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We propose a new statistical timing analysis algorithm, which produces arrival-time random variables for all internal signals and primary outputs for cell-based designs with all cell delays modeled as random variables. Our algorithm propagates probabilistic timing events through the circuit and obtains final probabilistic events (distributions) at all nodes. The new algorithm is deterministic and flexible in controlling run time and accuracy. However, the algorithm has exponential time complexity for circuits with reconvergent fanouts. In order to solve this problem, we further propose a fast approximate algorithm. Experiments show that this approximate algorithm speeds up the statistical timing analysis by at least an order of magnitude and produces results with small errors when compared with Monte Carlo methods.