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This paper presents a methodology for determining the probability of structural failures for VLSI circuits. An analytically based approach is used to perform simulations accurately and efficiently. This approach considers the specific IC layout and accounts for most of the fault mechanisms caused by global geometrical variations and local defects. A hierarchical model is proposed to describe the defect statistics including clustering. Strict analytical methods are used to find probabilities of failure for simple layout patterns. Then, the probability of failure for macrocells are calculated hierarchically. This methodology has been implemented in a CAD tool called RYE (Realistic Yield Evaluator). To demonstrate the effectiveness of this tool, the simulation results of several examples and the CPU time comparisons with Monte Carlo methods are also presented in this paper.