An engineer is interested in the effect of cutting speed (A), metal hardness (B), and cutting angle...

Question

An engineer is interested in the effect of cutting speed (A), metal hardness (B), and cutting angle (C) on the life of a cutting tool. Two levels of each factor are chosen, and two replicates of a 2³factorial design are run. The tool life data (in hours) are shown in the following table:

	Replicate
Treatment Combination	I	II
(1)	221	311
a	325	435
b	354	348
ab	552	472
c	440	453
ac	406	377
bc	605	500
abc	392	419

replicate 1 only. Suppose that a center point with four replicates is added to these eight factorial runs and the responses are 425, 400, 437, and 418.

(a) Estimate the facter effects.

(b) Test for lack of fit using α = 0.05

(c) Test for main effects and interactions using α = 0.05.

(d) Analyze residuals and draw conclusions.

David · Accepted Answer

(a)  Estimate the factor effects.  Which effects appear to be large?
From the normal probability plot of effects below, factors B, C, and the AC interaction appear to be significant.
 
 
(b)  Use the analysis of variance to confirm your conclusions for part (a).
The analysis of variance confirms the significance of  factors B, C, and the AC interaction. 
 
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An engineer is interested in the effect of cutting speed ( A ), metal hardness ( B ), and cutting angle ( C ) on the life of a cutting tool. Two levels of each factor are chosen, and two replicates of...

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