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Power dissipation in complementary metal-oxide-semiconductor (CMOS) circuits is heavily dependent on the signal properties of the primary inputs. Due to uncertainties in specification of such properties, the average power should be specified between a maximum and a minimum possible value. Due to the complex nature of the problem, it is practically impossible to use traditional power estimation techniques to determine such bounds. In this paper, we present a novel approach to accurately estimate the maximum and minimum bounds for average power using a technique which calculates the sensitivities of average power dissipation to uncertainties in specification of primary inputs. The sensitivities are calculated using a novel statistical technique and can be obtained as a by-product of average power estimation using Monte Carlo-based approaches. The signal properties are specified in terms of signal probability (probability of a signal being logic ONE) and signal activity (probability of signal switching). Results show that the maximum and minimum average power dissipation can vary widely if the primary input probabilities and activities are not specified accurately.