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Axiomatic Design 259

b. Match these two FRs considerations to any two of 39 generalized
design requirements
c. Look up solution principles to the conflict of these two FRs using a
Altschuller’s TRIZ matrix
d. Convert this general solution principle into a working project
solution

Decoupling methods 1 and 2 provide many opportunities in the case
of new design. The degree of freedom in applying them will become
limited in redesign situations with binding physical and financial con-
straints. Redesign scenarios that are classified as coupled, call for
another method that is based on tolerance optimization to reduce oper-
ational vulnerability.

3. Perform decoupling by tolerance optimization. Tolerances of the
FRs have a strong role to play in decoupling a design. The FRs are
always specified with some tolerances, y j t j ,j 1,…,m, where t j is
the half-tolerance of FR j and m is number of FRs in the array y.
Let’s assume that we have a 2
2 coupled design with

y 1 A 11 A 12 x 1
] { }
{ } [ A 21 A 22 x 2
y 2
In method 3, the issue is whether A 12 or A 21 can be neglected (A 12 0
or A 21 0) so that the design can be considered decoupled. If not, then
method 3 is required. The transferred variation of y 1 is given by

∂y 1 ∂y 1
y 1 x 1 x 2
∂x 1 ∂x 2

On the basis of customer specification, we need to maintain y 1 t j ;
thus the change in the FR(y 1 ) due to the changes in the design para-
meters is less than the tolerance specified by the customer. To achieve
a decoupled design, we need to make A 12 negligibly small, which trans-
lates into making t j (∂y 1 /∂x 2 ) x 2 , neglecting the off-diagonal element.
This is the essence of Theorem 8 in Suh (1990, p. 122).
In summary, the decoupling or uncoupling actions (DFSS algorithm
step 6) are

1. Start from high-level FRs (obtained from QFD phase 2 QFD).
2. Define high-level DPs.
3. Use the zigzagging process to map FRs to DPs to get the design
matrices and physical structure.