Abstract
<title>Abstract</title> <p>The Functional Resonance Analysis Method (FRAM) provides a powerful qualitative framework for modelling the emergence of risk in complex sociotechnical systems. However, its inability to aggregate function-level variability into measurable indices limits its use in quantitative safety management. This paper proposes a formal integration of the Choquet integral with respect to a Sugeno λ-measure into FRAM, enabling the rigorous quantification of non-additive interactions among function aspects. Within each FRAM function, aspect densities are elicited through a structured five-phase AHP-based protocol implemented as an interactive AI agent, which performs real-time matrix construction, consistency verification (CR < 0.10), Sugeno λ computation, and Shapley analysis. A function-level Variability Accumulation Index (VAI) is computed via the discrete Choquet integral, propagated across function couplings using a probabilistic OR operator, and aggregated at the system level through a second-order Choquet integral. The framework is validated through a nine-function model of the runway vehicle crossing clearance process, comprising nine operational functions and three organisational actor functions, grounded in three aviation incidents spanning 1984–2026: Aeroflot Flight 3352 (Omsk, 1984), LATAM Airlines Peru Flight 2213 (Lima, 2022), and Jazz Aviation Flight 646 (LaGuardia, 2026). ATC Situational Awareness (F1) emerges as the topological hub with the dominant Shapley value (φ_F1 = 0.367, coupling degree 11). Communication & Readback (F7) is positioned as a downstream intermediary of the formal clearance decision rather than an upstream verification gate, and a terminal function (F9) formalises the outcome state of the crossing sequence. Non-additive interactions between simultaneously degraded function pairs account for 10.9–16.5% of each incident's Choquet risk index — risk that is structurally invisible to any additive model. LATAM 2213 ranks as the highest-risk incident (C_µ = 0.710) because it is the only case in which all nine functions exhibit non-zero variability concurrently, producing the broadest systemic resonance. Aeroflot 3352 (C_µ = 0.644) demonstrates that depth of individual failure does not substitute for breadth of systemic coupling. The framework addresses a gap in the quantitative FRAM literature and positions the Choquet integral as a tractable, theoretically principled tool for resilience quantification in safety-critical systems.</p>