In order to ensure that engineering design is conducted as a rational process producing the best possible results given the context of the activity, a mathematics of design is needed. It is possible to develop such a mathematics based on the recognition that engineering design is a decision-making intensive process and adapting theories from other fields, such as economics and decision theory. We present here eight axioms and derive from them two theorems, which underlie the mathematics of design. Then we present a third theorem that, in the context of the axioms presented, imposes severe conditions upon design methodologies. Together, the axioms and theorems provide a framework that enables the development of a normative theory of design. This theory is applied to a simple example. The results, while intuitively obvious, are substantially different from the results of a “conventional” engineering design analysis.

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