# Consider a comparison between the k = 4 SCD of Equation 8.5 with the k = 4 CCD (N = 24 þ nc). Use n.

Consider a comparison between the k = 4 SCD of Equation 8.5

with the k = 4 CCD (N = 24 þ nc). Use n_{c} = 4 center runs for each

design, and use a = 2 for both designs

(a) Do the designs need to be rescaled? Explain.

(b) Make the same type of comparisons as in Exercise 8.1

Exercise 8.1

There is considerable interest in the use of saturated or

near saturated secondorder designs. One interesting comparison involves the

hexagon (k = 2) and the small composite design. Both involve six design points

(plus center runs). In this exercise, we make comparisons that take into

account variances of coefficients and prediction variance. However, before any

two designs can be compared, they must be adjusted so they have the same scale.

Consider the hexagon of Equation 7.22 and the k = 2 small composite design

listed in Section 8.1. For proper comparisons we have

For this scaling, both designs are on spheres of radius (apart from center runs).

(a) Compute N Var(b_{0})/^{2}

, NVar(b_{ii})/^{2} , NVar(b_{i})/^{2}

, NVar(b_{ij})/^{2} for both designs.

Comment.

(b) Compute N Var[^y(x)] ^{2} at the design center and

at all design points for both designs. Is this an illustration of rotatability?

(c) Construct FDS plots and VDGs for both designs. Comment

on which design you prefer and why.

(d) From part (b), is there an illustration of the

rotatability of the hexagon?

(e) Is the small composite design rotatable? Explain.