By: Davis Balestracci
06/16/2016
In my last column I explained how many situations have an inherent response surface, which is the “truth.” However, any experimental result represents this true response, which is unfortunately obscured by the process’s common-cause variation. Regardless of whether you are at a low state of knowledge (factorial) or a high state of knowledge, the same sound design principles apply.
The contour plot: a quadratic ‘French curve’
Response surface methodology’s objective is to model a situation by a power series truncated after the quadratic terms. In the case of three independent variables (x1, x2, x3), as in the tar scenario from my column, “90 Percent of DOE Is Half Planning,” in May 2016:
Y = B0 + (B1 x1) + (B2 x2) + (B3 x3) + (B12 x1 x2) + (B13 x1 x3) + (B23 x2 x3) + [B11 (x1**2)] + [B22 (x2**2)] + [B33 (x3** 2)]
Which designs give the best estimates of these B coefficients?