We use a scalable optical technique to characterize more than 21 000 circular nanomechanical devices made of suspended single- and double-layer graphene on cavities with different diameters (D) and depths (g). To maximize the contrast between suspended and broken membranes we used a model for selecting the optimal color filter. The method enables parallel and automatized image processing for yield statistics. We find the survival probability to be correlated with a structural mechanics scaling parameter given by D4/g3. Moreover, we extract a median adhesion energy of Γ = 0.9 J m-2 between the membrane and the native SiO2 at the bottom of the cavities.