Modern engineering has included the basic sciences and their accompanying mathematical theories among its primary tools. The theory of probability is one of the more recent entries into standard engineering practice in various technological disciplines. Probability and statistics serve useful functions in the solution of many engineering problems. However, not all technological manifestations of uncertainty are amenable to probabilistic representation. In this paper we identify the conceptual limitations of probabilistic and related theories as they occur in a wide range of (...) engineering tasks. We discuss the structure and properties of an alternative, non-probabilistic, method — convex modelling — for quantitatively representing uncertain phenomena. (shrink)