Question

6.1. An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 2^3 factorial design are run. The results are as follows: Treatment Replicate A B C 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? (Use Minitab) (b) Use the analysis of variance to confirm your conclusion for part (a) (Manual Calculation)

          6.1. An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 2^3 factorial design are run. The results are as follows:

Treatment Replicate
A B C 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? (Use Minitab)
(b) Use the analysis of variance to confirm your conclusion for part (a) (Manual Calculation)

6.1. An engineer is interested in the effects of cutting speed (A), tool geometry (B), and cutting angle on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 2^3 factorial design are run. The results are as follows:

Treatment Replicate
A B C 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? (Use Minitab)
(b) Use the analysis of variance to confirm your conclusion for part (a) (Manual Calculation)

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