An Enhanced Fuzzy Temporal Fault Tree Approach for System Risk Analysis: A Framework Using α-Cut Arithmetic Operations

Temporal fault tree analysis (TFTA) is a well-established method for modeling system failures that depend on specific event sequences. However, its practical use is often limited by the difficulty of acquiring precise component failure data, especially for high-reliability systems. To address this challenge, we propose an enhanced TFTA framework that incorporates expert judgments on component failures to evaluate system failure probabilities. Mathematical formulations for Priority-AND and Priority-OR gate operators are developed for qualitative expert opinions as input data, expressed as α-cut intervals of fuzzy numbers to systematically handle uncertainty and imprecision. Expert opinions are further synthesized using an α-cut interval-based similarity aggregation method (AISAM), where relative expert weights are accurately determined based on the comprehensive weighting scores of professional and academic parameters. The applicability of the proposed framework is demonstrated through a maritime case study on `ship collision due to operational negligence'. It accurately computes time-dependent top event probabilities. Furthermore, fuzzy importance measures such as Fussell-Vesely and risk reduction worth are employed to rank basic events based on their impact on system failure. This analysis highlighted `unguarded navigation' as the most critical contributor to system failure.