Applied Statistics and Probability for Engineers

510 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS

experimentation than a factorial, and as we have just seen, there is no assurance that it will

produce the correct results.

14-4 TWO-FACTOR FACTORIAL EXPERIMENTS

The simplest type of factorial experiment involves only two factors, say, Aand B. There are

alevels of factor Aand blevels of factor B. This two-factor factorial is shown in Table 14-3.

The experiment has nreplicates,and each replicate contains all abtreatment combinations.

Figure 14-7

Optimization

experiment using the

one-factor-at-a-

time method.

0.5

140

1.0 1.5 2.0 2.5

150

160

170

180

190

200

Temperature (

°F)

95%

90%

80%

70%

60%

Time (hr)

Table 14-3 Data Arrangement for a Two-Factor Factorial Design

Factor B

12 b Totals Averages

1

y 111 , y 112 , y 121 , y 122 , y 1 b 1 , y 1 b 2 ,

p , y 11 n p , y 12 n p , y 1 bn y 1 ..

2

y 211 , y 212 , y 221 , y 222 , y 2 b 1 , y 2 b 2 ,

FactorA p , y^21 n p , y^22 n p , y^2 bn y^2 ..

ya 11 , ya 12 , ya 21 , ya 22 , yab 1 , yab 2 ,

a p , ya 1 n p , ya 2 n p , yabn

Totals

Averages y. 1. y. 2. y.b. y...

y. 1. y. 2. y.b. yp

ya.. ya..

o

y 2 ..

y 1 ..

p

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