An article in the Journal of Coatings Technology (Vol. 60, 1988, pp. 27–32) describes 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 = Percent of polyester by weight of polyester/melamine (low value = 50%, high value 70%)
B = Percent cellulose acetate butyrate carboxylate (low value = 15%, high value = 30%)
C = Percent aluminum stearate (low value = 1%, high value = 3%)
D = Percent 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.
(a) Estimate the factor effects.
(b) From a normal probability plot of the effects, identify a tentative model for the data from this experiment.
(c) Using the apparently negligible factors as an estimate of error, test for significance of the factors identified in part (b). Use α = 0.05.
(d) What model would you use to describe the process, based on this experiment? Interpret the model. (e) Analyze the residuals from the model in part (d) and comment on your findings.