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A statistical model is proposed for estimating the chromatic dispersion in the passband of a filter using an arrayed waveguide grating (AWG) with random phase errors. The model is derived without assuming the independence of random errors and can be applied to AWGs with frequency-dependent array amplitude coefficients as well as conventional AWGs. The average and variance of the chromatic dispersion in the passband can be calculated by using simple expressions without random computation once the standard deviation and correlation of random phase errors are given. The behavior of the chromatic dispersion in a synchronized-router-based flat-passband filter consisting of a multiple-input AWG and cascaded Mach-Zehnder interferometers (MZIs) was investigated. The standard deviation of the chromatic dispersion monotonically increases with the standard deviation of random phase errors, and has a distinctive dependence on frequency. The average and standard deviation of the chromatic dispersion in the passband obtained by the model are in good agreement with those obtained by random simulation for both a synchronized-router-based flat-passband filter and conventional AWGs.