Turbidite bed thickness-frequency relationships within the Upper Devonian Brallier Formation of the Central Appalachian Basin follow the form of a negative exponential distribution. The presence of such distributions indicates that deposition occurred via Poisson-like stochastic processes, wherein initiation of turbidite formation was largely independent of rates of sediment accumulation along shelf margins. Autocorrelation analysis of bed thicknesses from these sections likewise strongly supports an interpretation of temporally stochastic deposition. Autocorrelograms of turbidite sandstone and inter-turbidite shale thicknesses fail to fall outside the expected range of a random arrangement of bed thickness. Consideration of the Brallier Formation relative to previously reported analyses of turbidites from other depositional systems indicates that the form of thickness-frequency relations within any turbidite system is strongly dependent upon gross morphology of the depositional system. As such, multi-sourced ramp turbidites are, in this case, found not to exhibit fractal scaling in their bed-thickness relationships, but rather an exponential form of scaling common to many sedimentary systems.