Effective verification methods are necessary for finding bugs in complex system design. Given domain specific knowledge, design verification engineers typically specify cross coverage for certain risky areas where bugs tend to appear. This paper proposes a pragmatic coverage model based on cross coverage. We address the verification on user specified cross coverage regions. The proposed analysis models the probability of exposing the bug within a given number of samplings, and derives the expected number of samples until bug detection. The approach is applicable to random, round-robin, and hybrid sampling strategies in recurring and nonrecurring cases based on our cross coverage model. We have written Matlab and C programs that use our formulas to calculate the probabilities. Experimental results show that our analysis is consistent with Monte Carlo simulation.