in total, such as human–vehicle coupling, human–road coupling, and human–environment coupling, so the value of n ranges from 1 to 10). Moreover, the higher the calculated T value, the more intricate the connections between various factors within the system, and the stronger the coupling, which thereby makes the occurrence of risk accidents more likely. The calculation formula for the coupling value T is as follows:

$$T(H,V,R,E,M)=\sum \sum \sum \sum \sum P_{jklos}{log}_2\left({\displaystyle \frac{P_{jklos}}{P_j·P_k·P_l·P_o·P_s}}\right).$$

(1)

In the formula, H denotes the human factors leading to bus accidents, V represents vehicle factors, R stands for road factors, E indicates environmental factors, and M signifies management factors. $P_{\mathrm{jklos}}$ designates the probability of multi-factor coupling occurrence when humans are in state j, vehicles in state k, roads in state l, the environment in state o, and management in state s, where the states are denoted by 0 and 1; 0 indicates that the risk factor does not occur, while 1 indicates that it does [25]. For instance, $P_{00001}$ represents the probability of an accident caused solely by management factors among the five factors leading to bus accidents. $P_{\mathrm{j}}$ denotes the probability of single-factor coupling occurrence when humans are in state j; $P_{\mathrm{k}}$ represents the probability of single-factor coupling occurrence when vehicles are in state k; $P_{\mathrm{l}}$ stands for the probability of single-factor coupling occurrence when roads are in state l; $P_{\mathrm{o}}$ indicates the probability of single-factor coupling occurrence when the environment is in state o; and $P_{\mathrm{s}}$ signifies the probability of single-factor coupling occurrence when management is in state s.

In the research on the risk coupling of bus traffic accidents, there exist multiple risk coupling scenarios, which include two-factor, three-factor, four-factor, and five-factor risk couplings.

(1) Two-factor coupling

When individual risk factors combine with one another to form pairwise combinations, two-factor risk coupling is thereby constituted, which primarily includes ten forms: human–vehicle, human–road, human–environment, human–management, vehicle–road, vehicle–environment, vehicle–management, road–environment, road–management, and environment–management. These are denoted as $T_{21}(H,V)$, $T_{22}(H,R)$, $T_{23}(H,E)$, $T_{24}(H,M)$, $T_{25}(V,R)$, $T_{26}(V,E)$, $T_{27}(V,M)$, $T_{28}(R,E)$, $T_{29}(R,M)$, and $T_{210}(E,M)$, respectively. Taking the human–vehicle two-factor risk coupling as an example, its detailed mathematical expression is presented in Formula (2), while the measurement models for other two-factor risk couplings can be derived through corresponding analogies based on Formula (2).

$$T_{21}(H,V)=\sum \sum P_{jk}{log}_2\left({\displaystyle \frac{P_{jk}}{P_j·P_k}}\right).$$

(2)

(2) Three-factor coupling

Three-factor risk coupling refers to the risk effect triggered by the interaction and mutual coupling among any three factors within the risk factor system of bus traffic accidents. Specifically, the three-factor risk coupling in bus traffic accidents can be subdivided into the following ten combinations: human–vehicle–road, human–vehicle–environment, human–vehicle–management, human–road–environment, human–road–management, human–environment–management, vehicle–road–environment, vehicle–road–management, vehicle–environment–management, and road–environment–management, which are denoted as $T_{31}(H,V,R)$, $T_{32}(H,V,E)$, $T_{33}(H,V,M)$, $T_{34}(H,R,E)$, $T_{35}(H,R,M)$, $T_{36}(H,E,M)$, $T_{37}(V,R,E)$, $T_{38}(V,R,M)$, $T_{39}(V,E,M)$, and $T_{310}(R,E,M)$, respectively. Taking the human–vehicle–road three-factor risk coupling as an example, its specific expression is shown in Formula (3), while the measurement models for other three-factor risk couplings can be derived through analogy with Formula (3).

$$T_{31}(H,V,R)=\sum \sum \sum P_{jkl}{log}_2\left({\displaystyle \frac{P_{jkl}}{P_j·P_k·P_l}}\right).$$

(3)

(3) Four-factor coupling

Four-factor risk coupling refers to the risk effect triggered by the interaction and mutual coupling among any four factors within the risk factor system of bus traffic accidents. Within this category, five distinct combinations can be identified: human–vehicle–road–environment, human–vehicle–road–management, human–vehicle–environment–management, human–road–environment–management, and vehicle–road–environment–management, which are denoted as $T_{41}(H,V,R,E)$, $T_{42}(H,V,R,M)$, $T_{43}(H,V,E,M)$, $T_{44}(H,R,E,M)$, and $T_{45}(H,R,E,M)$, respectively. Taking the human–vehicle–road–environment four-factor risk coupling as an example, its specific expression is shown in Formula (4), while the measurement models for other four-factor risk couplings can be derived by analogy with Formula (4).

$$T_{41}(H,V,R,E)=\sum \sum \sum P_{jklo}{log}_2\left({\displaystyle \frac{P_{jklo}}{P_j·P_k·P_l·P_o}}\right).$$

(4)

(4) Five-factor coupling

Five-factor risk coupling refers to the risk caused by the mutual coupling of all five factors within the risk factors of bus traffic accidents; currently, only one combination has been identified, namely human–vehicle–road–environment–management, which is denoted as $T_{51}(H,V,R,E,M)$. Its specific expression is consistent with Formula (1).

3.2. Introduction to the DEMATEL Risk Coupling Model

The Decision-Making Trial and Evaluation Laboratory (DEMATEL) is a model employed for analyzing factors within complex systems [26]; by exploring the interactions among various factors, it assists decision-makers in identifying key factors within intricate environments, thereby optimizing the decision-making process. The risk factors of bus accidents constitute a complex system, which encompasses a multitude of elements, including but not limited to driver behavior, traffic environment, vehicle conditions, weather conditions, and traffic signals. The application of the DEMATEL method not only enables the identification of the importance of each factor through the magnitude of centrality values but also allows for the revelation of causal relationships among them via causal degrees.

The calculation steps of the DEMATEL model are as follows:

The direct influence matrix of the DEMATEL model is constructed through the expert scoring method. To ensure the reliability of the results, this study strictly designs mechanisms for expert selection, scoring procedures, and reliability testing: Seven experts were selected, covering traffic industry supervision (two researchers from municipal transportation bureaus with 18–20 years of experience), bus enterprise practice (two safety directors from bus groups with 12–15 years of experience), and university academic research (three professors in transportation engineering who have presided over no less than three related research projects). A 5-point Likert scale was adopted to quantify the degree of influence between factors (0 points for no influence, 1 point for slight influence, 2 points for moderate influence, 3 points for strong influence, and 4 points for extremely strong influence), and scoring criteria were clarified with reference to accident case examples. Consensus was reached through two rounds of the Delphi method. After the first round of independent scoring, 12 divergent points with a coefficient of variation (CV) greater than 0.3 were identified; following a seminar where experts clarified the logical relationships, a second round of revised scoring was conducted. Ultimately, the CV of all factor pairs was less than 0.2. Reliability testing showed that the Cronbach’s alpha coefficient was 0.83 (indicating excellent internal consistency), and the Kendall’s coefficient of concordance increased from 0.62 in the first round to 0.79 in the second round, which verifies the reliability and consistency of the scoring results.The expert scoring method is adopted to construct the direct influence matrix A by comparing the interaction intensities among the risk factors of bus accidents.

$$A=\left(\begin{array}{cccc}0& x_{12}& \cdots & x_{1n}\\ x_{21}& 0& \cdots & x_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ x_{n1}& x_{n2}& \cdots & 0\end{array}\right).$$

(5)

(1) The row maximum method is employed to perform normalization processing on the direct influence matrix, thereby obtaining the coupling matrix B. Its expression is as follows:

$$B={\displaystyle \frac{1}{{max}_{i\in [1,n]}\left({\sum }_{j=1}^n{x}_{ij}\right)}}A.$$

(6)

In the formula, ${max}_{i\in [1,n]}\left({\sum }_{j=1}^n{x}_{ij}\right)$ denotes the maximum value of the sum of each row in matrix A.

(2) A comprehensive influence matrix V is constructed to facilitate subsequent quantitative analysis of the interactions among bus risk factors, and its calculation formula is as follows:

$$V=B{(E-B)}^{-1}.$$

(7)

In the formula, E is the identity matrix.

(3) Calculate the influence degree, influenced degree, centrality degree, and cause degree of each bus risk factor.

The influence degree is defined as the cumulative sum of the element values in each row of the comprehensive influence matrix V, which reflects the overall influence exerted by the elements in each row on other elements in bus accidents; that is, risk factors may not only directly affect the occurrence of bus accidents but also may indirectly exert an impact by influencing other factors, thereby forming a chain reaction. The influence degree is denoted as $D_{\mathrm{i}}$, and its calculation formula is as follows:

$$D_i=\sum _{j=1}^n{x}_{ij},(i=1,2,\dots ,n).$$

(8)

The influenced degree index refers to the sum of the values in each column of the comprehensive influence matrix V, which, in the analysis of bus risk factors, is conducive to reveal the dependence of a certain risk factor within the system. In other words, the magnitude of its value reflects the extent to which the factor is influenced by other factors. The influenced degree is denoted as $C_{\mathrm{i}}$, and its calculation formula is as follows:

$$C_i=\sum _{j=1}^n{x}_{ji},(i=1,2,\dots ,n).$$

(9)

Centrality is a key indicator for measuring the importance of bus risk factors within the system; factors with high centrality typically occupy a core position in the bus accident risk system, as they can not only exert an influence on other factors but also are prone to being affected by other factors. The value of centrality is equal to the sum of the influence degree and the influenced degree of a certain factor, which is denoted as $M_i^{\prime }$, and its calculation formula is as follows:

$$M_i^{\prime }=D_i+C_i.$$

(10)

The cause degree is defined as the difference between the influence degree and the influenced degree of a bus risk factor, which is denoted as $R_{\mathrm{i}}$. When the value of the cause degree is greater than 0, it indicates that the factor exerts a significant influence on other factors, and thus it is referred to as a cause factor; conversely, when the value of the cause degree is less than 0, the factor is regarded as a result factor. The cause degree can help analyze and understand the roles and functions of different risk factors within the public transport system, and by calculating the cause degree of each factor, it is possible to clearly identify which factors are the primary ones leading to the occurrence of risks (cause factors) and which factors are the consequences or reflections of risks (result factors). The calculation formula is as follows:

$$R_i=D_i-C_i.$$

(11)

(4) A reachability matrix F of risk factors is constructed to analyze the reachability of bus risk factors. The reachability matrix is a binary matrix used to quantitatively analyze the “influence reachability relationship” between bus accident risk factors. Its core function is to clarify whether a certain risk factor can trigger other risk factors through direct or indirect effects, thereby revealing the potential paths and association scope of risk coupling. Firstly, the overall influence matrix Z is determined, which is defined as the sum of the comprehensive influence matrix V and the identity matrix E, where $z_{\mathrm{ij}}$ represents an element of matrix Z. Subsequently, the reachability matrix F is confirmed by comparing the magnitude of $z_{\mathrm{ij}}$ with the threshold value $\lambda$. The confirmation formula for each element value $f_{\mathrm{ij}}$ in the risk factor reachability matrix F is as follows:

$$f_{ij}=\left\{\begin{array}{cc}1\hfill & z_{ij}\ge \lambda \hfill \\ 0\hfill & z_{ij}<\lambda \hfill \end{array}\right..$$

(12)

There are differences in threshold setting among different analysis objects. Referring to the threshold setting method used by Guan [27] in traffic risk analysis, the threshold $\lambda$ is determined as the sum of the mean value ($\alpha$) and standard deviation ($\beta$) of the elements in the comprehensive influence matrix V. The rationality of this standard lies in that the mean value reflects the average level of influence between factors, while the standard deviation represents the degree of dispersion of influence levels. The combination of the two can screen out the coupling relationships that “exceed the average influence level and have statistical discrimination” and eliminate the interference of random minor influences. Through reachability analysis, the possibility of risk coupling between nodes can be clarified, and potential coupling patterns can be revealed, thereby providing a solid foundation for risk analysis.

3.3. N-K/DEMATEL Risk Coupling Analysis Model

The N-K model is capable of revealing the interrelationships among different risk factors based on actual data and analyzing their impacts on the probability of accident occurrence. However, when assessing the coupling degree of risk factors, the model only focuses on the risk factors within core categories, which to a certain extent limits its effectiveness in identifying key factor nodes. Taking the application of the N-K model in the coupling analysis of bus accidents as an example, the analysis results merely indicate that the combined effect of human factors and vehicle factors will significantly increase the probability of bus operation risks, yet they fail to delve into more specific risk factors within human factors and vehicle factors.

The DEMATEL model possesses the capability to analyze the interactions among different risk factors and their centrality-based influences; however, it typically relies on expert opinions to determine the interactions and influence degrees between factors, which are susceptible to the impacts of multiple elements such as experts’ personal experiences, knowledge backgrounds, and cognitive biases, thereby potentially leading to deviations between the analysis results and the actual situation. Taking the risk analysis of bus accidents as an example, experts from different fields may exhibit variations in the degree of emphasis placed on certain risk factors, a phenomenon that could result in a divergence between the risk assessment outcomes and the actual mechanism underlying accident occurrences. Meanwhile, the DEMATEL model evaluates the importance of each risk factor by calculating their centrality and infers which factors qualify as “key factors”; nevertheless, this assessment method merely focuses on the direct connections and centrality among factors, and may overlook the potential risks of some low-centrality factors [28]. For instance, in a causal diagram, some factors located at the periphery—such as tire wear or blowouts, and the imperfection or damage of safety equipment—may appear insignificant when analyzed in isolation due to their low occurrence frequency. However, in actual bus accidents, these factors, when interacting with other key factors (e.g., driver fatigue, traffic density), may trigger severe accidents under specific circumstances.

To summarize, the N-K model, which is based on objective accident data analysis, exhibits a high level of objectivity; however, its analysis is primarily confined to factors within core categories. In contrast, the DEMATEL model, which tends to rely heavily on experiential judgments, carries a strong element of subjectivity, a characteristic that may result in a discrepancy between the identified key risk factors and the actual probability of accident occurrence. Consequently, this study, by comprehensively considering the advantages and disadvantages of these two models, integrates the objective data analysis of the N-K model with the subjective experiential judgments of the DEMATEL model. This integration not only takes into account the direct connections among risk factors but also delves into their potential coupling relationships, thereby enhancing both the accuracy and practicality of risk analysis.

Specifically, the N-K model is utilized to compute the coupling value T among bus risk factors, through which the influence exerted by the coupling of risk factors within the core domains of bus accidents on the probability of accident occurrence can be evaluated [29]. Subsequently, reachability analysis is performed by means of the comprehensive influence matrix V obtained from the DEMATEL model, a process that serves to uncover the potential coupling relationships existing among the nodes of various bus risk factors [30]. Following this, the DEMATEL model is applied to sort the centrality of each node corresponding to bus risk factors. Ultimately, the centrality of the nodes is revised in accordance with their coupling values, and the specific revision formula is presented in Formula (13); after such revision, factors characterized by higher centrality are identified as key risk factors.

$$M_i^{″}=\sigma \times M_i^{\prime }\times T_i.$$

(13)

In the formula, $M_i^{″}$ denotes the revised centrality of the risk factor, $M_i^{\prime }$ represents the centrality of the risk factor, $T_{\mathrm{i}}$ stands for the coupling value corresponding to the potential coupling form of the risk factor, and $\sigma$ is the correction coefficient.

4. Analysis of Key Factors Based on the N-K and DEMATEL Models

4.1. Analysis Based on the Calculation Results of the N-K Model

(1) The quantity and proportion of bus accidents caused by the coupling of different factors

Based on 178 bus traffic accident reports collected from 2004 to 2024, the occurrence frequency and probability data of core risk coupling events were statistically analyzed, where H denotes the human factors leading to bus accidents, V represents the vehicle factors, R stands for the road factors, E indicates the environmental factors, and M signifies the management factors. The specific values are presented in

Table 3. Statistics of bus traffic accident types.

Type	The Number of Accidents and the Proportion of Incidents
Single-factor	Risk coupling types	H	V	R	E	M
	Probability code name	$P_{10000}$	$P_{01000}$	$P_{00100}$	$P_{00010}$	$P_{00001}$
	Number of accidents	46	6	1	2	2
	Event proportion	0.258	0.034	0.006	0.011	0.011
Two-factor	Risk coupling types	H-V	H-R	H-E	H-M	V-R
	Probability code name	$P_{11000}$	$P_{10100}$	$P_{10010}$	$P_{10001}$	$P_{01100}$
	Number of accidents	7	10	2	45	2
	Event proportion	0.039	0.056	0.011	0.253	0.011
	Risk coupling types	V-E	V-M	R-E	R-M	E-M
	Probability code name	$P_{01010}$	$P_{01001}$	$P_{00110}$	$P_{00101}$	$P_{00011}$
	Number of accidents	3	8	1	1	1
	Event proportion	0.017	0.045	0.006	0.006	0.006
Three-factor	Risk coupling types	H-V-R	H-V-E	H-V-M	H-R-E	H-R-M
	Probability code name	$P_{11100}$	$P_{11010}$	$P_{11001}$	$P_{10110}$	$P_{10101}$
	Number of accidents	1	1	10	3	10
	Event proportion	0.006	0.006	0.056	0.017	0.056
	Risk coupling types	H-E-M	V-R-E	V-R-M	V-E-M	R-E-M
	Probability code name	$P_{10011}$	$P_{01110}$	$P_{01101}$	$P_{01011}$	$P_{00111}$
	Number of accidents	4	1	1	1	1
	Event proportion	0.022	0.006	0.006	0.006	0.006
Four-factor	Risk coupling types	H-V-R-E	H-V-R-M	H-V-E-M	H-R-E-M	V-R-E-M
	Probability code name	$P_{11110}$	$P_{11101}$	$P_{11011}$	$P_{10111}$	$P_{01111}$
	Number of accidents	1	1	1	1	2
	Event proportion	0.006	0.006	0.006	0.006	0.011
Five-factor	Risk coupling types	H-V-R-E-M
	Probability code name	$P_{11111}$
	Number of accidents	2
	Event proportion	0.011

.

(2) The calculation process for the probability of each risk coupling

Probability of single-factor coupling: taking bus accidents caused by human factors as an example, the calculation process for the single-factor risk coupling probability when the human factor is in state 0 is as follows:

$$\begin{array}{cc}\hfill P_{0....}& =P_{00000}+P_{01000}+P_{00100}+P_{00010}+P_{00001}+P_{01100}+P_{01010}\hfill \\ \hfill & +P_{01001}+P_{00110}+P_{00101}+P_{00011}+P_{01110}+P_{01101}\hfill \\ \hfill & +P_{01011}+P_{00111}+P_{01111}=0.188.\hfill \end{array}$$

(14)

Similarly, the specific calculation results of the coupling probabilities for other single factors under different states are presented in

Table 4. Single-factor coupling probability.

Single-Factor	Coupling Probability
Coupling Mode	$P_{0....}$	$P_{1....}$
H	0.188	0.812
Coupling Mode	$P_{.0...}$	$P_{.1...}$
V	0.730	0.270
Coupling Mode	$P_{..0..}$	$P_{..1..}$
R	0.781	0.219
Coupling Mode	$P_{...0.}$	$P_{...1.}$
E	0.848	0.152
Coupling Mode	$P_{....0}$	$P_{....1}$
M	0.489	0.511

.

Through the analysis of the probability of single-factor coupling, it was found that the probability of the human factor (H) being in a risky state reaches 0.812, which is significantly higher than that of the vehicle factor (0.270), road factor (0.219), and environmental factor (0.152). The probabilities of the management factor (M) being in risky and risk-free states are close (0.511/0.489). This result not only confirms the leading role of the human factor in accident risks but also reveals the universality of management loopholes.

Probability of two-factor coupling: taking bus accidents caused by the two-factor coupling of human and vehicle factors as an example, the calculation process for the two-factor risk coupling probability when both the human factor and the vehicle factor are in state 0 is as follows:

$$\begin{array}{cc}\hfill P_{00...}& =P_{00000}+P_{00100}+P_{00010}+P_{00001}+P_{00110}\hfill \\ \hfill & +P_{00101}+P_{00011}+P_{00111}=0.051.\hfill \end{array}$$

(15)

Similarly, the specific calculation results of the coupling probabilities for other two-factor combinations under different states are presented in

Table 5. Two-factor coupling probability.

Two-Factor	Coupling Probability
Coupling mode	$P_{00...}$	$P_{01...}$	$P_{10...}$	$P_{11...}$
H-V	0.051	0.135	0.68	0.135
Coupling mode	$P_{0.0..}$	$P_{0.1..}$	$P_{1.0..}$	$P_{1.1..}$
H-R	0.129	0.056	0.652	0.163
Coupling mode	$P_{0..0.}$	$P_{0..1.}$	$P_{1..0.}$	$P_{1..1.}$
H-E	0.118	0.067	0.730	0.084
Coupling mode	$P_{0...0}$	$P_{0...1}$	$P_{1...0}$	$P_{1...1}$
H-M	0.090	0.096	0.399	0.416
Coupling mode	$P_{.00..}$	$P_{.01..}$	$P_{.10..}$	$P_{.11..}$
V-R	0.573	0.157	0.208	0.062
Coupling mode	$P_{.0.0.}$	$P_{.0.1.}$	$P_{.1.0.}$	$P_{.1.1.}$
V-E	0.646	0.084	0.202	0.067
Coupling mode	$P_{.0..0}$	$P_{.0..1}$	$P_{.1..0}$	$P_{.1..1}$
V-M	0.365	0.365	0.124	0.146
Coupling mode	$P_{..00.}$	$P_{..01.}$	$P_{..10.}$	$P_{..11.}$
R-E	0.697	0.084	0.152	0.067
Coupling mode	$P_{..0.0}$	$P_{..0.1}$	$P_{..1.0}$	$P_{..1.1}$
R-M	0.376	0.404	0.112	0.107
Coupling mode	$P_{...00}$	$P_{...01}$	$P_{...10}$	$P_{...11}$
E-M	0.410	0.438	0.079	0.073

.

The analysis of the probability of two-factor coupling shows that in the “human-management” (H-M) coupling, the probability that both the human and management factors act as accident causes reaches 0.416, while the corresponding probability for the “human-vehicle” (H-V) coupling is 0.135. In contrast, the probabilities of risky states for couplings such as “vehicle-road” (V-R) and “road-management” (R-M) are less than 0.1. This indicates that attention should be paid to the correlation between the human factor and the management factor, as well as the vehicle factor, since the probability of their synergistic risk induction is significantly higher than that of combinations like vehicle–road and road–management. It also reflects that when management omissions are combined with human errors, the probability of accident risks will be amplified.

Probability of three-factor coupling: taking bus accidents caused by the three-factor coupling of human, vehicle, and road factors as an example, the calculation process for the three-factor risk coupling probability when the human factor, vehicle factor, and road factor are all in state 0 is as follows:

$$P_{000..}=P_{00000}+P_{00010}+P_{00001}+P_{00011}=0.028.$$

(16)

Similarly, the specific calculation results of the coupling probabilities for other three-factor combinations under different states are presented in

Table 6. Three-factor coupling probability.

Three-Factor	Coupling Probability
Coupling mode	$P_{000..}$	$P_{001..}$	$P_{010..}$	$P_{011..}$	$P_{100..}$	$P_{101..}$	$P_{110..}$	$P_{111..}$
H-V-R	0.028	0.022	0.101	0.034	0.545	0.135	0.107	0.028
Coupling mode	$P_{00.0.}$	$P_{00.1.}$	$P_{01.0.}$	$P_{01.1.}$	$P_{10.0.}$	$P_{10.1.}$	$P_{11.0.}$	$P_{11.1.}$
H-V-E	0.022	0.028	0.096	0.039	0.624	0.056	0.107	0.028
Coupling mode	$P_{00..0}$	$P_{00..1}$	$P_{01..0}$	$P_{01..1}$	$P_{10..0}$	$P_{10..1}$	$P_{11..0}$	$P_{11..1}$
H-V-M	0.022	0.028	0.067	0.067	0.343	0.337	0.056	0.079
Coupling mode	$P_{0.00.}$	$P_{0.01.}$	$P_{0.10.}$	$P_{0.11.}$	$P_{1.00.}$	$P_{1.01.}$	$P_{1.10.}$	$P_{1.11.}$
H-R-E	0.090	0.039	0.028	0.028	0.607	0.045	0.124	0.039
Coupling mode	$P_{0.0.0}$	$P_{0.0.1}$	$P_{0.1.0}$	$P_{0.1.1}$	$P_{1.0.0}$	$P_{1.0.1}$	$P_{1.1.0}$	$P_{1.1.1}$
H-R-M	0.062	0.067	0.028	0.028	0.315	0.337	0.084	0.079
Coupling mode	$P_{0..00}$	$P_{0..01}$	$P_{0..10}$	$P_{0..11}$	$P_{1..00}$	$P_{1..01}$	$P_{1..10}$	$P_{1..11}$
H-E-M	0.051	0.067	0.039	0.028	0.360	0.371	0.039	0.045
Coupling mode	$P_{.000.}$	$P_{.001.}$	$P_{.010.}$	$P_{.011.}$	$P_{.100.}$	$P_{.101.}$	$P_{.110.}$	$P_{.111.}$
V-R-E	0.522	0.051	0.124	0.034	0.174	0.034	0.028	0.034
Coupling mode	$P_{.00.0}$	$P_{.00.1}$	$P_{.01.0}$	$P_{.01.1}$	$P_{.10.0}$	$P_{.10.1}$	$P_{.11.0}$	$P_{.11.1}$
V-R-M	0.281	0.292	0.084	0.073	0.096	0.112	0.028	0.034
Coupling mode	$P_{..000}$	$P_{..001}$	$P_{..010}$	$P_{..011}$	$P_{..100}$	$P_{..101}$	$P_{..110}$	$P_{..111}$
V-E-M	0.320	0.326	0.045	0.039	0.090	0.112	0.034	0.034
Coupling mode	$P_{..000}$	$P_{..001}$	$P_{..010}$	$P_{..011}$	$P_{..100}$	$P_{..101}$	$P_{..110}$	$P_{..111}$
R-E-M	0.331	0.365	0.045	0.039	0.079	0.073	0.034	0.034

.

The analysis of the probability of three-factor coupling reveals that in the “human-vehicle-management” (H-V-M), “human-vehicle-road” (H-V-R), and “human-vehicle-environment” (H-V-E) couplings, the probabilities that all three factors are in risky states are 0.079, 0.028, and 0.028, respectively. These probabilities are significantly higher than those of three-factor coupling combinations without the involvement of the human factor, such as “vehicle-road-environment” (0.034). This shows that when the human factor and vehicle factor are combined with the management, road, or environmental factor, the risk synergy effect is more prominent, and it also confirms that “human-vehicle” is the core unit for risk induction in three-factor coupling.

Probability of four-factor coupling: taking bus accidents caused by the four-factor coupling of human, vehicle, road, and environmental factors as an example, the calculation process for the four-factor risk coupling probability when the human factor, vehicle factor, road factor, and environmental factor are all in state 0 is as follows:

$$P_{0000.}=P_{00000}+P_{00001}=0.011.$$

(17)

Similarly, the specific calculation results of the coupling probabilities for other four-factor combinations under different states are presented in

Table 7. Four-factor coupling probability.

Four-Factor	Coupling Probability
Coupling mode	$P_{0000.}$	$P_{1000.}$	$P_{0100.}$	$P_{0010.}$	$P_{0001.}$	$P_{1100.}$	$P_{1010.}$	$P_{1001.}$
	0.011	0.511	0.079	0.011	0.017	0.096	0.112	0.034
H-V-R-E	$P_{1111.}$	$P_{0111.}$	$P_{1011.}$	$P_{1101.}$	$P_{1110.}$	$P_{0011.}$	$P_{0101.}$	$P_{0110.}$
	0.017	0.022	0.011	0.011	0.011	0.022	0.017	0.017
Coupling mode	$P_{000.0}$	$P_{100.0}$	$P_{010.0}$	$P_{001.0}$	$P_{000.1}$	$P_{110.0}$	$P_{101.0}$	$P_{100.1}$
	0.011	0.270	0.051	0.011	0.017	0.045	0.073	0.275
H-V-R-M	$P_{111.1}$	$P_{011.1}$	$P_{101.1}$	$P_{110.1}$	$P_{111.0}$	$P_{001.1}$	$P_{010.1}$	$P_{011.0}$
	0.017	0.051	0.011	0.011	0.062	0.062	0.017	0.017
Coupling mode	$P_{00.00}$	$P_{10.00}$	$P_{01.00}$	$P_{00.10}$	$P_{00.01}$	$P_{11.00}$	$P_{10.10}$	$P_{10.01}$
	0.006	0.315	0.045	0.017	0.017	0.045	0.028	0.309
H-V-E-M	$P_{11.11}$	$P_{01.11}$	$P_{10.11}$	$P_{11.01}$	$P_{11.10}$	$P_{00.11}$	$P_{01.01}$	$P_{01.10}$
	0.022	0.051	0.011	0.011	0.062	0.028	0.017	0.017
Coupling mode	$P_{0.000}$	$P_{1.000}$	$P_{0.100}$	$P_{0.010}$	$P_{0.001}$	$P_{1.100}$	$P_{1.010}$	$P_{1.001}$
	0.034	0.298	0.017	0.028	0.056	0.062	0.017	0.309
H-R-E-M	$P_{1.111}$	$P_{0.111}$	$P_{1.011}$	$P_{1.101}$	$P_{1.110}$	$P_{0.011}$	$P_{0.101}$	$P_{0.110}$
	0.011	0.011	0.011	0.022	0.062	0.028	0.017	0.017
Coupling mode	$P_{.0000}$	$P_{.1000}$	$P_{.0100}$	$P_{.0010}$	$P_{.0001}$	$P_{.1100}$	$P_{.1010}$	$P_{.1001}$
	0.258	0.073	0.062	0.022	0.264	0.017	0.022	0.101
V-R-E-M	$P_{.1111}$	$P_{.0111}$	$P_{.1011}$	$P_{.1101}$	$P_{.1110}$	$P_{.0011}$	$P_{.0101}$	$P_{.0110}$
	0.022	0.062	0.028	0.011	0.011	0.011	0.011	0.022

.

The analysis of the probability of four-factor coupling indicates that in the “human-vehicle-environment-management” (H-V-E-M) coupling, the probability that all four factors are in risky states is significantly higher than that of other combinations. Moreover, the risk probabilities of four-factor couplings involving “human-vehicle” (such as H-V-R-E and H-V-R-M) are generally higher than those of combinations without “human-vehicle” (V-R-E-M). This shows that when the “human-vehicle” factor interacts synergistically with factors such as environment and management, the risk superposition effect is stronger. It further highlights the core risk-inducing role of “human-vehicle” in four-factor coupling and the necessity of multi-dimensional synergistic control.

Probability of five-factor coupling: in the state where the human factor, vehicle factor, road factor, environmental factor, and management factor are all 0, the calculation process for the five-factor risk coupling probability is as follows:

$$P_{00000}=0.$$

(18)

Similarly, the specific calculation results of the coupling probabilities for other five-factor combinations under different states are presented in

Table 8. Five-factor coupling probability.

Five-Factor	Coupling Probability
Coupling mode	$P_{00000}$	$P_{00001}$	$P_{00010}$	$P_{00011}$	$P_{00100}$	$P_{00101}$	$P_{00110}$	$P_{00111}$
	0.000	0.011	0.011	0.006	0.006	0.006	0.006	0.006
	$P_{01000}$	$P_{01001}$	$P_{01010}$	$P_{01011}$	$P_{01100}$	$P_{01101}$	$P_{01110}$	$P_{01111}$
	0.034	0.045	0.017	0.006	0.011	0.006	0.006	0.011
H-V-R-E-M	$P_{10000}$	$P_{10001}$	$P_{10010}$	$P_{10011}$	$P_{10100}$	$P_{10101}$	$P_{10110}$	$P_{10111}$
	0.258	0.253	0.011	0.022	0.056	0.056	0.017	0.006
	$P_{11000}$	$P_{11001}$	$P_{11010}$	$P_{11011}$	$P_{11100}$	$P_{11101}$	$P_{11110}$	$P_{11111}$
	0.039	0.056	0.006	0.006	0.006	0.006	0.006	0.011

.

(3) Calculation of risk coupling values

Based on the coupling probabilities of different types of risks, the coupling degree T values under the interaction of various risk factors are calculated by applying Formulas (1) to (4), and the detailed results are presented in

Table 9. Coupling values and sorting of different risk factor combinations.

Coupling Code	T Value	Sorting	Coupling Code	T Value	Sorting	Coupling Code	T Value	Sorting
$T_{21}(H,V)$	0.1579	10	$T_{31}(H,V,R)$	0.1685	8	$T_{41}(H,V,R,E)$	0.3043	3
$T_{22}(H,R)$	0.0063	20	$T_{32}(H,V,E)$	0.2252	5	$T_{42}(H,V,R,M)$	0.4437	2
$T_{23}(H,E)$	0.0460	14	$T_{33}(H,V,M)$	0.1580	9	$T_{43}(H,V,E,M)$	0.4718	1
$T_{24}(H,M)$	0.0015	22	$T_{34}(H,R,E)$	0.0830	11	$T_{44}(H,R,E,M)$	0.2330	4
$T_{25}(V,R)$	0.0002	26	$T_{35}(H,R,M)$	0.0068	19	$T_{45}(V,R,E,M)$	0.2130	6
$T_{26}(V,E)$	0.0169	18	$T_{36}(H,E,M)$	0.0505	13	$T_{51}(H,V,R,E,M)$	0.1751	7
$T_{27}(V,M)$	0.0009	24	$T_{37}(V,R,E)$	0.0570	12	——	——	——
$T_{28}(R,E)$	0.0331	16	$T_{38}(V,R,M)$	0.0018	21	——	——	——
$T_{29}(R,M)$	0.0010	23	$T_{39}(V,E,M)$	0.0208	17	——	——	——
$T_{210}(E,M)$	0.0005	25	$T_{310}(R,E,M)$	0.0354	15	——	——	——

.

The average values of T for two-factor coupling, three-factor coupling, four-factor coupling, and five-factor coupling are calculated, respectively, yielding $T_2=0.0264$, $T_3=0.0807$, $T_4=0.3332$, and $T_5=0.1751$, which indicates that $T_4>T_5>T_3>T_2$. Through analysis, the following conclusions are drawn:

A positive correlation is exhibited between the number of risk factors and the risk coupling value T; consequently, risk control strategies should be focused on preventing the synchronous coupling of multiple factors.

Among the four-factor couplings, the value of $T_{43}(H,V,E,M)$ is the highest; within the three-factor couplings, the value of $T_{32}(H,V,E)$ ranks the highest; and in the case of two-factor couplings, the value of $T_{21}(H,V)$ is the largest, with all of these couplings incorporating the human factor–vehicle factor $(H,V)$ combination. This finding indicates that when the human factor and the vehicle factor act in conjunction, the probability of risks occurring during bus operations increases significantly, thereby revealing that the human factor and the vehicle factor exert a decisive influence on ensuring the safe operation of public transport vehicles.

Among the four-factor couplings, the top three values in terms of numerical ranking are $T_{43}(H,V,E,M)$, $T_{42}(H,V,R,M)$, and $T_{41}(H,V,R,E)$, respectively; within the three-factor couplings, the top three values in numerical order are $T_{32}(H,V,E)$, $T_{31}(H,V,R)$, and $T_{33}(H,V,M)$ in sequence, while in the case of two-factor couplings, the top three values ranked by numerical magnitude are $T_{21}(H,V)$, $T_{24}(H,E)$, and $T_{28}(R,E)$, among which the environmental factor appears most frequently. This result indicates that the environmental factor possesses a significant risk-inducing capacity in the interaction of multiple factors.

4.2. Analysis of the Calculation Results of the DEMATEL Model

(1) Analysis of Risk Factors

By applying Formulas (5) to (11), the influence degree, influenced degree, centrality, and cause degree of the risk factors for bus accidents have been calculated and determined. The detailed values are presented in

Table 10. Calculation results of the DEMATEL model.

Risk Factors	Influence Degree	Influenced Degree	Centrality	Degree of Causation	Sort by Influence Degree	Sort by Influenced Degree	Sort by Centrality
X1	1.970	1.263	3.233	0.706	2	6	3
X2	1.730	0.653	2.392	1.085	4	15	6
X3	1.995	1.296	3.291	0.699	1	4	2
X4	1.753	1.283	3.036	0.470	3	5	4
X5	1.304	2.600	3.904	−1.296	6	1	1
X6	0.801	0.725	1.526	0.076	11	14	15
X7	0.636	0.419	1.055	0.216	15	25	23
X8	0.344	1.189	1.533	−0.844	24	8	14
X9	0.957	0.536	1.493	0.421	8	21	16
X10	0.501	0.493	0.993	0.008	22	23	24
X11	0.527	0.562	1.090	−0.035	21	20	22
X12	0.617	0.523	1.140	0.094	18	22	21
X13	0.294	0.336	0.630	−0.042	25	26	26
X14	0.613	0.604	1.217	0.009	19	18	20
X15	0.909	0.580	1.489	0.329	9	19	17
X16	0.705	0.740	1.445	−0.035	13	13	18
X17	0.580	1.325	1.905	−0.746	20	2	8
X18	0.357	1.314	1.670	−0.957	23	3	10
X19	1.088	0.628	1.716	0.460	7	17	9
X20	0.627	0.945	1.572	−0.318	17	9	13
X21	1.544	0.922	2.466	0.621	5	10	5
X22	0.702	1.252	1.954	−0.550	14	7	7
X23	0.749	0.850	1.598	−0.101	12	11	12
X24	0.801	0.838	1.639	−0.036	10	12	11
X25	0.633	0.629	1.262	0.004	16	16	19
X26	0.233	0.474	0.707	−0.241	26	24	25

.

The influence degree reflects the intensity of the effect exerted by a specific risk factor on other factors. According to the ranking results of influence degrees presented in Table 1 and Table 3, Table 4, Table 5, Table 6, Table 7, Table 8, Table 9 and Table 10, the top three risk factors are sequentially X3 (rear-end collisions caused by excessively close following distance), X1 (driver’s physical health status), and X4 (speeding). Factors with high influence degrees are capable of triggering a series of chain reactions among related factors. Therefore, before undertaking driving tasks, bus drivers must ensure that their health conditions are in an optimal state. During driving, drivers should strictly control vehicle speed to avoid speeding behaviors and maintain a safe distance so as to reduce the probability of unsafe incidents occurring.

On the other hand, according to the ranking of the influenced degrees of risk factors, the top three are sequentially X5 (judgment errors or operational errors), X17 (traffic congestion caused by excessive traffic flow), and X18 (the presence of blind spots or poor sight distance on road sections). A relatively high influenced degree indicates that these factors are more susceptible to the impacts of other risk factors. Therefore, when bus drivers encounter road sections with heavy traffic flow and poor sight distance, they should drive with greater caution to prevent the occurrence of unsafe incidents triggered by operational errors.

The centrality index is often employed to measure the significance of risk factors in bus accidents; specifically, the higher the value of centrality, the more prominent the influence of the risk factor on the occurrence of bus accidents. In accordance with the ranking results of risk factor centrality presented in Table 1 and Table 3, Table 4, Table 5, Table 6, Table 7, Table 8, Table 9 and Table 10, the top ten risk factors are, in sequence, X5 (judgment errors or operational errors), X3 (rear-end collisions caused by excessively close following distance), X1 (physical health status), X4 (speeding), X21 (impacts of weather conditions such as icy or snowy road surfaces), X2 (fatigue driving), X22 (imperfect safety management systems), X17 (traffic congestion resulting from excessive traffic flow), X19 (reduced road visibility caused by weather conditions such as haze), and X18 (the existence of blind spots or poor sight distance on road sections).

The cause degree index is frequently utilized to measure whether a risk factor is prone to being influenced by other factors or tends to exert an influence on other factors. By identifying the positivity or negativity of the cause degree value, risk factors can be categorized into cause factors (those with a positive cause degree value) and result factors (those with a negative cause degree value). Through statistical analysis, 14 risk factors have been classified as cause factors, while 12 risk factors have been categorized as result factors, with the ratio between the two being approximately 1:1. The causal relationships among the risk factors affecting the safe operation of public transport vehicles are illustrated in Figure 3.

(2) Analysis of Risk Factor Reachability

By calculating the mean value $\alpha =0.034$ and standard deviation $\beta =0.037$ of the elements in the comprehensive influence matrix V, the threshold $\lambda =0.071$ is obtained by summing these two values. The reachability matrix F is calculated using Formula (12). The results of the reachability analysis are integrated with those of the N-K model to reflect the coupling possibility between each risk factor and other factors, and the reachability of risk factors corresponds to the coupling forms of core categories. The detailed results are presented in

Table 11. Reachability analysis of risk factor nodes.

Risk Factors	Human	Vehicle	Road	Environment	Management	Potential Coupling Forms
X1	1	0	1	1	1	Human–Road–Environment–Management
X2	1	0	1	1	1	Human–Road–Environment–Management
X3	1	0	1	1	1	Human–Road–Environment–Management
X4	1	0	1	1	1	Human–Road–Environment–Management
X5	1	0	1	1	0	Human–Road–Environment
X6	1	0	1	0	1	Human–Road–Management
X7	1	0	0	0	1	Human–Management
X8	1	0	0	0	0	Human–Management
X9	1	1	0	0	1	Human–Vehicle–Management
X10	1	1	0	0	1	Human–Vehicle–Management
X11	1	1	0	0	1	Human–Vehicle–Management
X12	1	1	0	0	1	Human–Vehicle–Management
X13	0	1	0	0	0	Human–Vehicle
X14	1	0	1	0	0	Human–Road
X15	1	1	1	1	0	Human–Vehicle–Road–Environment
X16	1	0	1	0	1	Human–Road–Management
X17	1	0	1	0	0	Human–Road
X18	0	0	1	0	0	Human–Vehicle–Road–Environment
X19	1	1	1	1	0	Human–Vehicle–Road–Environment
X20	1	0	1	1	0	Human–Road–Environment
X21	1	0	1	1	0	Human–Road–Environment
X22	1	1	0	0	1	Human–Vehicle–Management
X23	1	0	0	0	1	Human–Management
X24	1	0	0	0	1	Human–Management
X25	1	0	0	0	1	Human–Management
X26	1	0	0	0	1	Human–Management

.

To conduct a more comprehensive analysis of the correlation characteristics of various factors in the risk system, the results of the reachability analysis and the N-K model analysis have been systematically integrated. This integration aims to clearly reflect the coupling possibility between each risk factor and other factors, while accurately establishing the corresponding relationship between the reachability of risk factors and the coupling forms of core categories. The reachability analysis clarifies the potential coupling forms of different risk factors. Through integration, it can be clearly observed that for each risk factor, its reachability characteristics determine the potential connection for it to have a coupling effect with other factors. Meanwhile, as a collection of key elements in the risk system, the coupling forms between core categories and various risk factors are also closely related to the reachability of risk factors.

4.3. Analysis of Key Factors Based on the N-K and DEMATEL Models

Based on the coupling modes and corresponding coupling values T of different types of risk factors calculated by the N-K model, as well as the potential coupling forms of each risk factor derived from the DEMATEL model, the coupling values of each risk factor are ultimately determined. Furthermore, the centrality of risk factors has been revised by applying Formula (13), with the calculation results being presented in Figure 4.

In Figure 4, the blue circular connecting lines reveal the results of the risk factor centrality based on the DEMATEL model, whereas the red diamond-shaped connecting lines demonstrate the results revised by the coupling value T. The risk factors X1, X2, X3, X4, X15, X18, and X19 with a corrected coupling value T centrality (red diamond connecting lines) greater than 2 are selected as the important risk factors for bus accidents. It is not difficult to observe that the human factors X1 (physical health status), X2 (fatigue driving), X3 (rear-end collisions caused by excessively close following distance), and X4 (speeding driving) exhibit particularly prominent capabilities in inducing risk coupling, with their importance clearly surpassing that of other factors. Therefore, the implementation of targeted management measures for human factors is of crucial importance, encompassing attention to drivers’ health conditions, prevention of fatigue driving and speeding behaviors, as well as maintenance of safe vehicle distances to avoid vehicle collisions. Furthermore, the revised centrality of the road factors X15 (road surface adhesion) and X18 (the presence of blind spots or poor sight distance on road sections) remains relatively high, indicating that they exert a significant force in triggering risk coupling. The centrality of the environmental factor X19 (reduced road visibility caused by weather conditions such as haze) also shows a high value, which similarly suggests that it possesses a significant force in inducing risk coupling and thus constitutes a key factor affecting the safe operation of buses.

5. Discussion

Based on the N-K model and the DEMATEL model, an in-depth analysis of these key factors has been conducted. Through calculations, the key risk factors affecting the safe operation of public transport vehicles have been identified. The research conclusions are as follows:

(1) According to the analysis results derived from the N-K model, it has been found that the key to controlling risk events lies in the effective prevention of coupling effects among multiple factors; in particular, the coupling of factors such as human–vehicle–environment–management and human–vehicle–road–management exerts a direct impact on the safe operation of public transport vehicles. Specifically, a high degree of coupling is exhibited between human factors and vehicle factors, thereby forming a strong coupling system, and this coupling relationship makes it prone to triggering greater risk concentration when these two factors interact with other risk factors. Therefore, human factors and vehicle factors are the core factors affecting the safe operation of public transport vehicles, and the risk values of these two factors often remain at the highest level in the coupling of multiple factors, which thus require special attention and management.

This conclusion is consistent with the findings of Kim’s research on intercity coach accidents on highways. A random parameter ordered Probit model was employed in their study, which revealed that the coupling effect of driver fatigue (a human factor) and slippery road surfaces (road–environmental factors) exerts heterogeneous impacts on the severity of coach accidents. It was explicitly pointed out that the coupling of multiple factors constitutes a key link in accident risk management and control [12]. However, compared with Kim’s research, which focused on intercity coaches on highways, the scenario of this study has been extended to the field of urban public transport, and management factors have been incorporated into the analytical framework of multi-factor coupling. This extension is more in line with the actual operation of urban public transport, as the operation of urban public transport is more closely associated with management factors such as public transport scheduling and driver safety training. In addition, by analyzing the Australian public transport accident dataset, Samerei pointed out that the causes of public transport accidents involve multiple dimensions, including driver characteristics, road environment, and the behaviors of traffic participants. This also confirms the significant impact of the interaction of multiple factors on the occurrence of accidents [14].

(2) Through the analysis of the DEMATEL model, it has been found in this study that five risk factors, namely judgment errors or operational errors, rear-end collisions caused by excessively close following distances, physical health status, speeding driving, and impacts of weather conditions such as icy or snowy road surfaces, possess the highest centrality values. The implementation of control measures on these key factors can effectively block the interaction paths between risk factors, thereby reducing the possibility of unsafe incidents occurring during the operation of buses.

The results of identifying key factors based on centrality values are consistent with the research conclusions of Kaplan on the severity of public transport accidents in the United States. A generalized ordered Logit model was adopted in their study, which found that driver operation behaviors and road environmental conditions are important factors affecting the severity of public transport accidents. This is consistent with the high-centrality characteristics of “judgment errors or operation errors” and “weather impacts such as icy or snowy road surfaces” in this study [13]. In this study, “driver’s physical health status” is further included in the category of high-centrality factors—a point rarely mentioned in the studies by Kaplan and Prato. However, the research conducted by Miyama on Japanese public transport drivers can provide support for this. It was verified in Miyama’s study that poor physical health and insufficient sleep of drivers are key risk factors leading to public transport accidents related to driver fatigue [3]. Meanwhile, through a questionnaire survey of 320 urban public transport drivers in China, Han found that speeding and following vehicles too closely are important causes of high-risk public transport accidents. This directly confirms the high-centrality characteristics of “speeding” and “rear-end collisions caused by too short following distance” in this study [2]. Different from Han’s research, which focused on the correlation between a single behavior and accidents, this study further clarifies the causal relationships and action paths among these high-centrality factors through the DEMATEL model. For example, it is found that “judgment errors” are not only independent risk factors, but also affected by “driver’s physical health status” and “icy or snowy road conditions”. This provides a more comprehensive understanding for systematically blocking the transmission of risks.

(3) In comparison with the N-K model, which can only reveal risk factors within core categories and their interactions, and the DEMATEL model, which relies on subjective experiential judgments, the integration of the N-K and DEMATEL models not only overcomes the limitations associated with their individual application but also enhances the accuracy and scientific rigor of risk identification. By revising the centrality of risk factors calculated by the DEMATEL model using the risk factor coupling value T derived from the N-K model, the key factors affecting the safety of public transport operations have been obtained. The analysis has revealed that human factors, road factors, and environmental factors play particularly prominent roles in triggering multiple risk couplings involving humans–vehicles–roads–environment–management, with their influence significantly exceeding that of other factors. The key factors affecting the safety of public transport operations include X1 (physical health status), X2 (fatigue driving), X3 (rear-end collisions caused by excessively close following distances), X4 (speeding driving), X15 (road surface adhesion), X18 (the presence of blind spots or poor sight distance on road sections), and X19 (reduced road visibility caused by weather conditions such as haze). Therefore, it is imperative to strengthen the supervision of drivers, provide necessary safety training, prevent fatigue driving and speeding behaviors, and pay constant attention to drivers’ health conditions. Furthermore, under adverse weather conditions, bus drivers are required to possess higher skills and vigilance; consequently, public transport companies should regularly conduct emergency driving training for drivers under severe weather conditions to ensure that they can properly respond to various unexpected situations.

The model integration approach adopted in this study is supported by Jiao’s research. It was pointed out in Jiao’s study that combining quantitative coupling analysis models (such as the N-K model) with causal relationship analysis models (such as the DEMATEL model) can make up for the limitations of a single model [28]. Different from Jiao, who integrated DEMATEL with Bayesian networks, this study chooses to combine DEMATEL with the N-K model, focusing more on quantifying the “coupling intensity” between factors rather than probabilistic reasoning. This difference makes the model more suitable for analyzing the nonlinear superposition effect of risk factors in public transport accidents. At the level of key factor management and control, the emphasis placed on “preventing fatigued driving” and “monitoring drivers’ health” in this study is consistent with the research suggestions put forward by Wang. By analyzing the dangerous driving behaviors of Chinese public transport drivers, Wang and his team found that enterprise management factors and drivers’ physical health status are the keys to reducing accident risks, and proposed that health examinations should be strengthened and the scheduling system should be optimized [21]. This study further refines the implementation path and puts forward the suggestion of “conducting regular emergency driving training for severe weather”. This suggestion can be supplemented by Hsu’s research. It was found in Hsu’s study that exposure to high temperatures at night increases the mortality rate of road traffic, indicating that severe environmental conditions require targeted driver training to improve their adaptive driving ability [32]. In addition, this study identifies “road surface adhesion (X15)” and “road section blind spots (X18)” as key road factors, which is consistent with the research conclusions of Ewing. By studying the relationship between environment and traffic safety, Ewing confirmed that road geometric characteristics and road surface conditions are closely related to accident risks [31].

6. Conclusions

This paper explores the coupling mechanism of risk factors contributing to bus traffic accidents and identifies the key factors influencing such accidents. Firstly, an accident statistical analysis method is employed to comprehensively identify and analyze the risk factors affecting bus traffic accidents from multiple perspectives, including the time periods when bus accidents occur, the characteristics of road sections, accident types, accident levels, and accident causes. Secondly, the N-K model is introduced, which, by incorporating the management dimension into the traditional four elements of road traffic, considers the interactive effects of single factors, two-factor combinations, and multi-factor combinations in a comprehensive manner, thereby delving into the coupling relationships of risks associated with bus traffic accidents. Subsequently, based on accident causes, 26 risk factors are summarized, and the DEMATEL model is adopted to conduct an analysis of the centrality and cause degree of these risk factors. Finally, the centrality of risk factors calculated by the DEMATEL model is revised using the N-K model, yielding the key factors that affect the safety of bus operations, providing a new research perspective for the analysis of risk factors of buses.

Based on the results of the analysis of bus accident risk factors, the following suggestions are put forward for the five factors:

(1) Human factors: Strengthen the driver training and assessment mechanism. Regular safety driving training shall be conducted for bus drivers to enhance their ability to respond to emergencies as well as their skills in identifying and dealing with driving fatigue. The working environment and rest conditions for drivers should be optimized, and reasonable schedules for driving and rest should be formulated to prevent the occurrence of driving fatigue. A more scientific shift arrangement and rest system need to be established to ensure that drivers maintain optimal mental and physical states. Meanwhile, passengers’ safety awareness should be raised: regular passenger safety education information shall be released through multiple channels such as in-vehicle advertisements, radio broadcasts, and social media to remind passengers to pay attention to safety during rides; in addition, new media platforms like WeChat official accounts should be utilized to irregularly publish evacuation routes and methods in emergency situations such as bus fires and rollovers.

(2) Vehicle factors: Vehicle inspections and maintenance work shall be conducted periodically, while the daily inspection and maintenance procedures for buses shall be strengthened to ensure that each bus can pass rigorous safety inspections before being put into operation, which cover key indicators such as tire wear conditions and engine performance, so as to guarantee the normal operation of all its functions. Furthermore, an intelligent vehicle management system should be introduced, and advanced vehicle monitoring technologies, such as the Global Positioning System (GPS) and remote diagnostic systems, shall be adopted to monitor in real time critical information including the driving status and mechanical faults of buses, thereby enabling the timely identification of potential risks and the implementation of early warning measures.

(3) Road factors: Optimize urban road planning and design. In the field of urban transportation planning, rationally arrange bus lanes to reduce the intersection and interference between buses and other vehicles, and prevent the occurrence of traffic congestion and accidents. Regular inspections and maintenance of road facilities shall be carried out; in particular, factors affecting traffic safety, such as road surface adhesion coefficients and road potholes, must be inspected and repaired periodically to avoid accidents caused by poor road conditions.

(4) Environmental factors: Emergency response plans and driver training. Emergency driving plans for severe weather conditions (such as heavy rain, heavy snow, and haze) should be strengthened, while drivers should receive training on safe driving techniques under adverse weather conditions. The weather early warning system needs to be improved by introducing a meteorological information system that can monitor weather changes in real time and send early warning information to bus companies promptly, so that drivers can be informed in a timely manner to prevent potential environmental risks. Enhance vehicle lighting and improve visibility. In situations with low visibility such as in heavy fog or at night, strengthen the lighting facilities of buses to ensure that buses can be detected in a timely manner by other traffic participants.

(5) Management factors: The transportation management system should be improved. A scientific bus scheduling system should be constructed, and bus routes and timetables should be reasonably planned to avoid overly crowded routes or frequent traffic convergences, thereby fundamentally reducing the probability of traffic accidents. The optimization of management factors needs to be deeply connected with national and local policy systems, and bus enterprises should be required to incorporate safety management into the responsibility system for all employees. Hard standards such as the proportion of safety investment, frequency of vehicle maintenance, and duration of driver training should be clearly defined. Emergency accident drills should be regularly conducted for employees of bus companies to improve their response speed and handling efficiency in emergency situations. In particular, after a traffic accident occurs, quick responses and timely handling should be made to minimize the impact of the accident. At the local level, measures can be refined based on regional risk characteristics—for example, strengthening the configuration of anti-skid and de-icing equipment for buses in winter, and improving the real-time road condition linkage mechanism for tunnels and water-adjacent road sections in rainy areas. Meanwhile, a monthly joint meeting system should be established among transportation departments, emergency management departments, and bus enterprises, and third-party institutions should be introduced to conduct safety assessments, so as to ensure the effective implementation of management measures.

When this study conducts the identification of risk factors and analysis of key factors for bus traffic accidents, bus safety data are usually not disclosed to the public. Therefore, the data sources of this study mainly rely on online searches and reviews of relevant academic papers, which results in certain limitations in the total amount and content of the data. If data support from bus companies can be obtained in the future, it will contribute to a more comprehensive analysis of the risk factors for bus traffic accidents. In the process of constructing the bus driving risk assessment model, the indicators currently selected are mainly based on traditional bus data. However, with the continuous advancement of science and technology, buses are developing in a more intelligent and unmanned direction, and more diverse and abundant vehicle operation data can be acquired. Therefore, future studies should consider incorporating the new-type data provided by intelligent public transport vehicles into consideration, in order to construct a more accurate and comprehensive bus driving risk assessment model. In addition, this study analyzes all accident samples as static events and does not consider the laws of accident occurrence over time. Specifically, the accident incidence rate and the intensity of the role of risk factors may vary during different time periods of a day (such as morning rush hours, nighttime, etc.), different days of a week (such as weekdays or weekends), and different seasons (such as rainy seasons, winter, etc.). This is especially true when regulated by environmental factors such as rainfall, snowfall, and high temperatures, where temporal heterogeneity may be more pronounced. This omission may lead to insufficient accuracy in the analysis of some risk factors.

Future research can advance in the direction of dynamic prediction and traceability of bus accident risks. Data such as bus GPS trajectory data, on-board monitoring video data, road infrastructure sensor data, real-time meteorological data, and bus enterprise management ledger data can be integrated. Hidden correlations between data of different dimensions are explored through deep learning models, and a dynamic accident risk prediction model is constructed. This model enables risk level prediction for different time scales and different road section types, and traces the core factor combination with the highest coupling probability of risk factors. Although existing studies have identified risk factors and their coupling relationships using the N-K model and DEMATEL model, the data sources still mainly rely on historical accident reports, which have data lag and fail to make full use of real-time dynamic data. In contrast, through the dynamic prediction and traceability of bus accident risks, the dynamic risk evolution process before an accident occurs can be captured more comprehensively. The dynamic prediction model can make up for the deficiency of traditional static analysis in the timeliness of risk early warning, provide more accurate real-time management and control basis for bus enterprises, and further enhance the initiative and pertinence of risk prevention and control. Future research can consider incorporating time periods and seasonal dimensions to further optimize the analysis model. For example, conduct stratified analysis according to different time periods of the day, construct accident risk models for each time period respectively, compare the differences in the influence coefficients of road, vehicle, and environmental factors in different time periods, and clarify the time-dependent characteristics of each factor. Further, introduce seasonal dummy variables into the model to quantify the regulatory effect of seasonal factors on accident risk, combine time series analysis methods, based on monthly or weekly accident data, explore the periodic patterns of accident occurrence, identify the time nodes with high accident rates, and provide data support for traffic management departments to formulate time-specific and season-specific safety control measures.