Applied Statistics and Probability for Engineers

570 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS

IMPORTANT TERMS AND CONCEPTS

In the E-book, click on any

term or concept below to

go to that subject.

Analysis of variance

(ANOVA)

Blocking and nuisance

factors

Confounding

Factorial Experiment

Fractional factorial design

Interaction

Main effect

Normal probability

plot of factor

effects

Orthogonal design

Regression model

Residual analysis

Two-level factorial

design

CD MATERIAL

Center points in a

factorial

Central composite

design

Mixed model

Random model

Response surface

Steepest ascent

Variance components

MIND-EXPANDING EXERCISES

(b) Fit a quadratic model to the data. Is this model satis-

factory?

(c) If it is important to minimize the ash value, where

would you run the process?

14-74. In their book Empirical Model Building and

Response Surfaces(John Wiley, 1987), G. E. P. Box and

N. R. Draper describe an experiment with three factors.

The data shown in the following table are a variation of

the original experiment on page 247 of their book.

Suppose that these data were collected in a semiconduc-

tor manufacturing process.

(a) The response y 1 is the average of three readings on

resistivity for a single wafer. Fit a quadratic model

to this response.

(b) The response y 2 is the standard deviation of the three

resistivity measurements. Fit a linear model to this

response.

(c) Where would you recommend that we set x 1 , x 2 , and

x 3 if the objective is to hold mean resistivity at 500

and minimize the standard deviation?

x 1 x 2 x 3 y 1 y 2 x 1 x 2 x 3 y 1 y 2

 1  1  1 24.00 12.49 1 0 0 501.67 92.50

0  1  1 120.33 8.39  1 1 0 264.00 63.50

1  1  1 213.67 42.83 0 1 0 427.00 88.61

 10  1 86.00 3.46 1 1 0 730.67 21.08

00  1 136.63 80.41  1  1 1 220.67 133.82

10  1 340.67 16.17 0  1 1 239.67 23.46

 11  1 112.33 27.57 1  1 1 422.00 18.52

01  1 256.33 4.62  1 0 1 199.00 29.44

11  1 271.67 23.63 0 0 1 485.33 44.67

 1  1 0 81.00 0.00 1 0 1 673.67 158.21

0  1 0 101.67 17.67  1 1 1 176.67 55.51

1  1 0 357.00 32.91 0 1 1 501.00 138.94

 1 0 0 171.33 15.01 1 1 1 1010.00 142.45

0 0 0 372.00 0.00

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