Page 623 - Design for Six Sigma a Roadmap for Product Development

576 Chapter Sixteen

The situation described in Fig. 16.2 is very common in most toler-
ance design circumstances. However, subject-matter knowledge also
plays a role in different circumstances. For example, if the design
parameters are all dimension-related, such as automobile body dimen-
sions, or mechanical parts dimensions, there is a full body of knowl-
edge regarding this, called geometric dimensioning and tolerance
(GDT), where the fundamental idea about tolerance design is really
the same as those for any other tolerance designs. However, many spe-
cial methods and terminologies are purely dimensional in nature.
In this chapter, we discuss all major tolerance design methods under
the tolerance design paradigm illustrated in Figs. 16.1 and 16.2.
Subject-germane tolerance design aspects, such as GDT, are not
included.
There are two classes of tolerance design methods: the traditional
tolerance design method and Taguchi’s tolerance design method.
Traditional tolerance design methods include worst-case tolerance
analysis, statistical tolerance analysis, and cost-based tolerance analy-
sis. Taguchi tolerance design methods include the relationship between
customer tolerance and producer’s tolerance, and tolerance design
experiments. All these methods are discussed in subsequent sections.

16.2 Worst-Case Tolerance

Worst-case tolerance is a tolerance design approach that is against the
worst-case scenario. Specifically, let us assume that the transfer function
between a higher-level requirement y with lower-level characteristics
is x 1 ,x 2 ,…x i ,…,x n is

y f(x 1 ,x 2 ,…,x i ,…,x n ) (16.1)
and it is further assumed that the target value for y is T, and the tol-
erance limit for y is 0 such that y is within specification if T 0
y T 0 . Sometimes it is possible for the tolerance limits to be asym-
metric, with y in the specification limit if T ′ 0 y T 0 , where
′ 0 is the left tolerance limit and 0 is the right tolerance limit.
...
For each x i , i 1 n, the target value for x i is T i and the tolerance
limit for x i is i , such that x i is within specification if T i i x i T i
i is satisfied. Sometimes it is also possible for the tolerance limit
for x i to be asymmetric, with x i within specification if T i ′ i x i T i
i is satisfied.
The worst-case tolerance design rule can be expressed by the follow-
ing formula:
T ′ 0 Min f(x 1 ,x 2 ,…,x i ,…,x n ) (16.2)
x i ∈ (T i i ,T i i ) i