A Total Cost Comparison of Alternative Tolerancing Formulae

[+] Author and Article Information
S. B. Graves

Center for Quality and Productivity Improvement, University of Wisconsin, 610 Walnut St., Madison, WI 53705

J. Manuf. Sci. Eng 121(4), 720-726 (Nov 01, 1999) (7 pages) doi:10.1115/1.2833122 History: Received January 01, 1998; Revised December 01, 1998; Online January 17, 2008


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.

Copyright © 1999 by The American Society of Mechanical Engineers
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