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The activity that most distinguishes engineering from mathematics and the physical sciences is the design of technologically challenging devices, products and systems. But, while ABET recognizes design as a decision-making process, our current educational system treats engineers as problem-solvers and delivers a largely deterministic treatment of the sciences. Problem solving and decision making involve significantly different considerations, not the least of which is that all decision-making is done under uncertainty and risk. Secondly, effective choices among design alternatives demand an understanding of the mathematics of decision making, which rarely appears in engineering curricula. Specifically, we teach the sciences but not how to use them. Decision makers typically earn 50-200 percent more than problem-solvers. The objective of this paper is to make the case that this gap in engineering education lowers the value of an engineering education for both the students and the faculty, and to provide suggestions on how to fix it. 

Recognizing expected utility as a valid design criterion, there are cases where uncertainty is such that this criterion fails to distinguish clearly between design alternatives. These cases may be characterized by broad and significantly overlapping utility probability distributions. Not uncommonly in such cases, the utility distributions of the alternatives may be highly correlated as the result of some uncertain variables being shared by the alternatives, because modeling assumptions may be the same across alternatives, or because difference information may be obtained by means of an independent source. Because expected utility is evaluated for alternatives independently, maximization of expected utility typically fails to take these correlations into account, thus failing to make use of all available design information. Correlation in expected utility across design alternatives can be taken into account only by computing the expected utility difference, namely the "differential expected utility," between pairs of design alternatives. However, performing this calculation can present significant difficulties of which excessive computing times may be key. This paper outlines the mathematics of differential utility and presents an example case, showing how a few simplifying assumptions enabled the computations to be completed with approximately 24 hours of desktop computing time. The use of differential utility in design decision making can, in some cases, provide significant additional clarity, assuring better design choices. 

Tolerancing began with the notion of limits imposed on the dimensions of realized parts both to maintain functional geometric dimensionality and to enable cost-effective part fabrication and inspection. Increasingly however, component fabrication depends on more than part geometry as many parts are fabricated as a result of a "recipe" rather than dimensional instructions for material addition or removal. Referred to as process tolerancing, this is the case, for example, with IC chips. In the case of tolerance optimization, a typical objective is cost minimization while achieving required functionality or "quality." This paper takes a different look at tolerances, suggesting that rather than ensuring merely that parts achieve a desired functionality at minimum cost, the underlying goal of product design is to make money, more is better and tolerances comprise additional design variables amenable to optimization in a decision theoretic framework. We further recognize that tolerances introduce additional product attributes that relate to product characteristics such as consistency, quality, reliability and durability. These important attributes complicate the computation of the expected utility of candidate designs, requiring additional computational steps for their determination. The resulting theory of tolerancing illuminates the assumptions and limitations inherent to Taguchi's loss function. We illustrate the theory using the example of tolerancing for an apple pie, which conveniently demands consideration of tolerances on both quantities and processes, and the interaction among these tolerances.