# Accident Risk Analysis of Gas Tankers in Maritime Transport Using an Integrated Fuzzy Approach
## 3 Methodology
### Fault Tree Analysis (FTA)  
Fault Tree Analysis (FTA) is a deductive, top-down analytical method widely used in reliability engineering and risk assessment to identify and evaluate combinations of hardware, software, human, and external factors that can lead to system failures [56]. This systematic graphical representation facilitates the identification of critical system vulnerabilities and potential causes, enabling engineers to identify areas for improvement and implement effective mitigation strategies [57]. FTA applications range from nuclear power plants and critical infrastructure to aerospace and automotive systems [56]. For example, in the context of reliability-centred maintenance, FTA is used to develop models that not only predict potential failures but also guide maintenance priorities by identifying major failure propagation paths within a system [57]. Similarly, in safety-critical sectors, FTA is regularly paired with other methodologies such as event tree analysis, Bayesian networks, or Markov chains to provide a more comprehensive view of system behaviour under failure conditions [58]. This integration is necessary to address both qualitative and quantitative aspects of risk assessment and thus support proactive risk mitigation measures in various engineering applications [57; 58]. Overall, the evolution of Fault Tree Analysis from its roots in classical Boolean logic to its current integrations with other probabilistic and fuzzy methods demonstrates its enduring importance as a fundamental tool in the analysis, design, and continuous improvement of complex systems [59]. Its capacity to visually map failure structures and assess uncertainties has made FTA the cornerstone of reliability engineering and risk assessment in numerous high-risk industries. In summary, FTA remains an indispensable analytical tool in safety and risk assessment. Its evolution from a simple logical method to a sophisticated hybrid framework integrating fuzzy logic, Bayesian reasoning, dynamic analysis, and formal model checking enables it to address increasingly complex and uncertain environments within a variety of industries [60]. Ongoing research and applications of these advanced FTA methods underline their critical role in proactively identifying and mitigating potential system failures, thereby improving overall system safety and reliability [61]. An example diagram of an FTA is provided in Figure 4 below. Fault Tree Analysis (FTA) is a well-established methodology in risk and reliability assessment that facilitates the systematic identification of potential causes leading to an un  
Figure 4: FTA diagram. desired event [62]. In its traditional form, FTA uses logical gates (AND, OR) to hierarchically structure failure events and support qualitative and quantitative assessments of system vulnerabilities [60]. The equations used for FTA are given as (Equations (8)-(10)) [63]. \[P_{T}=\prod_{i=1}^{m}p_{i} \tag{8}\]  
where \(p_{i}\) represents the probability of failure of each basic event. The probability of the basic event \(p_{i}\) is estimated based on the definition of the initial state, as shown in Equation (8). \[P_{1}=\sum_{N_{L}=1}^{m}\frac{N_{L}}{T_{n}\cdot T_{t}} \tag{9}\]  
The inclusion ratio of factor \(N_{L}\) in the initial event \(l\) represents its contribution rate. \(m\) indicates the number of primary events where the factor contributes to the initial event [63]. \(T_{n}\) represents the total number of accidents examined, and \(T_{t}\) is the total duration of the accident data. Once the probability of each factor is determined, the analysis proceeds by investigating how significantly the factor contributes to the top event. The significant factor is calculated based on the Fussed-Vesely Method [64].