A total cost comparison of alternative tolerancing formulae

An important part of many engineering design projects is to specific, the a mount of variability permitted in critical characteristics of materials, co mponents, and assembly. Different formulae have been suggested for relating input and output specifications. This article reviews the four basic toler ancing formulae that have appeared in the literature and shows that each so lves a slightly different problem. In particular, optimal tolerances are ba sed on costs and the probability distributions of input characteristics. Ex amples of alternative cost-distribution models are provided that support th e use of each of the four basic formulae as well as a solution not related to any of these formulae. This establishes that optimal tolerancing is infl uenced by issues not explicitly considered in the traditional debate over w orst-case vs. statistical tolerancing. The approach here differs from previ ous optimal tolerancing studies in two respects. First, earlier work optimi zed the allocation of tolerances to components to achieve a given assembly tolerance, while we seek global optima. Second, earlier studies advocated a n author's favorite model, while we explore the relative domains of applica bility of alternative formulae.