Critical infrastructure is the backbone of modern societies. To meet increasing demand under resource-constrained and multihazard conditions, policy-makers are tapping into infrastructure resiliency: its capacity to withstand and recover from disruptions. Thus, resiliency-aware uncertainty quantification is key to identify tipping points, yet it remains computationally inaccessible. This paper maps resiliency measures to well understood time-dependent reliability computations, porting insights and methods from reliability theory to the service of critical infrastructure resiliency and upkeep efforts. For large-scale applications, we use particle integration methods (PIMs)—a family of sequential Monte Carlo methods with wide-ranging applications—and propose their optimal tuning in terms of their variance and number of limit-state function evaluations. We obtain consistent and unbiased probability estimates in applications to dynamical systems, network reliability, and resilience analysis, demonstrating PIMs as practical yet under-appreciated tools. For example, we obtain probability estimates of order 10-14 in networks with over 10,000 random variables.