Time dependent reliability analysis and life time predictions solving the first passage problem for complex structures and systems is one of the most demanding challenge in engineering. In the project we envisage to attack this problem by combining the fundamental concepts of probability density evolution and statistical emulation of limit states in time. Probability density evolution being based directly on the fundamental physical principle of preservation of probability will be used to achieve a trajectory-based formulation of the reliability problem in time, which reduces the dimensionality of the sample space drastically for efficient identification of the failure trajectories. Targeted stochastic sampling, using subset simulation, will identify these failure trajectories at some specific points in time. The resulting support points in space and time are used to establish a temporal and spatial kriging model in form of a stochastic field, which describes the stochastic evolution of the limit states with high efficiency and low dimensionality. This approach will not only allow for efficient identification of failure probabilities and, potentially rare but critical, failure events, but it will also enable a transparent and structured analysis of how these failure events evolve in order to implement most effective design measure for risk mitigation.