Question 2) An engineer is interested in the effect of cutting speed (A), metal
ID: 3362479 • Letter: Q
Question
Question 2) 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 Draw the design matrix Calculate the main effects of A(cutting speed), B(hardness) and interaction AC only Based on the following ANOVA table, analyze the effects Replicate Treatment Combination Analysis or variance for lire (cae a units) 311 435 348 472 453 377 500 419 221 325 Source DF MS 1332 1332 0.54 0.483 1 28392 28392 11.53 0.009 1 20592 20592 8.36 0.020 506 0.21 0.662 1 56882 56882 23.10 0.001 2352 2352 0.96 0.357 4830 48301.96 0.199 ab 552 506 ac bc abc 406 605 392 A*B*C Error Total 15 134588 8 19700 2463 S=49.6236 R-Sq 85.36% R-Sg (adj ) =72.56% =Explanation / Answer
a]
Full Factorial Design
Factors: 3 Base Design: 3, 8
Runs: 16 Replicates: 2
Blocks: 1 Center pts (total): 0
All terms are free from aliasing.
Design Table
Run A B C
1 - - -
2 + - -
3 - + -
4 + + -
5 - - +
6 + - +
7 - + +
8 + + +
9 - - -
10 + - -
11 - + -
12 + + -
13 - - +
14 + - +
15 - + +
16 + + +
b]
Coded Coefficients
Term Effect Coef SE Coef T-Value P-Value VIF
Constant 413.1 12.5 33.12 0.000
A 18.2 9.1 12.5 0.73 0.480 1.00
B 84.3 42.1 12.5 3.38 0.006 1.00
C 71.7 35.9 12.5 2.88 0.015 1.00
A*C -119.3 -59.6 12.5 -4.78 0.001 1.00
Regression Equation in Uncoded Units
resp = 413.1 + 9.1 A + 42.1 B + 35.9 C - 59.6 A*C
c]
effect A,AB,BC,ABC > Alpha = 0.05
therefore they are insignificant effect.
and effect B ,C,AC < Alpha = 0.05
therefore they are significant.
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