The influence of fluctuations and periodical driving on temporal characteristics of short overdamped Josephson junctions is analyzed. We obtain the standard deviation of the switching time in the presence of a dichotomous driving force for arbitrary noise intensity and in the frequency range of practical interest. For sinusoidal driving the resonant activation effect has been observed. The mean switching time and its standard deviation have a minimum as a function of driving frequency. As a consequence the optimization of the system for fast operation will simultaneously lead to the minimization of timing errors.