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The existence of near-closed sets makes the power estimation of sequential circuits more complicated and time consuming. If caution is not taken, the Monte Carlo-based power estimation techniques for sequential circuits can wrongly terminate the simulation with undesired results. In this paper, we have developed a strategy for a statistical power estimation technique to take into account the possible existence of near-closed sets. We propose an algorithm that partitions states into near-closed sets, if they do exist, and a technique that reduces the computation time of the probabilities of states if state transition graph (STG) is available. If STG is not available, we propose a Monte Carlo-based technique with a warm-up period. The results show that the partitioning algorithm also serves as a detector that signifies whether there may exist near-closed sets. The computation time of state probability can be reduced up to 50% in cases when near-closed sets are present. The relative error of the estimated individual node activity by the Monte Carlo-based technique with a warm-up period is within 3% of the result of long run simulation.