An article in the Journal of Coatings Technology (1988,

Chapter 14, Problem 80SE

(choose chapter or problem)

Problem 80SE

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.

(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 a = 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.