Construct a 2_IV^4-1 design for the problem in Exercise 14-80. Select the data for the eight runs that would have been required for this design. Analyze these runs and compare your conclusions to those obtained in Exercise 14-80 for the full factorial.

Exercise 14-80

An article in the Journal of Coatings Technology (1988, Vol. 60, pp. 27–32) described a 24 factorial design used for studying a silver automobile basecoat. The response variable is distinctness of image (DOI). The variables used in the experiment are 

A = Percentage of polyester by weight of polyester/melamine (low value = 50%, high value = 70%)

B = Percentage of cellulose acetate butyrate carboxylate (low value = 15%, high value = 30%)

C = Percentage of aluminum stearate (low value = 1%, high value = 3%)

D = Percentage of acid catalyst (low value = 0.25%, high value = 0.50%)

The responses are (1) = 63.8, a = 77.6, b = 68.8, ab = 76.5, c = 72.5, ac = 77.2, bc = 77.7, abc = 84.5, d = 60.6, ad = 64.9, bd = 72.7, abd = 73.3, cd = 68.0, acd = 76.3, bcd = 76.0, and abcd = 75.9.