Bulk niobium has long been the material of choice for superconducting radio-frequency applications. An alternative approach is the superconductor-insulator-superconductor (SIS) multilayer structure, which enables the use of brittle high-$T_c$ materials such as NbTiN. At present, SIS coatings are limited to flat samples, with the single-cell TESLA cavity representing a key milestone. Extending coating processes to non-flat geometries is expected to introduce macroscopic inhomogeneities in coating thickness. We model these variations using Gaussian random fields parametrized by a spatial correlation length, and generated by solving a stochastic partial differential equation. The resulting field is incorporated into the boundary condition of the cavity eigenvalue problem, from which quantities of interest—such as the quality factor—are computed. This procedure is repeated for eight correlation lengths, with 2048 samples per correlation length, where the resulting quality factors are recorded. Our results show that the quality factors follow a normal distribution. The standard deviation increases with the correlation length and can be statistically distinguished. In contrast, the mean values remain largely unchanged, with only a few significant differences. In extreme cases, depending on the correlation length, the quality factor may differ from the uniform case by 2 % to 6 %.