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With aggressive scaling down of feature sizes in VLSI fabrication, process variations have become a critical issue in designs, especially for high-performance ICs. Usually having level-sensitive latches for their speed, high-performance IC designs need to verify the clock schedules. With process variations, the verification needs to compute the probability of correct clocking. Because of complex statistical correlations, traditional iterative approaches are difficult to get accurate results. Instead, a statistical checking of the structural conditions for correct clocking is proposed, where the central problem is to compute the probability of having a positive cycle in a graph with random edge weights. The proposed method only traverses the graph once to avoid the correlations among iterations, and it considers not only data delay variations but also clock skew variations. Experimental results showed that the proposed approach has an error of 0.14% on average in comparisons with the Monte Carlo simulations.