Brownlee (1960) described an experiment designed to study two different annealing methods used in making of cans. Three coils of material were selected from the populations of coils made by each of the two methods. From each coil two samples were taken from each of two locations on the coil. The response is the life of the can. Let denote the mean response for the ith method of annealing and the jth location, and let y be the response for the kth coil for that combination of factors. The data are shown below.

a. Justify the choice of the linear model where c(a)~N(0, Bajk = Hij + c(a)ux + Ic

(a) + j 1)), lc

(a) ~ N(0, 2(1)), and e ~ N(0. ).

b. Fit the linear model, complete the analysis of variance table, test the usual fixed effect hypotheses, and estimate the variance components.

c. Apply the AVE method to estimate the variance components. Note the difference in the estimates of x based on the two different annealing methods. Comment on Brownlee's statement that more coils would be required for a definitive study.

d. In the row of the AOV table for the coils within methods effect, the row labeled 3(1) in our notation, Brownlee gives EMS = + may Compare this with the expression for the expected value in your table. Comment on the effect of this difference with respect to parameter estimation and to testing the hypothesis H)= 0. Section 14.5