Interval type-2 fuzzy fault tree analysis for risk prioritization and uncertainty quantification in simulated train door safety systems

The traditional Fault Tree Analysis (FTA) has limitations in its capacity to process imprecise, incomplete, and subjective failure data that is usually found in railway door safety systems. To overcome this weakness, this paper proposed a new Fuzzy Fault Tree Analysis (FFTA) model based on Interval Type-2 Fuzzy Sets (IT2FS). A two-parameter Weibull distribution is used to model failure probabilities of basic events in a realistic way for the representation of time-dependent failure behaviour based on expert elicitation and maintenance data. Fuzzy logic gates are used to construct the fault tree, and fuzzy probability propagation is carried out through α-cut decomposition, which is backed by a convexity theorem that guarantees valid interval behaviour in the decomposition. To prioritize critical events, an Adapted Wasserstein Distance (AWD) based Fuzzy Importance Index (FII) is proposed, along with a convergence theorem proving the stability of fuzzy failure estimates with the increase in expert information. The actionable numerical values are derived through the Weighted Divided Search Enhanced Karnik-Mendel (WDEKM) algorithm to transform system-level fuzzy risk outputs into actionable numerical values. The framework is implemented in Python 3.11, using standard scientific libraries. Findings indicate the proposed method’s high performance with a Fuzzy Priority Index of 0.0214, Fuzzy Criticality Index of 0.0186, and better sensitivity values (SI = 0.69, NSC = 0.63, RCR = 16.8) than the existing models. These results prove that the proposed framework provides more informative uncertainty-aware risk estimates and sensitivity indicators for safety and maintenance prioritization in railway door systems.