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Axiomatic Design 245

8.4.1 The zigzagging process
In the faucet example, the design is considered complete when the
mapping from the functional domain to the physical domain is
accomplished. However, in many design assignments of higher com-
plexity, such as the transmission vane oil pump (Sec. 8.4.3), a process
of cascading the high-level conceptual requirements is needed. The
objective of this process is to decompose both the FRs and the DPs
and the PVs for further detailing before manufacturing implementa-
tion. The process should be detailed such that it will enable the map-
ping from FRs to DPs in a certain decomposition level and from the
DPs to the FRs of a further detailed level. The zigzagging process of
axiomatic design does just that (Fig. 8.5). This process requires the
decomposition in a solution neutral environment, where the DPs are
chosen after the FRs are defined, and not vice versa. When the FRs
are defined, we have to “zig” to the physical domain, and after proper
DP selection, we have to “zag” to the functional domain for further
decomposition. This process is in direct contrast to the traditional
cascading processes, which utilizes only one domain, treating the
design as the sum of functions or the sum of parts.
The process of zigzagging must continue until no further decompo-
sition can be done. This is warranted, for example, when material
properties or geometric dimensions are reached. Theoretically, the
process can proceed to the physical and chemical structure of the
design. The result of this process is the creation of the hierarchical
tree, a physical structure, for the FRs and the DPs. This is the major

Relationship Mapping Mapping
CAs FRs DPs PVs

FR DP PV
1 1 1
FR FR DP DP PV PV
11 12 11 12 11 12
Zig- Zig-
zagging zagging

Customer Functional Physical Process
Domain Domain Domain Domain
Figure 8.5 The zigzagging process.