Tolerancing for an Apple Pie

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. There has emerged an extensive literature on both geometric and process tolerancing, much of it with a focus on tolerance optimization. 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, and tolerances comprise additional design variables amenable to optimization in a decision theoretic framework. We recognize that a theory of tolerancing must apply equally to processes and procedures, and note 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. Nonetheless, their proper consideration is an important element in the evaluation of product design alternatives. The resulting theory of tolerancing presented here is illustrated using the example of tolerancing for an apple pie.