AXIOMATIC DESIGN IN SOFTWARE DESIGN FOR SIX SIGMA (DFSS) - Software Design for Six-Sigma: A Roadmap for Excellence - page 332

FR 2 FR 2 FR 2

DP 2

DP 2 DP 2

(2) (2)

(2)

(1)

(1)

(1)

DP 1 DP 1

DP 1

FR 1 FR 1 FR 1

(a) Uncoupled Design
Path Independence

(b) Decoupled Design
Path Independence

(c) Coupled Design
Path Independence

FR 1
FR 2 OX

XO DP 1 FR 1

FR 2 OX

XX DP 1 FR 1

FR 2 XX

XX DP 1

= = =

DP 2 DP 2 DP 2

FIGURE 13.2 Design categories according to axiom 1.

design is a one-to-one mapping. Another design that obeys axiom 1, though with
a known design sequence, is called decoupled. In a decoupled design, matrix A is
a lower or an upper triangular matrix. The decoupled design may be treated as
an uncoupled design when the DPs are adjusted in some sequence conveyed by
the matrix. Uncoupled and decoupled design entities possess conceptual robustness
(i.e., the DPs can be changed to affect specific requirements without affecting other
FRs unintentionally). A coupled design definitely results in a design matrix with
several requirements, m, greater than the number of DPs, p. Square design matrices
( m p ) may be classified as a coupled design when the off-diagonal matrix elements

are nonzeros. Graphically, the three design classifications are depicted in Figure 13.2
for 2

=

2 design matrix case. Notice that we denote the nonzero mapping relationship
in the respective design matrices by “ X. ” On the other hand, “0” denotes the absence
of such a relationship.
Consider the uncoupled design in Figure 13.2(a). The uncoupled design possesses
the path independence property, that is, the design team could set the design to level
(1) as a starting point and move to setting (2) by changing DP1 first (moving east
to the right of the page or parallel to DP1) and then changing DP2 (moving toward
the top of the page or parallel to DP2). Because of the path independence property
of the uncoupled design, the team could move start from setting (1) to setting (2) by
changing DP2 first (moving toward the top of the page or parallel to DP2) and then
changing DP1 second (moving east or parallel to DP1). Both paths are equivalent,
that is, they accomplish the same result. Notice also that the FR's independence is
depicted as orthogonal coordinates as well as perpendicular DP axes that parallel its
respective FR in the diagonal matrix.
Path independence is characterized mathematically by a diagonal design matrix
(uncoupled design). Path independence is a very desirable property of an uncoupled
design and implies full control of the design team and ultimately the customer (user)

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