An engineer is interested in the effects of cutting speed

(A), tool geometry (B), and cutting angle (C) on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 23 factorial design are run. The results are as follows:

Replicate A B C Treatment Combination I II III

− − − (1) 22 31 25

+ − − a 32 43 29

− + − b 35 34 50

+ + − ab 55 47 46

− − + c 44 45 38

+ − + ac 40 37 36

− + + bc 60 50 54

+ + + abc 39 41 47

(a) Estimate the factor effects. Which effects appear to be large?

(b) Use the analysis of variance to confirm your conclusions for part (a).

(c) Write down a regression model for predicting tool life

(in hours) based on the results of this experiment.

(d) Analyze the residuals. Are there any obvious problems?

(e) On the basis of an analysis of main effect and interaction plots, what coded factor levels of A, B, and C would you recommend using?