We study the frequency doubling in a quadratic nonlinear photonic crystal consisting of periodically poled structures mediated by uniform layers with random lengths. These structures can be formed by new local impact methods for ferroelectric crystal structuring. The statistical frequency doubling theory is developed for such structures. The effect of the number of random layers and variation in their thicknesses on the second-harmonic conversion efficiency is clarified. It is demonstrated that a proper choice of the intermediate layer thickness can enhance or suppress the conversion efficiency. A new type of the Maker-fringes-like second-harmonic intensity oscillations is predicted.