Minimum-Cost Tolerance Allocation
Kenneth W. Chase, Ph.D.
Brigham Young University
Dr. Chase has taught mechanical engineering at the Brigham Young University since 1968. An advo-
cate of computer technology, he has served as a consultant to industry on numerous projects involving
engineering software applications. He served as a reviewer of the Motorola Six Sigma Program at its
inception. He also served on an NSF select panel for evaluating tolerance analysis research needs. In
1984, he founded the ADCATS consortium for the development of CAD-based tools for tolerance analy-
sis of mechanical assemblies. More than 30 sponsored graduate theses have been devoted to the devel-
opment of the tolerance technology contained in the CATS software. Several faculty and students are
currently involved in a broad spectrum of research projects and industry case studies on statistical
variation analysis. Past and current sponsors include Allied Signal, Boeing, Cummins, FMC, Ford, GE,
HP, Hughes, IBM, Motorola, Sandia Labs, Texas Instruments, and the US Navy.
Tolerance Allocation Using Least Cost Optimization
A promising method of tolerance allocation uses optimization techniques to assign component tolerances
that minimize the cost of production of an assembly. This is accomplished by defining a cost-versus-
tolerance curve for each component part in the assembly. An optimization algorithm varies the tolerance
for each component and searches systematically for the combination of tolerances that minimize the cost.
1-D Tolerance Allocation
Fig. 14-1 illustrates the concept simply for a three component assembly. Three cost-versus-tolerance
curves are shown. Three tolerances (T1, T2, T3 ) are initially selected. The corresponding cost of produc-
tion is C1 + C2 + C3. The optimization algorithm tries to increase the tolerances to reduce cost; however, the
specified assembly tolerance limits the tolerance size. If tolerance T1 is increased, then tolerance T2 or T3
must decrease to keep from violating the