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

(a) Analyze the data from this experiment.

(b) Find an appropriate regression model that explains tool life in terms of the variables used in the experiment.

(c) Analyze the residuals from this experiment.

David · Accepted Answer

a) From the normal probability plot of effects below, factors B, C, and the AC interaction appear 
to be significant.
 
b) The regression model is: 
CACBAijk xx.x.x.x..y 41674416736667516670833340   
 
Design Expert Output 
  Coefficient  Standard 95% CI 95% CI 
 Factor Estimate DF Error Low High VIF 
  Intercept 40.83 1 1.12 38.48 43.19 
  A-Cutting Speed 0.17 1 1.12 -2.19 2.52 1.00 
  B-Tool Geometry 5.67 1 1.12 3.31 8.02 1.00 
  C-Cutting Angle 3.42 1 1.12 1.06 5.77 1.00 
  AC -4.42 1 1.

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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