R. D. Snee (“Experimenting with a Large Number of Variables,” in Experiments in Industry: Design, Analysis and Interpretation of Results, by R. D. Snee, L. B. Hare, and J. B.

Trout, Editors, ASQC, 1985) describes an experiment in which a 25−1 design with I = ABCDE was used to investigate the effects of five factors on the color of a chemical product.

The factors are A = solvent∕reactant, B = catalyst∕reactant, C = temperature, D = reactant purity, and E = reactant pH.

The responses obtained are as follows:

e = −0.63 d = 6.79 a = 2.51 ade = 5.47 b = −2.68 bde = 3.45 abe = 1.66 abd = 5.68 c = 2.06 cde = 5.22 ace = 1.22 acd = 4.38 bce = −2.09 bcd = 4.30 abc = 1.93 abcde = 4.05

(a) Prepare a normal probability plot of the effects. Which effects seem active?

(b) Calculate the residuals. Construct a normal probability plot of the residuals and plot the residuals versus the fitted values. Comment on the plots.

(c) If any factors are negligible, collapse the 25−1 design into a full factorial in the active factors. Comment on the resulting design, and interpret the results.