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Arrayed waveguide gratings (AWGs) are important components for the realization of wavelength-division multiplexing optical networks. Their filtering performance is limited by the existence of phase errors in the grating waveguides due to fabrication imperfections. In this paper, the statistical properties of the phase errors are related to the waveguide imperfections using a variation of the effective index method. The filtering quality of the AWG is then investigated by considering the behavior of its transfer function in the presence of random phase errors. The probability density function of the transfer function's sidelobes is evaluated numerically, and the results are justified using theoretical considerations. Finally, the behavior of the maximum sidelobe level is also analyzed numerically, and universal diagrams are presented that allow the estimation of its mean value, standard deviation, and cumulative distribution function for every specific AWG.