It fails when a certain proportion of the filament has evaporated. The evaporation rate is pretty constant, assuming either a getter or large enough bulb that t

It fails when a certain proportion of the filament has evaporated. The evaporation rate is pretty constant, assuming either a getter or large enough bulb that the evaporated tungsten doesn't change the environment. So you would expect some form of bell curve distribution around the design lifetime. Bath tub curves tend to come from large assemblies of reliable components