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

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 23 factorial design are run. The
tool life data (in hours) are shown in the
following table.
a) Compute the estimates of the effects and their
standard errors for this design.
b) Perform the analysis of variance using the tratio
c) Establish the regression model.
d) Perform the analysis of variance using the f-ratio.

Treatment

combination

Replicate

I

Replicate

II

311

453

Treatment

combination

Replicate

I

Replicate

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

Explanation / Answer

•Main effects are estimated

A=1/4n [ a+ab+ac+abc-(1)-b-c-bc]

=1/8(325+435)+(552+472)+(406+377)+(392+419)-(221+311)- 354+348)-(440+453) (605+550)=146

•Sum of squares for A

SSSPEED =(146)2/16 = 1332

Source dof SS MS F P Speed 1 1332 1322 0.49 0.502 Hardness 1 28932 28932 10.42 0.01 Angle 1 20592 20592 7.56 0.023 Speed, 1 506 506 0.19 0.677 Hardness Speed, 1 56882 56882 20.87 0 Angle Hardness, 1 2352 2352 0.86 0.377 Angle Error 9 24530 2726 Total 15 134588

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