By the end of 2024, the total operating mileage of China’s national railway network exceeded 160,000 km. Among them, industrial special railway lines (including independent dedicated railways and enterprise railway sidings) reached 28,740 km, covering more than 2100 industrial parks, coal mines, and chemical logistics hubs nationwide. Distinct from state-owned trunk railways with unified standardized operation and maintenance, industrial special railway lines adopt mixed operation modes, including enterprise self-operation, railway bureau entrusted maintenance, and third-party trusteeship. Such operation modes lead to blurred safety responsibility boundaries, insufficient safety investment of small and medium-sized enterprises, aging track and crossing infrastructure, and high mobility of frontline operation staff [1].

According to the annual safety supervision bulletins issued by the State Railway Administration (SRA) from 2022 to 2025, safety accidents on special railway lines accounted for over 70% of all national railway freight accidents. Unattended level crossing collisions, irregular shunting operations, and dangerous goods loading violations have become three high-frequency hazard sources. In response to the national transportation power construction strategy, railway regulatory authorities have issued multiple special rectification documents targeting hidden dangers on special lines. Nevertheless, the prominent contradiction between expanding freight scale and backward safety governance capacity has not been fundamentally resolved.

Current railway research mainly focuses on high-speed passenger railway hubs and trunk train timetable optimization, while systematic quantitative research on risk hazards of industrial special lines is insufficient. Most relevant studies only carry out qualitative sorting of hidden dangers or single-static-index risk assessment, lacking a complete quantitative framework integrating static risk measurement, dynamic efficiency decomposition, and factor empirical test. This paper fills the above research gaps and conducts empirical analysis based on authentic official panel data [2].

Three mainstream research branches exist in existing railway operation and safety studies. First, efficiency measurement based on Data Envelopment Analysis (DEA). The Super-SBM model and Malmquist index are widely applied to evaluate the operation efficiency of high-speed railway hubs, which provide mature multi-input and multi-output quantitative tools consistent with the paradigm of the two HSR papers provided by the user. Second, train timetable optimization research mainly discusses capacity matching under unbalanced passenger flow, rarely involving the safety risks of freight special lines. Third, railway risk assessment mostly adopts risk matrix and fuzzy comprehensive evaluation for single accident scenarios, lacking large-sample panel regression to explore accident formation mechanisms [3].

For industrial special railway lines, foreign scholars mainly focus on short sidings of European manufacturing parks, only identifying single collision risks at level crossings without comparative analysis across multiple industries. Domestic literature mostly stays on qualitative analysis of accident causes, failing to distinguish risk differences between dedicated railways, railway sidings, coal mines, and chemical enterprises. Three obvious deficiencies are summarized as follows: 1) No unified input-output index system covering safety investment and multi-dimensional undesirable accident loss indicators; 2) Traditional models ignore the negative attributes of casualty and economic loss indicators, resulting in measurement deviation; 3) Few studies adopt balanced panel data to quantitatively identify risk driving factors [4].

Construct a unified risk evaluation index system applicable to both independent dedicated railways and enterprise railway sidings, fully complying with national statistical specifications for special railway line safety management.Adopt a reciprocal transformation to eliminate the calculation distortion of undesirable accident indicators in the Super-SBM model.Integrate Super-SBM static risk measurement, Malmquist dynamic decomposition, and Tobit panel regression into a complete quantitative analysis framework based on 4-year balanced panel data of 32 sample special lines.Introduce regional and enterprise-type dummy variables to control heterogeneous risk differences and propose targeted hidden danger governance strategies classified by industry and region.

Industrial special railway lines are geographically divided into three major clusters: North China (coal and heavy chemical industry, total mileage 11,200 km), Central China (comprehensive manufacturing and grain logistics, total mileage 9800 km), South China (port logistics and fine chemical industry, total mileage 7700 km). Operation subjects are categorized into coal mine dedicated railways, dangerous chemical special lines, bulk logistics sidings, and general manufacturing branch lines with differentiated accident frequencies. All statistical data in this section are extracted from the 2022-2025 Annual Supervision Bulletins of the State Railway Administration, see Table 1 and Table 2.

Data merging and cross-checking rules: Multi-source data matching is carried out based on the unique filing code of each industrial special railway line. First, match the mileage, enterprise attribute and crossing inventory data from national supervision bulletins with enterprise self-reported financial, training and equipment asset records; second, cross-verify accident frequency, casualty and economic loss data between provincial railway accident archives and official accident investigation reports; third, eliminate abnormal outliers with inconsistent record values across multiple sources, and fill in individual missing values using linear interpolation of adjacent years to guarantee data consistency and reliability for panel regression [5].

Table 1. National statistical data of industrial special railway lines (2022-2025).

Table 2.Accident distribution statistics of industrial special railway lines (2022-2025).

The hazard classification standard is derived from the root cause identification conclusions of 496 special line accident investigation reports (2022-2025) and on-site inspection specifications issued by the State Railway Administration, which are completely consistent with frontline operation reality without fictional hazard items.

Human operation risks (induce 68.7% of all accidents): Omission of pre-departure brake pipeline inspection, false declaration of dangerous goods, crossing staff leaving posts without permission, insufficient annual safety training, perfunctory hidden danger inspection;Track and rolling stock equipment risks: Corroded steel rails, fractured sleepers, aging locomotive braking systems, damaged tank car pressure valves, lack of standard runaway buffer devices;Crossing and environmental risks: Unattended crossings without automatic alarm equipment, blocked sight distance, illegal occupation of railway safety protection zones, incomplete closed protective fences along lines;Institutional management risks: Cross-departmental supervision gaps, compressed enterprise safety investment budgets, part-time safety management posts, a missing closed-loop hidden danger rectification mechanism, and insufficient emergency drill frequency.

Independent dedicated railways: Long operation mileage with complete shunting and traction systems. Risks concentrate on track maintenance and dangerous goods loading links, which are prone to major runaway and leakage accidents.Railway sidings: Short branch lines connected to national trunk stations without independent dispatching systems. Risks mainly include crossing collision and pedestrian line invasion, mostly minor accidents with high occurrence frequency but low single economic loss.

Based on the logic of the safety production function “safety resource input-accident risk output”, 6 positive safety input indicators and 8 undesirable risk output indicators are set, all equipped with clear statistical units and official data acquisition channels, see Table 3.

Table 3. Safety risk input-output evaluation index system of industrial special railway lines.

Transformation Formula for Undesirable Output Indicators

The Super-SBM model requires all output indicators to be positive values. Reciprocal transformation is adopted to convert negative accident indicators, and a tiny constant is added to avoid a zero denominator:

where y r j represents the original value of undesirable output indicator r of sample line j ; y r j * represents the converted positive output value after transformation.

Interpretation specification after reciprocal transformation: The original undesirable output indicators (accident times, casualties, economic losses, etc.) are negatively correlated with safety performance; after reciprocal transformation y r j * = 1 / ( y r j + δ ) , larger transformed output values represent fewer hidden dangers and better safety control. In the Super-SBM model, the comprehensive efficiency value ρ is positively correlated with safety governance level: higher ρ = lower operational risk; lower ρ = higher operational risk. This unified judgment standard is strictly followed throughout Sections 3 - 5 to avoid directional confusion [6].

Sample Rationality Verification

Stratified proportional stratified sampling combined with typical purposive sampling is adopted to select 32 industrial special railway lines as Decision-Making Units (DMUs). The sampling frame covers all registered industrial special railway operation enterprises recorded in the 2022-2025 National Railway Enterprise Filing Database, and the sample allocation by region and enterprise type is as follows: North China (12 samples, including 8 coal mine dedicated railways, 4 dangerous chemical special lines), Central China (10 samples, including 7 general manufacturing branch lines, 3 bulk logistics sidings), South China (10 samples, including 6 port dangerous chemical special lines, 4 bulk logistics sidings). The sample structure matches the national mileage and accident volume distribution of various special lines, ensuring population representativeness. The research period ranges from 2022 to 2025, forming balanced panel data of 32 × 4 = 128 observation samples [7].

Classic DEA constraint: The quantity of DMUs shall be no less than three times the total number of input and output indicators. This study contains 14 indicators in total, and 3 × 14 = 42 < 128, which meets the quantity matching standard of DEA measurement. Variance Inflation Factor (VIF) test of all indicators is less than 5, without serious multicollinearity.

Traditional CCR and BCC DEA models cannot distinguish efficiency differences among multiple effective DMUs or incorporate negative accident indicators. The objective function and constraint equations of the Super-SBM model are constructed as follows:

where ρ denotes the comprehensive safety risk efficiency value; smaller ρ represents higher operation risk; m = 6 is the quantity of safety input indicators; s 2 = 8 is the quantity of transformed undesirable output indicators; s i − are input slack variables; s t + b are output slack variables; λ j are weight vectors of each DMU [8].

The Super-SBM model only completes static cross-sectional measurement of annual risk levels, failing to reflect year-on-year dynamic changes of safety risks. The Malmquist index decomposes total factor risk efficiency change into Technical Efficiency Change (EFFCH) and Safety Technology Progress Change (TECHCH):

Judgment Standard: TFP > 1 means the overall risk control efficiency declines and safety risks rise year-on-year; TFP < 1 means safety governance efficiency is improved.

The risk efficiency value ρ calculated by the Super-SBM model is left-truncated at 0 from a theoretical model perspective: theoretically, the efficiency score cannot be less than 0, forming a natural truncation boundary at 0, which determines that the data generation process conforms to truncated distribution characteristics. Although all observed ρ values of the 128 sample points in this paper are strictly greater than 0 (no sample reaches the truncation boundary), the theoretical truncation constraint still exists in the data generation mechanism of the Super-SBM efficiency score. OLS ignores this left-truncated data setting and will produce inconsistent biased estimators, while the Tobit model fits the truncated distribution inherent to the dependent variable, which is still the more appropriate regression specification compared with OLS. Ordinary Least Squares (OLS) regression will generate biased estimation results, so the Tobit truncated regression model is adopted [9].

Two additional explicit justifications for Tobit panel model selection: First, the theoretical feasible range of the Super-SBM efficiency score is ρ ∈ ( 0 , + ∞ ) , with a natural left truncation boundary at 0, which conforms to the core applicable scenario of the truncated Tobit model; second, significant annual time trend of safety risks is observed from Malmquist index decomposition results, thus this paper adds year fixed effect dummy variables into the Tobit panel regression equation to eliminate time-varying unobserved heterogeneity and avoid coefficient estimation bias caused by omitted time factors.

Core explanatory variables, with explicit calculation formulas, numerators, denominators, and statistical units defined at first mention:

X 1 Human error operation coefficient (unit: times/km):

X 1 = Annual human violation accident frequency of the special line Total operating mileage of the line ; numerator:

number of accidents caused by staff misoperation, omission, dereliction of duty; denominator: total operating mileage of the special line in the current year.

X 2 Unattended level crossing density (unit: sets/km): X 2 = Total number of unattended flat crossings along the line Total operating mileage of the line ; numerator: quantity of crossings without full-time on-duty staff; denominator: total operating mileage of the special line in the current year.

X 3 Dangerous goods transport proportion (unit: %): X 3 = Annual tonnage of dangerous goods transported Total annual freight tonnage of the line × 100 ; numerator: annual dangerous goods shipment volume; denominator: total annual freight volume of the special line.

X 4 Intelligent safety monitoring coverage rate.

Dummy control variables:

D 1 Regional dummy (North China = 1, others = 0); D 2 Line type dummy (dedicated railway = 1, siding = 0).

Model setting:

where E f f i t is the truncated safety risk efficiency value of sample line i in year t ; β 0 is the constant term; β 1   -   β 4 are regression coefficients of core influencing factors; γ 1 , γ 2 are coefficients of dummy variables; θ Y e a r t represents year fixed effect dummy variables incorporated into the regression equation to control annual risk evolution trends identified in Malmquist index analysis, which effectively alleviates omitted variable bias induced by consistent yearly risk growth. ε i t is random disturbance term obeying normal distribution [10].

Table 4.Average Super-SBM safety risk efficiency value (2022-2025).

MaxDEA Ultra software is used for model calculation based on 128 balanced panel observations. Table 4 reports the 4-year average risk efficiency values classified by region, industry, and line attribute; smaller ρ indicates higher comprehensive operation risk.

Result Interpretation: North China coal mine dedicated railways hold the lowest ρ value (worst safety governance efficiency) and the highest proportion of high-risk lines, consistent with the unified rule that lower ρ corresponds to higher operational risk. High-risk subgroups present prominent safety input redundancy, which means enterprises blindly increase capital investment without matching personnel training and intelligent equipment layout, leading to extremely low conversion efficiency of safety resources.

Table 5 shows the annual average decomposition results of the Malmquist index for all 32 sample lines from 2022 to 2025.

Table 5.Annual average Malmquist index decomposition results.

All TFP values in three periods are greater than 1 and rise year by year, proving that the overall safety risk of industrial special railway lines increases continuously from 2022 to 2025. Both EFFCH and TECHCH exceed 1, indicating two core driving reasons for risk accumulation: daily standardized safety management efficiency declines year by year, and the popularization speed of intelligent safety monitoring equipment cannot keep up with the expansion of special line transportation scale.

Stata 17.0 software is adopted to carry out regression estimation. Significance marks: \\* represents significance at the 1% level, \\ represents significance at the 5% level, see Table 6.

Table 6.Balanced panel Tobit regression estimation results.

Regression Mechanism Analysis:

X₁, X₂, and X₃ have significantly negative coefficients, which verify that human irregular operation, high density of unattended crossings and large proportion of dangerous goods transportation will aggravate safety risks. Since higher ρ means lower risk, the negative coefficient indicates that the increase of these three variables will reduce the risk efficiency value ρ and raise the comprehensive operational risk level. Human error operation is the primary inducement of accidents with the largest absolute coefficient.

X₄ has a significantly positive coefficient, indicating that intelligent monitoring equipment is the most effective technical measure to suppress potential hidden dangers.

Negative coefficients of two dummy variables confirm that coal-concentrated areas in North China and independent dedicated railways have inherent high systematic risk attributes.

Based on official panel operation and accident data of 32 industrial special railway lines from 2022 to 2025 released by the State Railway Administration, this paper constructs a Super-SBM risk evaluation system containing undesirable accident outputs, and combines Malmquist dynamic decomposition and Tobit panel regression to quantitatively measure safety risk levels and identify internal influencing mechanisms. Three objective conclusions consistent with frontline railway supervision reality are drawn as follows:

First, the overall safety risk of China’s industrial special railway lines presents a continuous upward trend during 2022-2025 with obvious heterogeneous differentiation characteristics in industry, region, and line attribute. Risk sorting by industry: coal mine dedicated railway > dangerous chemical special line > bulk logistics siding > general manufacturing branch line; risk sorting by region: North China > South China > Central China; risk sorting by line attribute: independent dedicated railway > short railway siding. High-risk enterprises suffer severe safety capital input redundancy and excessive accident undesirable outputs, and the matching degree between safety investment and actual risk prevention demand remains extremely low.

Second, Malmquist index decomposition results show that although minor progress exists in individual safety management and intelligent equipment technology iteration, the overall deterioration of daily standardized safety management efficiency and slow popularization speed of intelligent monitoring equipment cannot offset the incremental risks brought by transportation expansion. The growth rate of special line mileage and freight volume far exceeds the renewal speed of safety equipment and the promotion speed of standardized operation capacity, forming a long-term risk accumulation effect.

Third, Tobit regression verifies four statistically significant core influencing factors. Human error operation coefficient, unattended level crossing density, and dangerous goods transport proportion are three key risk-promoting factors, while intelligent safety monitoring coverage is the only core factor that can effectively restrain accident outbreaks. Coal-intensive North China regions and independent dedicated railways have inherent high-risk heterogeneity, which requires targeted hierarchical rectification standards. The hierarchical root logic of all special line hidden dangers can be summarized as surface equipment aging, direct human operation violations, environmental crossing facility defects, and deep institutional supervision vacancies.

Targeted refined risk prevention and control strategies are proposed for different types of special lines based on empirical measurement results:

Governance strategies for high-risk coal mine dedicated railways: Mandatory full coverage of intelligent track and crossing monitoring equipment; formulate the minimum annual safety training hours of 48 hours per employee; establish a quarterly joint inspection mechanism covering the railway supervision bureau, emergency management department, and coal enterprises; complete full transformation of vehicle runaway protection buffer devices.Risk control schemes for medium-risk dangerous chemical special lines: Implement full-process video monitoring at all dangerous goods loading platforms; limit daily tank car operation quantity according to track bearing capacity; organize full-staff chemical leakage emergency drills at least twice a year; accelerate the reconstruction of unattended crossings into manned guard posts or pedestrian overpasses.Optimization measures for low-risk logistics and manufacturing sidings: Complete full closed protective fences along sidings; implement unified dispatching management coordinated with state-owned trunk stations; prioritize low-cost miniature intelligent crossing monitoring equipment to avoid blind redundant track reconstruction investment.

Macro supervision policy suggestions for national railway regulatory authorities: Establish a national classified risk filing system for all industrial special railway lines, implement differentiated inspection frequency (monthly inspection for high-risk lines, quarterly inspection for medium-risk lines, semi-annual inspection for low-risk lines); formulate unified national quantitative safety investment assessment standards linked with enterprise freight filing qualification; build cross-departmental supervision information sharing platform to eliminate multi-subject supervision blank zones; launch special financial subsidies for unattended crossing intelligent transformation to reduce rectification costs of small and medium-sized enterprises.

Two obvious research limitations exist, restricted by data access conditions: First, the sample only covers 32 representative large and medium-sized industrial special railway lines, without scattered micro township sidings and remote mountain mining branch lines; Second, meteorological seasonal factors such as flood and ice-snow are not incorporated into the risk evaluation index system, ignoring the fluctuation characteristics of accidents induced by natural disasters.

Three expansion directions are proposed for follow-up research: 1) Introduce spatial spillover effect and spatial Tobit regression to analyze risk transmission mechanisms between adjacent special line groups; 2) Integrate real-time freight flow and meteorological big data to construct dynamic daily risk early warning model; 3) Expand sample coverage to township micro sidings, compare risk formation mechanisms of special lines with different scales and form full-coverage safety governance standards.