In an increasingly turbulent global environment, supply chains face multifaceted disruptions ranging from pandemics to geopolitical crises and climate shocks. While the concept of supply chain resilience (SCR) has gained prominence, most existing models fail to accurately capture the nonlinear, dynamic behavior of organizations facing disruption. Building on this gap, this study proposes a mathematically robust and behaviorally coherent model of resilience based on hyperbolic tangent functions. The model accounts for the complete disruption cycle (degradation, latency, recovery) and is characterized by seven interpretable parameters that enable smooth, bounded, and asymmetric performance trajectories over time. A set of six resilience indicators is derived to evaluate critical system dimensions such as cumulative loss, recovery speed, and adaptive robustness. Applied to four organizational scenarios (healthcare, manufacturing, retail, and tech startup), the model reveals distinct resilience archetypes, demonstrating its ability to differentiate strategic response profiles. A web-based interface further enables real-time evaluation and scenario planning. The proposed framework contributes a unified, customizable, and operational tool for quantitative resilience analysis, bridging the gap between conceptual models and actionable decision support in crisis management.