The problem of quality control of radiological systems is discussed in relation to the management and quantitative tools normally applied to it. An alternative approach is to consider the problem in terms of a control loop in which the sets of quality control measurements are compared with their previous values in the context of a numerical model of the system to produce quantitative corrections. A preliminary study of the method applied to mammographic quality control is discussed. By modelling the system with an appropriate set of simultaneous linear equations relating changes in the controlled parameters to the quality control measurements obtained, it is possible to identify quantitative changes in the controlled parameters from measured quality control data using the inverse of the model in matrix form. This method essentially encapsulates knowledge about the system in the form of the linear model. This is distinct from current work attempting to apply artificial intelligence knowledge-based techniques to the problem. (4 pages)