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DFSS Transfer Function and Scorecards 203

5. Regression transfer equations are obtained when the FRs are
regressed over all input variables of interest. Multiple regressions cou-
pled with multivariate analysis of variance (MANOVA) and Covariance
(MANCOVA) are typically used.

6.4.2 Transfer function and optimization
Transfer functions* are fundamental design knowledge to be treated
as living documents in the design guides and best practices within Six
Sigma deployment and outside the deployment initial reach. Transfer
functions are usually recorded and optimized in design scorecards.
Some of the transfer functions are readily available from existing
knowledge. Others will require some intellectual (e.g., derivation) and
monetary capital to obtain.
A transfer function is the means for optimization in the DFSS algo-
rithm. Optimization is a design activity where we shift the mean to
target and reduce the variability for all the responses in the DFSS pro-
ject scope in the respective structure. However, this optimization is not
arbitrary. The selection of DPs for an FR that will be used for opti-
mization depends on the physical mapping and the design type from
coupling perspective. If the design is uncoupled, that is, if there is a
one-to-one mapping between FRs and DPs, then each FR can be opti-
mized separately via its respective DP. Hence, we will have optimiza-
tion studies equal to the number of FRs. If the design is decoupled, the
optimization routine must follow the coupling sequence revealed by
the design matrices in the structure (Chap. 7). In coupled scenarios,
the selection of DPs to be included in the study depends on the poten-
tial control needed and affordable cost. The selection should be done in
a manner that will enable target values to be varied during experi-
ments with no major impact on design cost. The greater the number of
potential design parameters that are identified, the greater the oppor-
tunity for optimization of function in the presence of noise.
A key philosophy of robust design is that during the optimization
phase, inexpensive parameters can be identified and studied, and can be
combined in a way that will result in performance that is insensitive
to noise. The team’s task is to determine the combined best settings
(parameter targets) for each design parameter, which have been judged
by the design team to have potential to improve the system. By varying
the parameter target levels in the transfer function (design point), a
region of nonlinearity can be identified. This area of nonlinearity is the
most optimized setting for the parameter under study (Fig. 6.12).

*We are assuming continuity and existence of first-order derivatives in our discussions
of transfer functions.