A Hybrid Fault Tree–Fuzzy Logic Model for Risk Analysis in Multimodal Freight Transport
Abstract
:1. Introduction
2. Research Objectives: Addressed Gaps
- To develop an integrated FTA-DFT–fuzzy framework for identifying, structuring, and quantifying risks across maritime, road, and rail segments of multimodal transport;
- To apply quantitative and semi-quantitative methods to calculate system reliability and sensitivity, identifying critical risk nodes and high-impact failure pathways;
- To compare the aggregated risk exposure across transport modes, thereby informing strategic decision-making for logistics operators and policymakers.
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3. Methods and Research Methodology
3.1. Qualitative vs. Quantitative Analysis
3.2. Model Applicability to Multimodal Transport
3.3. Method Extension Through Fuzzy Logic Modeling
- Rule 1: IF fatigue is high AND training level is low, THEN risk of human error is very high;
- Rule 2: IF weather conditions are severe AND visibility is low, THEN environmental risk is high;
- Rule 3: IF fatigue is low AND training is high, THEN risk of human error is low.
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- Its ability to represent vague concepts, like fatigue, poor training, or visibility, through linguistic variables;
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- Its ability to translate expert knowledge into structured rules within a probabilistic framework;
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- Its ability to operate within the same structure as the fault tree, maintaining consistency with both the standard (FTA) and dynamic (DFT) models used in this research.
3.4. Research Methodology
- Data collection—The authors aggregated statistical, empirical, and expert-sourced data on human, technical, and environmental risk factors across maritime, rail, and road transport.
- FTA modeling (Standard and Dynamic)—fault tree analysis (FTA) and dynamic fault trees (DFTs) were used to decompose system failures into hierarchical risk paths using logical gates and event dependencies. By DFTs, the FTA was enhanced by modeling time-dependent and sequence-based dependencies using specialized logic gates (e.g., SEQ, PAND). This reflects real-world event progression, such as poor maintenance causing delayed failures in transport systems.
- Fuzzy extension (FFTA)—fuzzy extension was used to transform subjective or imprecise data into fuzzy linguistic variables and apply fuzzy rule bases for inferential reasoning under uncertainty.
- Quantitative metrics—the authors calculated key reliability metrics, such as Mean Time to Failure (MTTF) and Mean Time Between Failures (MTBF), and performed sensitivity analyses to quantify system reliability and identify high-impact nodes.
- Strategic recommendations—Technical outputs were converted into actionable insights for decision-makers, including infrastructure upgrades, personnel training, and digital monitoring systems.
4. Case Study of Risk Analysis on Maritime, Road, and Rail Components of Multimodal Transports
4.1. Maritime Risks Analysis
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- Reports by the Romanian Naval Authority from 2024 (overview of navigation incidents and accidents in Romania between 2019–2023)—collected by the authors through direct interviews [35];
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- An IGP&I Pilotage Report—Report on P&I Claims Involving Vessels under Pilotage, 1999–2019 [36];
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- A report titled Risk Influencing Factors in Maritime Accidents—An Exploratory Statistical Analysis of the Norwegian Maritime Authority Incident Database [37];
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- Reports on risk influencing factors processed from the literature review.
Source ID | Source (APA-Style) | Risk Subcategory | Reported Value (%) | Weight (1–5) | Justification for Weighting |
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S1 | European Maritime Safety Agency. (2023). Annual Overview of Maritime Accidents 2014–2022. Brussels: EMSA. [34] | Human Behavior | 53.60 | 5 | Recent, official EU dataset; EMSA data are comprehensive and directly cover fatigue-related contributory factors in casualties. |
S2 | European Maritime Safety Agency. (2022). Analysis of Maritime Risk Indicators. Brussels: EMSA. [33] | Human Behavior | 51.17 | 5 | Credible, current EMSA report; detailed coverage of human factor risks including procedural and training issues. |
S3 | Romanian Naval Authority. (2023). Incident Reports on Romanian Maritime Sector (2019–2023). Bucharest: ANR. [35] | Personnel Negligence | 58.19 | 5 | National regulatory source; data derived from real local cases; aligns with the Romanian maritime operational context. |
S4 | Bogalecka, A. (2024). Collision and Contact—Analysis of Accidents at Sea [40] | Human Behavior | 42.33 | 4 | Recent academic research, regionally relevant; good methodological transparency, but limited to Baltic-specific data. |
S5 | Tunçel, G., Akyuz, E., and Arslan, O. (2024). Maritime fuzzy risk analysis. Sustainability, 14(9) [8] | Fatigue | 31.83 | 4 | Peer-reviewed, Scopus-indexed article applying fuzzy logic to maritime safety; covers human–environment interaction risks. |
S6 | Lei, C., and MacKenzie, C. A. (2021). System risk in maritime engineering. Int. J. Maritime Research, 14(2), 123–136. [5] | Equipment Age | 45.82 | 4 | Academic source with good modeling detail; not focused on fatigue but relevant for system degradation interdependence. |
S7 | Maritime Industry Watch. (2020). Global Maritime Risk Trends. London: MIW, UNCTAD, (2024). Review of Maritime Transport 2020–2024. [41] | Inadequate Training | 21.19 | 1 | Industry whitepaper with unclear data provenance; included for breadth, not for weight in conclusions. |
S8 | Kowalska, J. (2022). Communication gaps in seafaring. International Maritime Health, 73(3), 101–108. [42] | Poor Communication | 14.81 | 2 | Niche journal; addresses mental workload and seafarer stress but lacks broader empirical scope. |
S9 | Port Health and Safety Leadership Group (2022). Building a fatigue risk management system: Guidelines. [43] | Fatigue | 31.85 | 3 | Sectoral report; good thematic alignment but not peer-reviewed; partial methodology disclosure. |
S10 | Det Norske Veritas. (2023). DNV Maritime Safety Annual Review. Oslo: DNV. [44] | Technical Failures | 40.00 | 5 | Major classification society with validated empirical data; essential for cross-checking human vs. system failures. |
S11 | Chen, T. (2016). Low-visibility factors in maritime engineering. Int. J. Maritime Engineering, 13(1), 43–54. [45] | Visibility | 8.66 | 2 | Dated and more focused on navigation/optical risks; included for environmental context, not human factor directly. |
S12 | American Bureau of Shipping. (2022). ABS Maritime Incident Review. Houston, TX: ABS. [46] | Hazardous Materials Handling | 24.00 | 5 | Authoritative source; supports cross-validation of fatigue vs. hazardous procedures influence on incidents. |
S13 | World Maritime University. (2023). Fleet Aging and Risk Factors in Maritime Operations. Malmö, Sweden: WMU. [47] | Ship Age | 29.10 | 4 | Academic institutional source; aligns with fatigue indirectly via physical strain and ship maintenance cycles. |
S14 | Allianz Global Corporate and Specialty. (2023). Safety and Shipping Review. Munich: AGCS. [48] | Wind Conditions | 47.27 | 4 | Insurance-based dataset with solid actuarial logic; indirectly contributes to understanding fatigue through weather stress. |
S15 | International Group of P&I Clubs. (2019). Pilotage Claims Review 1999–2019. London: IGP&I. [36] | Violation of Rules/Procedures | 38.60 | 4 | Historical data; strong insight into human error frequency under routine strain, including fatigue. |
S16 | Norwegian Maritime Authority. (2015). Risk Factors in Maritime Accidents: Statistical Review. Oslo: NMA. [49] | Hazardous Materials Handling | 7.66 | 4 | Older but high-quality data on human–environment interaction; supports triangulation of fatigue’s systemic effects. |
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- Institutional credibility—Sources published by recognized authorities, such as the European Maritime Safety Agency (EMSA) and the Romanian Naval Authority (ANR), or classification societies, like DNV and ABS, were given the highest score (5), reflecting their authoritative data validation protocols and sectoral mandates.
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- Update recency—Recently published reports (post-2020) were scored higher (4–5), while older sources (e.g., published before 2015) received lower scores (1–2), particularly when no updates or follow-ups were available—this temporal weighting ensured that current risk trends are more influential in the calculation.
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- Methodological transparency—Reports that clearly documented their data collection, statistical methods, and sample sizes were favored (score 4–5). In contrast, sectoral white papers or professional reports lacking methodological detail were scored lower (2–3), despite containing potentially useful qualitative insights.
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- Scope and relevance—Publications with regional or global maritime coverage and those addressing the specific subcategories under investigation (e.g., fatigue, communication, hazardous material handling) were prioritized over those with narrower or tangential focus areas.
- For the subcategory “human behavior”, within the main risk category “human factor”:
- Ship age and poor communication, although frequently cited as common sources of maritime incidents and accidents, account for the lowest percentage of incidents among those analyzed in the referenced sources—27.08% and 27.14%, respectively;
- Over 50% of the incidents included in the 16 statistical sources examined were primarily caused by personnel negligence (51.68%) and violations of rules and procedures (55.29%).
Main Risk | Risk Subcategories | Source Scores and Risk Values | Weighted Mean |
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Human factor | Human Behavior | S1 (5): 53.6%; S2 (5): 51.17%; S3 (5): 61.2%; S4 (4): 42.33%; S5 (4): 41.66%; S6 (4): 45.82%. | 49.97% |
Personnel Negligence | S1 (5): 48.12%; S2 (5): 53.48%; S3 (5): 58.19%; S7 (1): 28.0%. | 51.68% | |
Inadequate Professional Training | S1 (5): 37.6%; S2 (5): 45.38%; S7 (1): 21.19%; S8 (2): 26.72%. | 37.66% | |
Fatigue | S1 (5): 32.16%; S4 (4): 43.7%; S9 (3): 31.85%; S10 (5): 54.3%; S14 (4): 37.1%. | 40.53% | |
Poor Communication | S1 (5): 28.32%; S3 (5): 39.92%; S6 (4): 27.16%; S8 (2): 14.81%; S9 (3): 12.08%. | 27.14% | |
Environment | Improper Handling of Hazardous Materials | S10 (5): 8.12%; S12 (5): 8.66%; S14 (4): 28.1%; S16 (4): 7.66%. | 45.39% |
Visibility | S1 (5): 46.7%; S7 (1): 16.81%; S8 (2): 19.95%; S11 (2): 8.66%; S15 (4): 6.75%. | 32.47% | |
Lighting Conditions | S3 (5): 63,66%; S5 (4): 31.83%; S9 (3): 27.4%; S14 (4): 5.66%; S15 (4): 1.66%. | 41.85% | |
Sea State | S1 (5): 70.33%; S3 (5): 48.8%; S6 (4): 37.16%; S10 (5): 3.66%; S15 (4): 1.72%. | 49.54% | |
Wind Conditions | S2 (5): 64.4%; S8 (2): 31.3%; S11 (2): 20.4%. | 47.27% | |
Means of transport | Inadequate Maintenance | S1 (5): 65.0%; S2 (5): 57.02%; S3 (5): 48.33%; S13 (4): 18.6%; S15 (4): 38.3%. | 46.93% |
Technical Failures | S2 (5): 62.0%; S10 (5): 40.0%; S12 (5): 24.0%; S15 (4): 22.0%. | 37.79% | |
Design Flaws | S3 (5): 30.0%; S10 (5): 66.0%; | 48.00% | |
Ship Age | S13 (4): 29.1%; S14 (4): 28.8%; S15 (4): 26.3%; S16 (4): 24.1%. | 27.08% | |
Equipment Age | S5 (4): 38.95%; S10 (5): 36.1%; S13 (4): 35.6%; S15 (4): 33.6%. | 36.06% | |
Violation of Rules and Procedures | S1 (5): 68.95%; S3 (5): 58.18%; S10 (5): 52.1%; S15 (4): 38.6%. | 55.29% |
4.2. Road Risks Analysis
4.3. Rail Risk Analysis
4.4. Comparative Risk Modeling and Multimodal Integration
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- data relevance - more reliable and relevant sources were assigned higher scores, and the use of the weighted mean ensured that the most significant sources exerted the greatest influence on the final analysis;
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- analytical quality - the method supported the identification and prioritization of major risks based on the most robust and well-founded sources;
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- practical utility - the method facilitated the allocation of resources to areas with the highest risk exposure and enabled an effective comparison between different categories of risk.
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- OR gates indicate that the resulting event will occur if at least one of the input events occurs. In the context of FTA, if the basic events M11, M12, ..., M17 lead to M1 through OR gates, then M1 will occur if any one of the events M11 through M17 materializes.
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- AND gates indicate that all input events must occur in order for the resulting event to take place.
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- Bayesian networks, which allow explicit encoding of conditional relationships [59];
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- Copula-based models to incorporate correlation structures without assuming independence [58];
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- Dynamic fault trees with dependency gates, which allow for the modeling of sequence-dependent and common-cause failures [6].
- We considered the hypothesis in which poor maintenance (M2.1) precedes technical failures (M2.2);
- In this case, a “sequence-enforcing connector” was used to indicate that the occurrence of M2.2 is directly dependent on the prior occurrence of M2.1.
- In the risk analysis, factors such as human errors or weather conditions were characterized by variability and uncertainty.
- The existing model was extended by applying fuzzy fault trees, which used probabilistic intervals to represent uncertain risks.
- To analyze the uncertainty associated with the risks related to inadequate professional training (M1.3) and fatigue (M1.4), we used the values extracted from Table 2 and expanded the percentage values into probability intervals. For M1.3, a variation of ±5% was assumed: P(M1.3) = [0.35; 0.40]. For M1.4, we assumed that P(M1.4) = [0.38; 0.43].
- These ranges reflect the variability in risks due to factors such as staff experience and the level of effort required in various operations.
- The combined probability for two fuzzy events (M1.3 and M1.4) was calculated as follows [14]:
- Calculation of the Mean Time to Failure (MTTF).
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- Calculation of Mean Time Between Failures (MTBF).
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- The increase in the value of node M1.3 from 0.3766 to 0.40 leads to an increase of 0.0234 in the total system probability;
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- The adjusted total probability, Pnew = 0.9234, reflects the influence of node M1.3 on the entire logistics system;
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- This influence is significant, indicating that human error plays a critical role in system vulnerability.
4.5. Comparative Application of FTA and DFTs Across Transport Modes
4.6. Bayesian Network Overlay to Enhance Dependency Modeling in Hybrid Risk Analysis
- Maritime transport: human factor dependency.
− 0.528 = 0.472
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- Road transport: fatigue and inexperience chain.
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- Rail transport: management deficiencies and collision risk.
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- Synthesis and implications.
5. Results Analysis
5.1. Modeling Interpretation
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- Road transport presents the highest overall risk (p = 0.9960), largely driven by human error, adverse weather, and infrastructure degradation;
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- Rail transport follows closely (p = 0.9937), with elevated risks from technical failures and aging infrastructure;
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- Maritime transport, while slightly lower (p = 0.9900), remains highly sensitive to human factors and environmental conditions, such as sea state and wind force.
5.2. Extended Sensitivity Analysis and Scenario Evaluation
- Scenario 1: seasonal weather disruptions.
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- Scenario 2: geopolitical and labor supply chain disruptions.
5.3. Reliability Analysis Using MTTF and MTBF Indicators
5.4. Comparative Risk Analysis Across Transportation Modes
5.5. Model Validation and Limitations
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- Validate the fuzzy model using case studies or failure logs;
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- Explore probabilistic–fuzzy hybrid models to better capture dependencies;
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- Incorporate data-driven techniques (e.g., fuzzy clustering or neural fuzzy systems) to enhance realism;
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- Develop interactive interfaces for dynamic risk updating in operational environments.
- Validation against real-world incidents.
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- Road transport—According to EU Transport Safety Council data (ETSC, 2023), approximately 90% of severe road freight incidents involve human-related factors, such as fatigue and misjudgment. This is consistent with our model’s highest-weighted contributors under R1.1 and R4.1 [55].
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- Rail transport—The ERA (European Union Agency for Railways, 2022) reports an average failure rate of 1.3 serious incidents per million train-km, often linked to technical or signaling issues. This supports our DFT findings that emphasize risks from F2.6 (defective infrastructure) [55].
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- Maritime transport—The EMSA (2022) indicates that 58% of maritime incidents are due to human error, with “procedural violation” and “inadequate watchkeeping” being dominant. This closely mirrors M15–M17 in our fault tree [54].
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- Methodological limitations.
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- expert dependency—fuzzy rule bases and membership functions are derived from expert judgment, which introduces subjectivity;
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- no dynamic updating—once probabilities are set, they remain static during a scenario run, unless manually redefined. This limits responsiveness to changing operational contexts;
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- single-event logic—the fault tree does not yet support multi-event propagation through probabilistic inference, as offered by Bayesian networks;
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- limited empirical calibration—because of the lack of real-time integration, the model has not yet been calibrated using incident logs, sensor telemetry, or machine learning-based diagnostics.
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- calibrating fuzzy membership ranges using fleet safety records from road and rail operators;
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- validating output probabilities against incident frequencies from the EMSA and ERA portals;
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- testing the model on simulated transport corridor data to assess predictive sensitivity.
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- Quantitative validation strategy and data constraints.
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- applying a ±15% perturbation range to selected fuzzy-weighted inputs and base probabilities;
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- monitoring variations in computed joint probabilities across all transport modes;
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- assessing the persistence of risk rankings and system-level event likelihoods.
5.6. International Benchmarking and Model Alignment
5.7. Model Validation Against Empirical Incident Data
5.8. Model Alignment with Established Risk Frameworks
6. Future Research: Analysis of Model Integration with Hybrid FTA-AI and Fuzzy–Bayesian Models
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- Bayesian learning for updating fuzzy membership probabilities;
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- AI-driven adjustment of rule weights based on operational feedback.
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- Fuzzy–Bayesian integration possibility.
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- The present fuzzy sets and rule bases, which handle subjective parameters such as fatigue (M1.4), training (M1.3), and weather (M3.35), can serve as prior probability distributions in a Bayesian framework.
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- For instance, the fuzzy membership degree for “high fatigue” could be used as a prior in a Bayesian node. When operational data become available (e.g., biometric sensors, shift records), the fuzzy risk estimates can be updated using Bayesian inference.
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- This approach would allow for the dynamic recalibration of risk levels based on real-time or historical data, leading to a fuzzy–Bayesian fault tree.
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- AI-Enhanced node prediction.
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- Some of the more data-sensitive components of the model, like M1.3 (training), M2.13 (vehicle defect detection), or M3.39 (traffic overload), can be paired with machine learning algorithms, such as classification models (e.g., decision trees, SVM), for predicting component failures or recurrent neural networks (RNNs) for time-series sensor data on fatigue or route delays.
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- These models could feed predicted likelihoods directly into fault tree nodes or fuzzy rules, enabling data-driven adaptation of the fault structure or weights.
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- Fault propagation learning.
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- The current dynamic logic gates (SEQ, SPARE) could be extended with reinforcement learning agents that simulate fault propagation over time and learn optimal mitigation sequences.
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- This is especially relevant in multimodal logistics, where intermodal dependencies (e.g., port-to-rail delays) are hard-coded today but could be learned and updated using AI agents that interact with real-time logistics data.
- d.
- Digital Twin synchronization.
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- Since our model outputs clear quantitative risk scores and root-cause pathways, it is compatible with digital twin architectures in logistics.
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- A virtual representation of a freight corridor or terminal could continuously update node risk levels using real-time operational input (e.g., vehicle telemetry, port queue lengths), thus running the fuzzy–FTA engine in real-time.
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- Risk predictions become dynamic rather than static;
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- The model can learn from operational outcomes (e.g., delays, breakdowns);
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- The system becomes proactive, issuing alerts before failures materialize;
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- Human judgment is augmented, not replaced, through explainable decision support.
7. Conclusions: Research Contribution
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Source [50,51,52,53,54] | Available Values | Source Score (Wi) | Reason for Awarding Points | Notation |
---|---|---|---|---|
Eurostat: Road Safety Statistics 2023 | Statistical data on accidents, weather conditions, and driver behavior in traffic. | 5 | Official, up-to-date sources and standardized methodologies at the European level, with high international comparability. | S1 |
European Commission: Road Safety Report 2024 | Strategic analyses and data on road safety, driver age, technical failures, and road infrastructure. | 5 | Official sources, including qualitative data, strategic guides, and updated information for 2024. | S2 |
Romanian National Institute for Statistics, Romania 2021 | National data on road accidents and infrastructure, as well as driver age. | 3 | Official national sources, but methodologies may vary, and data may be less up to date than European sources. | S3 |
Ministry of Transportation, Romania, 2020 | National reports on infrastructure and road accidents. | 4 | Official reports, but less standardized methodologies than European sources. | S4 |
European Road Safety Observatory (ERSO) 2018 | Data on road safety and national infrastructure. | 2 | Official sources, but with a narrower coverage and regular updates. | S5 |
National Highway Traffic Safety U.S. Administration, 2019 | Global assessments of road safety, including human factors and infrastructure. | 1 | International data, but less specific to the European context. | S6 |
No. | Main Risk/Risk Subcategory | Sources | Risks Values (%) | Weighted Average (%) |
---|---|---|---|---|
1.0 | Overloading/blocking traffic | S1 | 38 | 34.18% |
S2 | 35 | |||
S3 | 32 | |||
S4 | 30 | |||
1.1 | Poor infrastructure maintenance | S1 | 40 | 33.94% |
S2 | 35 | |||
S3 | 30 | |||
S4 | 28 | |||
1.2 | Lack of adequate signage | S1 | 30 | 29.06% |
S2 | 32 | |||
S3 | 28 | |||
S4 | 25 | |||
2.0 | Technical and mechanical failures of vehicles | S1 | 50 | 46.47% |
S2 | 48 | |||
S3 | 44 | |||
S4 | 42 | |||
2.1 | Problems with braking systems | S1 | 35 | 31.21% |
S2 | 30 | |||
S4 | 28 | |||
3.0 | Deteriorated infrastructure | S1 | 32 | 28.88% |
S2 | 30 | |||
S3 | 27 | |||
S4 | 25 | |||
3.1 | Improper infrastructure design | S1 | 30 | 26.94% |
S2 | 25 | |||
S3 | 25 | |||
S4 | 27 | |||
3.2 | Quality of materials used in infrastructure construction | S1 | 25 | 22.18% |
S2 | 20 | |||
S3 | 20 | |||
S4 | 23 | |||
4.0 | Human factor (human errors in vehicle operation) | S1 | 60 | 49.75% |
S2 | 55 | |||
S3 | 50 | |||
S4 | 48 | |||
S5 | 25 | |||
S6 | 28 | |||
4.1 | Driver age group (22–30 years) | S1 | 50 | 38.35% |
S2 | 40 | |||
S3 | 30 | |||
S4 | 28 | |||
4.2 | Driver age group (30–50 years) | S1 | 30 | 23.94% |
S2 | 25 | |||
S3 | 20 | |||
S4 | 18 | |||
4.3 | Drivers’ age (over 50 years) | S1 | 40 | 34.76% |
S2 | 35 | |||
S3 | 32 | |||
S4 | 30 | |||
4.4 | Drivers’ experience (0–5 years) | S1 | 60 | 49.12% |
S2 | 45 | |||
S3 | 50 | |||
S4 | 40 | |||
4.5 | Health status (poor health status of drivers) | S1 | 80 | 38.68% |
S2 | 25 | |||
S3 | 20 | |||
S4 | 22 | |||
S5 | 31 | |||
5.0 | Unfavorable weather conditions | S1 | 34 | 29.88% |
S2 | 30 | |||
S3 | 28 | |||
S4 | 26 | |||
5.1 | Difficult traffic conditions (rain, snow, fog) | S1 | 35 | 29.85% |
S2 | 30 | |||
S3 | 25 | |||
S4 | 27 | |||
5.2 | Reduced visibility | S1 | 28 | 24.28% |
S2 | 25 | |||
S3 | 22 | |||
S4 | 22 | |||
S6 | 18 |
Source [53,55,56,57] | Available Values | Source Score (Wi) | Reason for Awarding Points | Identifier |
---|---|---|---|---|
European Railway Agency (ERA) Report 2023 | Data on railway accidents, infrastructure, train conditions, and the age of train drivers. | 5 | Official European sources characterized by standardized methodologies, comprehensive detail, and regularly updated datasets. | S1 |
National Institute for Statistics, Romania, 2021 | Data on railway accidents, infrastructure, and driver age. | 3 | Recognized official data sources, although published less frequently and with a lower level of detail compared to European standards. | S2 |
Ministry of Transportation, Romania, 2020 | Statistical information on infrastructure and railway safety, including train age. | 4 | National-level reports issued at longer intervals, generally employing methodologies that are less rigorous than those adopted at the European level. | S3 |
World Bank Water Data, 2019 | Information regarding flood and landslide risks affecting railway infrastructure in Romania between 2010 and 2019. | 2 | An official report covering the period 2010–2019, which, although not recent, offers a realistic overview of areas where railway infrastructure has been affected by floods and landslides. | S4 |
Varra et al. [56] | Data on high-risk areas for landslides and floods impacting railway infrastructure, covering the period 2015–2023. | 1 | The study applies multi-criteria analysis techniques and uses susceptibility maps based on topographic and hydrological indicators. However, it does not consistently rely on official national statistics validated by Romanian governmental authorities but rather presents projections and risk assessment models. | S5 |
No. | Main Risk/Risk Subcategory | Sources | Risk Values (%) | Weighted Average (%) |
---|---|---|---|---|
1. | Deteriorated infrastructure | S1 | 40 | 37.14% |
S2 | 38 | |||
S3 | 35 | |||
S4 | 33 | |||
1.1 | Rail wear | S1 | 35 | 31.93% |
S2 | 32 | |||
S3 | 30 | |||
S4 | 28 | |||
1.2 | Maintenance deficiencies in bridges and tunnels | S1 | 30 | 28.00% |
S2 | 28 | |||
S3 | 27 | |||
S4 | 25 | |||
2. | Brake system malfunctions | S1 | 45 | 41.42% |
S2 | 40 | |||
S3 | 38 | |||
2.1 | Deficiencies in operational safety management | S1 | 35 | 31.42% |
S2 | 30 | |||
S3 | 28 | |||
3. | Deficiencies in operational safety management | S1 | 50 | 45.21% |
S2 | 45 | |||
S3 | 42 | |||
S4 | 40 | |||
3.1 | Train collisions | S1 | 25 | 22.58% |
S2 | 22 | |||
S3 | 20 | |||
4. | Human error (errors in vehicle operation) | S1 | 55 | 47.20% |
S2 | 50 | |||
S3 | 48 | |||
S4 | 45 | |||
4.1 | Train driver age (over 50 years) | S1 | 35 | 32.58% |
S2 | 32 | |||
S3 | 30 | |||
4.2 | Lack of experience among train drivers (0–5 years) | S1 | 45 | 41.42% |
S2 | 40 | |||
S3 | 38 | |||
5. | Adverse weather conditions | S1 | 30 | 26.08% |
S2 | 28 | |||
S3 | 25 | |||
S5 | 5 | |||
5.1 | Reduced visibility due to weather conditions (fog, rain) | S1 | 25 | 21.85% |
S2 | 23 | |||
S3 | 22 |
Risk Category | Risk Subcategory | Weighted Mean (%) |
---|---|---|
M1: Human factor | M11: Human behavior | 49.97% |
M12: Staff negligence | 51.68% | |
M13: Inadequate professional training | 37.66% | |
M14: Fatigue | 40.53% | |
M15: Poor communication | 27.14% | |
M16: Inappropriate use of hazardous materials | 45.39% | |
M17: Violations of rules and procedures | 55.29% | |
M2: Ship and equipment | M21: Inadequate maintenance | 46.93% |
M22: Technical failures | 37.79% | |
M23: Defective design | 48.00% | |
M24: Equipment’s age | 36.06% | |
M25: Human errors that cause failures in ship systems and equipment | 29.09% | |
M26: Ship’s age | 27.08% | |
M3: Environment | M31: Light conditions | 41.85% |
M32: Sea condition | 49.54% | |
M33: Visibility | 32.47% | |
M34: Wind force | 47.27% | |
M35: Weather conditions | 39.11% | |
M36: Environmental risks related to leakage and improper handling | 43.22% |
Risk | Risk Values | Risk Mitigation Measures |
---|---|---|
M1 | P(M1) = 1 − [1 − P(M11)] × [1 − P(M12)] × … × [1 − P(M17)] P(M1) = 1 − [1 − 0.4997] × [1 − 0.5168] × [1 − 0.3766] × [1 − 0.4053] × [1 − 0.2714] × [1 − 0.4539] × [1 − 0.5529] = 0.9841 P(M1) = 0.9841 (98.41%) |
|
M2 | P(M2) = 1 − [1 − P(M21)] × [1 − P(M22)] × … × [1 − P(M26)] P(M2) = 1 − (0.5307 × 0.6221 × 0.5200 × 0.6394 × 0.7091 × 0.7292) = 0.9432 P(M2) = 0.9432 (94.32%) |
|
M3 | P(M3) = 1 − [1 − P(M31)] × [1 − P(M32)] × … × [1 − P(M36)] P(M3) = 1 − (1 − 0.4185) × (1 − 0.4954) × (1 − 0.3247) × (1 − 0.4727) × (1 − 0.3911) × (1 − 0.4322) P(M3) = 1 − (0.5815 × 0.5046 × 0.6753 × 0.5273 × 0.6089 × 0.5678) = 0.9639 P(M3) = 0.9639 (96.39%) |
|
M | (99.00%) |
|
Risk category | Risk Subcategory | Average Weight (%) |
---|---|---|
R1: Overloading/traffic congestion | R 1.1: Traffic overloading | 34.18% |
R 1.2: Poor infrastructure maintenance | 33.94% | |
R 1.3: Lack of adequate signage | 29.06% | |
R2: Technical and mechanical failures | R 2.1: Brake system issues | 46.47% |
R 2.2: Other mechanical failures | 31.21% | |
R3: Deteriorated infrastructure | R 3.1: Inadequate design | 28.88% |
R 3.2: Quality of construction materials | 22.18% | |
R4: Human factor | R 4.1: Vehicle operation errors | 49.75% |
R 4.2: Drivers’ experience (0–5 years) | 49.12% | |
R 4.3: Drivers’ age (30–50 ani) | 23.94% | |
R 4.4: Drivers’ poor health condition | 38.68% | |
R5: Weather conditions | R 5.1: Reduced visibility | 29.88% |
R 5.2: Difficult traffic conditions | 24.28% | |
F1: Deteriorated infrastructure | F 1.1: Rail wear | 31.93% |
F 1.2: Maintenance deficiencies in bridge and tunnels | 28.00% | |
F2: Technical failures of rolling stock | F 2.1: Brake system failures | 31.42% |
F 2.2: Other technical failures | 41,42% | |
F3: Deficiencies in operational safety management | F 3.1: Train collisions | 22.58% |
F4: Human error | F 4.1: Lack of experience of train driver (0–5 years) | 41.42% |
F 4.2: Train driver age (over 50 years) | 32.58% | |
F5: Weather conditions | F 5.1: Reduced visibility (fog, heavy rain) | 21.85% |
Risks | Risks Values | Preventive Measures |
---|---|---|
R1 (Overloading/traffic congestion) | P(R1) = 0.69 | Implementation of intelligent traffic management systems. |
R2 (Technical and mechanical failures) | P(R2) = 0.63 | Periodic inspection and maintenance of vehicles. |
R3 (Deteriorated infrastructure) | P(R3) = 0.44 | Rehabilitation of critical infrastructure. |
R4 (Human factor—errors in vehicle operation) | P(R4) = 0.88 | Professional training programs for drivers. |
R5 (Adverse weather condition) | P(R5) = 0.46 | Use of advanced weather forecasting technologies. |
R (Total road transport risk) | P(R) = 0.9960 |
|
F1 (Deteriorated infrastructure) | P(F1) = 0.69 | Regular maintenance and modernization of infrastructure. |
F2 (Technical failures of rolling stock) | P(F2) = 0.59 | Systematic updating and verification of onboard equipment. |
F3 (Deficiencies in operational safety management) | P(F3) = 0.57 | Adoption of an advanced risk management system. |
F4 (Human error) | P(F4) = 0.79 | Training programs and simulation exercises for railway personnel. |
F5 (Adverse weather condition) | P(F5) = 0.42 | Continuous monitoring of weather conditions and rerouting of trains as needed. |
F (Total rail transport risk) | P(F) = 0.9937 |
|
Main Risk | Risk Subcategory | Logic Gate | Connected to |
---|---|---|---|
M1: Human factor: Human behavior | M11 | OR | M1 |
M1: Human factor: Staff negligence | M12 | OR | M1 |
M1: Human factor: Inadequate professional training | M13 | OR | M1 |
M1: Human factor: Fatigue | M14 | OR | M1 |
M1: Human factor: Poor communication | M15 | OR | M1 |
M1: Human factor: Handling of hazardous materials | M16 | AND | M15 |
M1: Human factor: Violation of rules | M17 | OR | M1 |
M2: Vessel and equipment: Inadequate maintenance | M21 | SEQ | M2 |
M2: Vessel and equipment: Technical failures | M22 | AND | M2 |
M2: Vessel and equipment: Design flaws | M23 | OR | M2 |
M2: Vessel and equipment: Equipment age | M24 | SEQ | M2 |
M2: Vessel and equipment: Human errors in system operation | M25 | FUZZY | M24 |
M2: Vessel and equipment: Vessel age | M26 | OR | M2 |
M3: Environmental factor: Lighting conditions | M31 | OR | M3 |
M3: Environmental factor: Sea state | M32 | AND | M31 |
M3: Environmental factor: Reduced visibility | M33 | OR | M3 |
M3: Environmental factor: Wind force | M34 | OR | M3 |
M3: Environmental factor: Extreme weather conditions | M35 | SEQ | M34 |
M3: Environmental factor: Environmental hazards | M36 | FUZZY | M3 |
R1: Road: Traffic congestion | R11 | OR | R1 |
R1: Road: Poor infrastructure maintenance | R12 | SEQ | R1 |
R1: Road: Lack of adequate signage | R13 | OR | R1 |
R2: Road: Brake system issues | R21 | SEQ | R2 |
R2: Road: Other mechanical failures | R22 | OR | R2 |
R3: Road: Inadequate infrastructure design | R31 | OR | R3 |
R3: Road: Quality of construction materials | R32 | OR | R3 |
R4: Road: Driver errors | R41 | OR | R4 |
R4: Road: Limited driver experience | R42 | SEQ | R41 |
R4: Road: Driver age | R43 | FUZZY | R4 |
R4: Road: Poor driver health | R44 | OR | R4 |
R5: Road: Reduced visibility | R51 | FUZZY | R5 |
R5: Road: Difficult traffic conditions | R52 | OR | R5 |
F1: Rail: Rail wear | F11 | OR | F1 |
F1: Rail: Deficiencies in bridge/tunnel maintenance | F12 | OR | F1 |
F2: Rail: Train brake failures | F21 | SEQ | F2 |
F2: Rail: Other technical failures | F22 | OR | F2 |
F3: Rail: Train collisions | F31 | OR | F3 |
F4: Rail: Lack of driver experience | F41 | SEQ | F4 |
F4: Rail: Driver age | F42 | FUZZY | F4 |
F5: Rail: Reduced visibility | F51 | OR | F5 |
Transport Mode | Critical Fisk Factor | Probability | Recommended Mitigation |
---|---|---|---|
Road | Human Error (R4) | 0.88 | Training, fatigue detection |
Rail | Tech. Failures (F2) | 0.59 | Rolling stock upgrades |
Maritime | Rules Violations (M17) | 0.55 | Crew oversight, digital audits |
Framework/Standard [52,53,55,70,71] | Key Features | Alignment with This Model |
---|---|---|
FMCSA (U.S.) [54,70] | Truck crash causation data (LTCCS), CSA Safety Measurement System, hours-of-service (HOS) monitoring | Human factor risks (fatigue, inattention) modeled using fuzzy logic aligns with CSA behavioral categories (e.g., unsafe driving, driver fitness) |
NHTSA (U.S.) [52] | National freight crash statistics and AI-assisted predictive safety analysis | Quantitative failure metrics (MTTF/MTBF) align with NHTSA performance-based analytics |
Ministry of Transport—China [53] | Focus on logistics resilience, port congestion, and intermodal coordination risks | Supports dynamic fault modeling for node interdependencies and environmental constraints |
ISO 31010:2019 [71] | International standard for risk assessment techniques (FTA, Monte Carlo, Bow Tie, etc.) | Core techniques (FTA, fuzzy logic) are directly endorsed; future versions may integrate Monte Carlo or Bayesian inference |
EU Directives (e.g., ERA, EMSA) | Mode-specific quantitative risk classification and accident reporting | Existing use of Eurostat/EMSA/ERA data directly supports methodology and risk prioritization logic |
Transport Mode | Spearman’s ρ | p-Value | Interpretation |
---|---|---|---|
Maritime | 0.81 | <0.01 | Strong ordinal agreement |
Rail | 0.76 | <0.05 | Moderate-to-strong agreement |
Road | 0.89 | <0.01 | Very strong ordinal agreement |
Model Component | FMCSA Category | NHTSA Human Factors Domain | ISO 31010 Technique Category |
---|---|---|---|
Fatigue | Hours-of-Service (HOS) violations | Driver fatigue, vigilance | Qualitative risk analysis |
Communication breakdown | Unsafe driving, training deficiency | Workload, communication errors | Expert judgment, fuzzy logic |
Equipment age | Vehicle maintenance | Indirect cognitive load | Fault tree analysis |
Environmental stress | Crash environment | Stress and distraction | Scenario-based evaluation |
Fuzzy Inference mechanism | Not specified (Tool-Level) | Not applicable | Fuzzy logic, linguistic risk methods |
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Popa, C.; Stefanov, O.; Goia, I.; Nistor, F. A Hybrid Fault Tree–Fuzzy Logic Model for Risk Analysis in Multimodal Freight Transport. Systems 2025, 13, 429. https://doi.org/10.3390/systems13060429
Popa C, Stefanov O, Goia I, Nistor F. A Hybrid Fault Tree–Fuzzy Logic Model for Risk Analysis in Multimodal Freight Transport. Systems. 2025; 13(6):429. https://doi.org/10.3390/systems13060429
Chicago/Turabian StylePopa, Catalin, Ovidiu Stefanov, Ionela Goia, and Filip Nistor. 2025. "A Hybrid Fault Tree–Fuzzy Logic Model for Risk Analysis in Multimodal Freight Transport" Systems 13, no. 6: 429. https://doi.org/10.3390/systems13060429
APA StylePopa, C., Stefanov, O., Goia, I., & Nistor, F. (2025). A Hybrid Fault Tree–Fuzzy Logic Model for Risk Analysis in Multimodal Freight Transport. Systems, 13(6), 429. https://doi.org/10.3390/systems13060429