Why do my Single Parameter Sensitivities in DesignXplorer vary so much with the value of the parameter?
My response surfaces are linear, so according to generic definition of the sensitivity, the sensitivities should
be the tangent of the surface which is (almost) constant. But the sensitivities shown in "Single Parameter Sensitivies"
were not the tangents and varied a lot as I changed the value of a parameter. And these sensitivities are very different
from the sensitivities under the six-sigma analysis.
First of all, Single Parameter Sensitivity (SPS) is different from correlation-based sensitivities, e.g., Pearson Linear (PLS)
or Spearman Rank (SRS) Sensitivity used in ANSYS PDS and DX Six Sigma Analysis.
SPS is more of a local sensitivity, while PLS or SRS is more of global sensitivity, that gives sensitivity value at a certain location
in the design space of all parameters. For instance, for two input variables (X1 & X2), if we want to evaluate sensitivity of
output Y wrt X1 at location (X1*,X2*), we evaluate the output Y of locations (points) along the axis X2 = X2*; X1 discretized
at a certain interval between its specified bounds, while X2=X2* is kept throughout. The SPS is then formulated as follows:
Ysps(X1 | X2*) = Ymax - Ymin -------(1); subject to X1 discretization, and X2=X2*
Ysps(X2 | X1*) = Ymax - Ymin -------(2); subject to X2 discretization, and X1=X1*
Now, in order to have the same comparison basis, we want to normalize (1) and (2). What we do is normalize them with Yave,
which is the average for all output Y evaluations of (1) and (2). The SPSs are then normalized as follows:
Ysps(X1 | X2*) = (Ymax - Ymin) / Yave
Ysps(X2 | X1*) = (Ymax - Ymin) / Yave