One risk inherent in the use of software components has been that the behavior of assemblies of components is discovered only after their integration. The objective of our work is to enable designers to use known (and certified) component properties as parameters to models that can be used to predict assembly-level properties. Our concern in this paper is with empirical component properties and compositional reasoning, rather than formal properties and reasoning. Empirical component properties must be measured; assessing the effectiveness of predictions based on these properties also involves measurement. This, in turn, introduces systematic and random measurement error. As a consequence, statistical models are needed to describe empirical component properties and predictions. In this position paper, we identify the statistical models that we have found useful in our research, and which we believe can form a basis for standard industry labels for component properties and prediction theories.