Page 283 - Design for Six Sigma a Roadmap for Product Development

Axiomatic Design 253

TABLE 8.1 Functional Independence Measures by Design Category

Design Reangularity R Semangularity S Comments
Uncoupled 1 1 R S 1
Decoupled 1 1 R S
Coupled 1 1 R could be greater
or less than S

p ⎛ ⎞
S ∏ ⎜ A jj ⎟ (8.7)
j 1 ⎜ p ⎟
⎜ ∑ A 2 ⎟
⎜ kj ⎟
⎝ k 1 ⎠
where A ij are the elements of the design matrix (Suh 1990). Both of these
measures are normalized by the magnitudes of the columns in the design
matrix of the transfer functions. These measures can be understood in
the context of vectors algebra where the arrays of DPs and FRs should
be handled as vectors. Two vectors are orthogonal when the dot prod-
uct between them is zero. Reangularity R is a measure of DP orthogo-
nality in p-dimensional space; it is the absolute value of the product of
sine function of all the angle pairs of the design matrix in the transfer
function. R is maximum when the DPs are orthogonal. As the degree
of coupling increases, R will decrease. This orthogonality measure
can’t assure axiom 1 satisfaction as the DPs can be orthogonal but not
parallel to the FRs; that is, the one-to-one mapping can’t be assured,
hence semangularity S. This measure reflects the angular relationship
between the corresponding axes of DPs and FRs. S is the product of
the absolute values of the diagonal elements of the design matrix. When
S 1, the DPs parallel the FRs and uncoupled design is achieved. The
different possibilities of design categories (according to axiom 1) in
these two measures are given in Table 8.1.

8.5.1 The implication of coupling on design
The term “design” in the context of this book is not limited to product
design. It should be extended to operations, manufacturing, or pro-
duction—the processes by which the design entity is embodied.
Axiom 1 is concerned with concept synthesis such that a healthy con-
cept can be chosen. This axiom ensures that a potential for a Six
Sigma capability in the design entity is established. This assurance
should be made in both the physical (matrix A) and process (matrix B)
mappings.