In this paper, we experimentally analyze the error of delay and leakage models used for gate-level statistical analysis, which comes from the local random variation of process. Experimental results indicated that the statistical gate delay model derived without considering the local random variation showed the maximum error of more than 20% in standard deviation in comparison to those obtained considering the local random variation. Moreover, the statistical gate leakage model showed the maximum error of 10% in mean value and over 300% error in standard deviation, when it did not consider the local random variation. In summary, while not considered by most of the conventional gate-level statistical models, the local random variation of process needs be reflected properly to improve the statistical estimation accuracy of the circuit delay and leakage at the gate level.