Universal Scaling of Cascade-Failure Lifetime in Complex Networks

Cascading failures can dismantle critical infrastructures long before individual components reach their design limits. Yet quantifying the lifetime of such cascades remains difficult because breakdown probability depends simultaneously on network scale, load statistics and external disturbances. Through large-scale Monte-Carlo simulations on two-dimensional lattices covering four orders of magnitude in size, we show that the reciprocal lifetime collapses onto a single master curve when plotted against a dimensionless amplification factor that combines network size with the redistributed load per failure. This scaling law holds for five qualitatively different initial-load distributions—uniform, lognormal, gamma, power-law and Gaussian—thus defining a distribution-independent indicator of network robustness. A mean-field cascade map provides an analytic explanation and yields a closed safety bound that prevents the cascade from ever crossing the site-percolation threshold. The bound also shows that uniform disturbances translate the entire master curve horizontally, enabling accelerated lifetime qualification of large networks via small surrogates. These findings convert numerical evidence into actionable design rules and demonstrate how a seemingly complex phenomenon reduces to two control parameters: the amplification factor and the disturbance margin, together guaranteeing immunity against complete lifetime collapse.