Page 284 - Design for Six Sigma a Roadmap for Product Development

254 Chapter Eight

In the context of Sec. 8.4 and Fig. 8.2, we can express both mappings
mathematically as

(8.8)
{FR} m
1 [A] m
p {DP} p
1
(8.9)
{DP} p
1 [B] p
n {PV} n
1
or equivalently

(8.10)
{FR} m
1 [C] {PV} n
1
where A is the design mapping matrix, B is the process mapping
matrix, and [C] m
n [A][B] is the overall design matrix. In either
mapping, we seek to satisfy the independence axiom, axiom 1.
Therefore the product matrix C should be diagonal, that is, uncoupled.
The A and B matrices can be categorized from coupling perspective
according to Eqs. (8.1) to (8.3). Accordingly, the different possibilities
that can be taken by matrix C are given in Table 8.2. The following
conclusions can be deduced:
■ A decoupled design may be an upper or a lower triangular type of
matrix depending on the formulation.
■ For the overall design entity (product and process) to be totally
uncoupled, both matrices should be uncoupled.

Uncoupled designs are not only desirable from controllability, quality,
and robustness standpoints but also have potential for high probability
of producibility, that is, reduced defect per opportunity (DPO). A decou-
pled design is the next choice when uncoupled design cannot be
achieved; however, the revealed sequence of adjustment should be fol-
lowed in executing the synthesis process of creative and incremental
design situations. Uncoupled and decoupled designs have higher
potentials to achieve Six Sigma capability in all FRs than do the cou-
pled designs. Design for Six Sigma in the conceptual sense is defined

TABLE 8.2 Possibilities of Matrix [C]

[A]/[B]
Legend
: Upper triangular matrix
: Lower triangular matrix
: Diagonal matrix
: Coupled matrix (Upper, lower and diagonal)