A Total Cost Comparison of Alternative Tolerancing Formulae

Abstract

An important part of many engineering design projects is to specify the amount of variability permitted in critical characteristics of materials, components, and assembly. Different formulae have been suggested for relating input and output specifications. This article reviews the four basic tolerancing formulae that have appeared in the literature and shows that each solves a slightly different problem. In particular, optimal tolerances are based on costs and the probability distributions of input characteristics. Examples of alternative cost-distribution models are provided that support the 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 influenced by issues not explicitly considered in the traditional debate over worst-case vs. statistical tolerancing. The approach here differs from previous optimal tolerancing studies in two respects. First, earlier work optimized the allocation of tolerances to components to achieve a given assembly tolerance, while we seek global optima. Second, earlier studies advocated an author’s favorite model, while we explore the relative domains of applicability of alternative formulae.