Engineering design is increasingly recognized as a decision-making process. This recognition brings with it the richness of many well-developed theories and methods from economics, operations research, decision sciences, and other disciplines. Done correctly, it forces the process of engineering design into a total systems context, and demands that design decisions account for a product’s total life cycle. It also provides a theory of design that is based on a rigorous set of axioms that underlie value theory. But the rigor of decision-based design also places stringent conditions on the process of engineering design that eliminate popular approaches such as Quality Function Deployment. This paper presents the underlying notions of decision-based design, points to some of the axioms that underlie the theory of decision-based design, and discusses the consequences of the theory on engineering education.

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 analy.iis.^ Excellent insights into issues of decision making are provided by Lewis Canoll, Alice in Wonderland. Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 04/01/2015 Terms of Use: http://asme.org/terms '' Ten alternatives pose 10! = 3,628,800 possible preference orderings. The probability that all ten people have the same preference ordering is roughly (10!) "' -10^".

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Many modern approaches to engineering design seek to optimize design in order to maximize the value of the system to its customers. These approaches rely on the formulation of a system utility function as a measure of system worth. It is shown here that, under certain circumstances, however, such a measure cannot exist. It is then indicated that these circumstances comprise the rule rather than the exception. Finally it is shown that pursuing the objective of design optimization as defined by the customers via contemporary approaches can lead the designer to highly inappropriate and undesirable designs. As a consequence of this, it becomes apparent that the methods of Total Quality Management (TQM) and Quality Function Deployment (QFD) can lead to highly erroneous results.

Mathematical models encompassing virtually all aspects of engineered products are in widespread use. Indeed, entire industries exist in support of some models: finite element models, computational fluid dynamics models, electric power grid load-flow models, process models, simulation models, and so on. Nonetheless, the purpose, construction, and use of models is not adequately understood. One major issue is that no model perfectly represents reality. Therefore models always diverge from reality somewhere, and they are always inaccurate by some amount. Estimation of model error and the use of model-generated results in support of engineering design decision making are key to the successful use of models.