The effects of varying electrode geometry (ball and ring) and size (radius), dielectric liquid (castor oil and Diala((R)) oil), and specimen thickness on the dielectric breakdown of a commercial-grade alumina were investigated. The breakdown strength was expressed in terms of the maximum electric field in the ceramic calculated by finite element analysis (FEA) at the breakdown voltage. The breakdown strength decreased systematically with increasing electrode radius and specimen thickness, and the strength was higher in the Diala((R)) oil (dielectric constant, epsilon(r)=2.3 +/- 0.06) as compared to the castor oil (epsilon(r)=4.6 +/- 0.13). These effects of the electrode geometry, specimen thickness, and of the dielectric liquid on the breakdown strength of the alumina were analyzed with a weakest-link failure model employing Laplace and Weibull distributions for a population of defects in the material. The measured size or scaling effects of the electrodes, specimen thickness, and of the dielectric liquid on breakdown strength were in better agreement with the Laplace distribution for a population of surface defects. The dielectric breakdown is likely initiated at surface pits produced by grain pullout. The measured area concentration of surface pits agreed with the defect density analyzed from the weakest-link failure theory. FEA of specimens containing surface and subsurface cavities revealed that electric field concentrations were always greater for surface pits as compared to subsurface cavities. There is, in fact, no electric field concentration at a subsurface cavity located more than about 100-800m below the surface depending on the top electrode size.