Page 273 - Design for Six Sigma a Roadmap for Product Development

Axiomatic Design 243

In the decoupled design case, matrix A is a lower/upper triangle
matrix, in which the maximum number of nonzero sensitivity coeffi-
cients equals p(p 1)/2 and A ij 0 for i 1, j and i 1,p. A decoupled
design is represented by
{ } [ A 11 0 0 ]{ } (8.2)
y 1
x 1

A 21 A 22

0

y m A m1 A m2 A mm x m
The decoupled design may be treated as uncoupled design when the
x values are adjusted in some sequence conveyed by the matrix.
Uncoupled and decoupled design entities possess conceptual robustness;
that is, the x terms can be changed to affect other requirements in order
to fit the customer attributes. Definitely, a coupled design results when
the matrix has the number of requirements m greater than the number
of x values p or when the physics is binding to such an extent that off-
diagonal sensitivity elements are nonzero. The coupled design may be
uncoupled or decoupled by “smartly” adding m p extra x terms to the
problem formulation. A coupled design is represented by
{ } [ A 11 A 12 A 1p ]{ } (8.3)
x 1
y 1

A 21 A 22

A (m 1 )p
y m A m1 A m (p 1) A mp x m
An example of design categories is presented in Fig. 8.4, which dis-
plays two possible arrangements of the generic water faucet. The
uncoupled architecture will have higher reliability and more customer
satisfaction since the multiple adjustment of the two FRs can be done
independently to fit customer demands.
The coupling of functional requirements is categorized as a design
vulnerability. The DFSS team does not need to mix this concept with
physical integration or consolidation of design parameters (DPs); that
is, the one-to-one mapping for uncoupled design does not eliminate
hosting more than one function in a component (see Sec. 10.2 for more
details).
Uncoupling or decoupling of design matrices is the activity that fol-
lows their identification via “zigzagging” activity as soon as it is iden-
tified. Coupling occurs when a concept lacks certain design parameters
or fails to meet its constraints. In performing the zigzagging process,
the team will identify design constraints. Constraints are usually con-
fused with functional requirements (FRs). Functional requirements
represent what a design does; they are performance-related, and can
be specified within some tolerance. Criteria such as cost, reliability,