Page 183 - Design for Six Sigma a Roadmap for Product Development

156 Chapter Five

Y=f(x)
FRs (CTQs)
CAs • DPs PVs
• • • •
• • • •
• • •
Y=f(x)
Physical mapping Process mapping
Figure 5.13 The design process mappings.

second mapping from CTSs to the functional requirements (FRs). This
mapping is very critical as it yields the definition of the high-level min-
imum set of functional requirements needed to accomplish the design
value from the customer perspective. Once the minimum set of FRs
are defined, the physical mapping should start. This mapping involves
the FR domain and the codomain design parameter (DP). It represents
the structuring activity and can be represented mathematically by
design matrices (mapping) or, graphically, by block diagrams. The col-
lection of design matrices forms the conceptual structure.
The process mapping is the last mapping and involves the DP
domain and the process variables (PV) codomain. This mapping can be
represented by matrices as well and provides the process structure
needed to translate the DPs to PVs in manufacturing or production
environments.
The zigzagging process of axiomatic design is a conceptual modeling
technique that reveals how the design is coupled in the FRs. In the
physical mapping, the FRs are the array of responses denoted as the
array y.* Coupling of the FRs is a design weakness that negatively
affects controllability and adjustability of the design entity. Coupling
can be defined as the degree of lack of independence between the FRs,
propagates over the design mappings, and limits the potential for Six
Sigma design. Uncoupled designs are not only desirable in terms of
controllability, quality, and robustness standpoints but also have a
potential for high probability of producibility, namely, reduced defect
per opportunity (DPO).
When a design matrix is square, where the number of FRs equals
the number of DPs, and diagonal, the design is called independent or
uncoupled. An uncoupled design is a one-to-one mapping.

*Mathematical bolded notation implies an array or a matrix.