We introduce a new model for an earthquake fault system that is composed of noninteracting simple lattice models with different levels of damage denoted by q. The undamaged lattice models (q=0) have Gutenberg-Richter scaling with a cumulative exponent β=1/2, whereas the damaged models do not have well defined scaling. However, if we consider the "fault system" consisting of all models, damaged and undamaged, we get excellent scaling with the exponent depending on the relative frequency with which faults with a particular amount of damage occur in the fault system. This paradigm combines the idea that Gutenberg-Richter scaling is associated with an underlying critical point with the notion that the structure of a fault system also affects the statistical distribution of earthquakes. In addition, it provides a framework in which the variation, from one tectonic region to another, of the scaling exponent, or b value, can be understood.