Electromigration data have been described by lognormal distributions. Although the origin of the lognormal distribution of electromigration lifetimes is not entirely clear, it has been argued that the diffusion process in connection with the effect of microstructure on electromigration provides the basis for the lognormal distribution. In copper dual-damascene interconnects the main diffusivity path is along the copper/capping layer interface. This interfacial diffusion is affected by the orientation of the grains. As the copper grain sizes seem to follow lognormal distributions in typical dual-damascene process technology and due to the influence of microstructure on the electromigration process, the lognormal distribution has been used as the underlying statistics for electromigration lifetimes. However, it has been discussed whether this choice is the most appropriate. The understanding of the electromigration lifetime distribution is crucial for the extrapolation of the times to failure obtained empirically from accelerated tests to real operating conditions, as performed by a modified form of the Black equation. Moreover, it has been shown that the microstructure plays a key role regarding the failure mechanisms in copper dual-damascene interconnects. It affects electromigration in different ways. Grain boundaries are natural locations of atomic flux divergence, they act as fast diffusivity paths for vacancy diffusion, and they act as sites of annihilation and production of vacancies. We have investigated the effect of the microstructure and the origin of the statistical distribution of electromigration times to failure as a function of the distribution of copper grain sizes. The effect of lognormal grain size distributions on the distribution of electromigration lifetimes of fully three-dimensional copper dual-damascene interconnect structures is studied based on numerical simulations. We have applied a continuum multi-physics electromigration model that incorporates the effects of grain boundaries for stress build-up. Moreover, we have developed a tool to include the microstructure into the simulations based on a given statistical distribution of grains sizes.