Applied Statistics and Probability for Engineers

534 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS

EXAMPLE 14-4 Consider the surface roughness experiment originally described in Example 14-2. This is a 2^3

factorial design in the factors feed rate (A), depth of cut (B), and tool angle (C), with n 2

replicates. Table 14-16 presents the observed surface roughness data.

The main effects may be estimated using Equations 14-15 through 14-21. The effect of A,

for example, is

and the sum of squares for Ais found using Equation 14-23:

It is easy to verify that the other effects are

B  1.625

C  0.875

AB  1.375

AC  0.125

BC 0.625

ABC 1.125

Examining the magnitude of the effects clearly shows that feed rate (factor A) is dominant,

followed by depth of cut (B) and the ABinteraction, although the interaction effect is rela-

tively small. The analysis of variance, summarized in Table 14-17, confirms our interpretation

of the effect estimates.

Minitab will analyze 2kfactorial designs. The output from the Minitab DOE (Design of

Experiments) module for this experiment is shown in Table 14-18. The upper portion of the table

displays the effect estimates and regression coefficients for each factorial effect. However, a



12722

2182

SSA 45.5625

1 ContrastA 22

n 2 k



1

8

3274 3.375



1

4122

322  27  23  40  16  20  21  184

A

1

4 n

3 aabacabc 112 bcbc 4

Table 14-16 Surface Roughness Data for Example 14-4

Treatment Design Factors Surface

Combinations ABC Roughness Totals

112  1  1  1 9, 7 16

a 1  1  1 10, 12 22

b  11  1 9, 11 20

ab 11  1 12, 15 27

c  1  1 1 11, 10 21

ac 1  1 1 10, 13 23

bc  1 1 1 10, 8 18

abc 1 1 1 16, 14 30

c 14 .qxd 5/9/02 7:54 PM Page 534 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH112 FIN L: