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DFSS Transfer Function and Scorecards 201

FR
FR/ DP 2

FR/ DP 1

DP 1

2
(DP' 1 , DP' )

DP 2
Figure 6.11 Gradients of a transfer function.

Notice that the transfer function in more than one dimension is either
a surface (two variables) or a volume (more than two variables). In this
method, we vary the parameters one at a time by an infinitesimal
amount and observe FR. Gradients of other FRs are collected simul-
taneously. This approach creates an incremental area or volume
(formed from the infinitesimal variation in the respective parameters)
around the design point of interest, where the transfer function will be
valid. Extrapolation is not valid anywhere else for any FR.
This analysis identifies sensitive DPs that affect the mean of an FR,
usually referred to as the adjustment parameters. An FR adjustment
parameter will have a relatively large gradient magnitude compared
to the other parameter gradients. DPs that affect the variance of an
FR are called variability parameters. In the absence of historical data,
the variance of an FR can be estimated using Taylor series expansion
as

P L K FR 2
2
2 (6.8)

FR j
j 1 x i variance
x
sensitivities