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TA B L E 13E,2 Data for the Experiment in Exercise 13.2 Replicate Run 221 325 35

ID: 3310493 • Letter: T

Question

TA B L E 13E,2 Data for the Experiment in Exercise 13.2 Replicate Run 221 325 354 552 440 406 605 392 311 435 348 472 453 377 500 419 ab ac bc abc A process engineer is trying to improve the life of a cutting tool. He has run a 2 experiment using cutting speed (A), metal hardness (B), and cutting angle (C) as the factors. The data from two replicates are shown in Table 13E.2. (a) Do any of the three factors affect tool life? (b) What combination of factor levels produces the 13.4. longest tool life? (c) Is there a combination of cutting speed and cut- ting angle that always gives good results regard- less of metal hardness?

Explanation / Answer

Main effects: -

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+500)

=146

Sum of squares for A

SSSpeed=(146)^2/16=1332

Similarly, we would compute for all other factors with the below formulas: -

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

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

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

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

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

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

a)

Hardness and angle affect tool life (looking at the p-value)

b)

Speed and Angle (looking at the p-value)

c)

Speed and Angle is producing good results

Source DF 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

a)

Hardness and angle affect tool life (looking at the p-value)

b)

Speed and Angle (looking at the p-value)

c)

Speed and Angle is producing good results