Page 272 - Design for Six Sigma a Roadmap for Product Development

242 Chapter Eight

Per axiom 1, the ideal case is to have a one-to-one mapping so that
a specific x can be adjusted to satisfy its corresponding y without
affecting other requirements. This will give the DFSS team the advan-
tage of vulnerability-free design, which allows a Six Sigma feasible
design with unprecedented improvement flexibility. Axiom 2 states
that the independent design that minimizes the information content is
the best. Because of ignorance and other inhibitors, the exact deploy-
ment of design axiom on the redesign side might be infeasible because
of technological and cost limitations. Under these circumstances, dif-
ferent degrees of conceptual vulnerabilities are established in the mea-
sures (criteria) related to the unsatisfied axiom (Fig. 8.3). For example,
a degree of coupling may be created as a result of axiom 1 violation. A
conceptually weak design may have limited chances to succeed in an
operational vulnerability improvement phase.
When matrix A is a square diagonal matrix, that is, m p and
A ji 0 when i j and 0 elsewhere, the design is called uncoupled,
which means that each y can be adjusted or changed independent of
the other y. An uncoupled design is a one-to-one mapping and is rep-
resented by

{ } [ A 11 0 0 ] { } (8.1)
x 1
y 1

0

A 22

0
y m 0 0 A mm x m
Design Axioms Design Weaknesses
Coupling
– Axiom 1: The Independence Axiom Violation

Complexity

– Axiom 2: The Information Axiom Violation

Figure 8.3 Design vulnerabilities produced when the axioms are violated.