Applied Statistics and Probability for Engineers

522 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS

The F-ratios for all three main effects and the interactions are formed by dividing the mean

square for the effect of interest by the error mean square. Since the experimenter has selected

0.05, the critical value for each of these F-ratios is f0.05,1,85.32. Alternately, we could

use the P-value approach. The P-values for all the test statistics are shown in the last column

of Table 14-11. Inspection of these P-values is revealing. There is a strong main effect of feed

rate, since the F-ratio is well into the critical region. However, there is some indication of an

effect due to the depth of cut, since P= 0.0710 is not much greater than 0.05. The next

largest effect is the ABor feed rate depth of cut interaction. Most likely, both feed rate and

depth of cut are important process variables.

Obviously, factorial experiments with three or more factors can require many runs, par-

ticularly if some of the factors have several (more than two) levels. This point of view leads

us to the class of factorial designs considered in Section 14-7 with all factors at two levels.

These designs are easy to set up and analyze, and they may be used as the basis of many other

useful experimental designs.

Table 14-11 Minitab ANOVA for Example 14-2

ANOVA (Balanced Designs)

Factor Type Levels Values

Feed fixed 2 20 30

Depth fixed 2 0.025 0.040

Angle fixed 2 15 25

Analysis of Variance for Roughness

Source DF SS MS F P

Feed 1 45.563 45.563 18.69 0.003

Depth 1 10.563 10.563 4.33 0.071

Angle 1 3.063 3.063 1.26 0.295

Feed*Depth 1 7.563 7.563 3.10 0.116

Feed*Angle 1 0.062 0.062 0.03 0.877

Depth*Angle 1 1.563 1.563 0.64 0.446

Feed*Depth*Angle 1 5.062 5.062 2.08 0.188

Error 8 19.500 2.437

Total 15 92.938

Table 14-10 Coded Surface Roughness Data for Example 14-2

Depth of Cut (B)

0.025 inch 0.040 inch

Tool Angle (C) Tool Angle (C)

15  25  15  25 

911 910

20 inches per minute 7 10 11 8 75

10 10 12 16

30 inches per minute 12 13 15 14 102

yip

Feed Rate

(A)

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