For critical infrastructure, survivability and recovery in all-hazard environments are issues of concern, and pose extremely difficult modeling challenges. Model capabilities must encompass cascading failures of interdependent, interconnected infrastructures. A major recent research emphasis on community resiliency has emerged due to the recognition that it is not enough to model the initial failure of infrastructure systems. To understand and improve system resilience, it is also necessary to model the post-failure, recovery phase of infrastructure debilitation. A method that holds great promise for such modeling involves extending the probabilistic risk analysis technique into the time domain. The method computes the time evolution of overall mission failure probability by evaluating initial mission failure probability, effects onset times, and system repair times for single or combinations of critical infrastructure systems. The approach involves the aggregation of scenario and facility functional diagram inputs into an overall evaluation of system viability. A bottom-up fault-tree analysis is used. The approach is unique in that time evolution of the probability of outage is built-in as a stochastic finite difference equation with initial deterministic and stochastic conditions, and includes subsystem damage threshold probability distributions and time constants of effects and repairs. Output is provided in the form of system mission conditional outage probability versus time. The approach is useful for identifying high consequence infrastructure system failure points and the most effective system protection measures in terms of limiting both the incidence and duration of system debilitation. The method can also be used to evaluate the efficacy of alternative system recovery options.