Abstract: The influence of amplitude, phase and position errors on the performance of an antenna array is analyzed and studied in this paper. On the assumption that each type of these random errors obeys the Gauss distribution, the expectation of the antenna array power pattern is analyzed, and the theoretical formula of variance is derived for the first time. In addition, theoretical upper and lower boundaries on which the power pattern falls on with a given probability are derived by using the Chebyshev's inequality. The effectiveness and accuracy of all the obtained theoretical equations are verified by Monte Carlo simulation. The simulation results show that the influence of the random implementation errors on the power pattern can be accurately predicted by using the proposed technique. Hence, it provides significant guidance for the practical array antenna design.