Applied Statistics and Probability for Engineers

546 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS

we know that the treatment combination bis in the other block. Thus, elements of this

second block are

EXAMPLE 14-6 An experiment is performed to investigate the effect of four factors on the terminal miss dis-

tance of a shoulder-fired ground-to-air-missile. The four factors are target type (A), seeker

type (B), target altitude (C), and target range (D). Each factor may be conveniently run at two

levels, and the optical tracking system will allow terminal miss distance to be measured to the

nearest foot. Two different operators or gunners are used in the flight test and, since there may

be differences between operators, the test engineers decided to conduct the 2^4 design in two

blocks with ABCDconfounded. Thus, the defining contrast is

The experimental design and the resulting data are shown in Fig. 14-26. The effect esti-

mates obtained from Minitab are shown in Table 14-22. A normal probability plot of the

effects in Fig. 14-27 reveals thatA(target type),D(target range),AD, andAChave large

effects. A confirming analysis of variance, pooling the three-factor interactions as error, is

shown in Table 14-23. Since theACandADinteractions are significant, it is logical to

conclude thatA(target type),C(target altitude), andD(target range) all have important

effects on the miss distance and that there are interactions between target type and alti-

tude and target type and range. Notice that theABCDeffect is treated as blocks in this

analysis.

Lx 1 x 2 x 3 x 4

bbc b^2 cc

bac abc

babab^2 a

b 112 b

= Run in block 1

= Run in block 2

A

C

B

bc abc

c

b

ac

a

ab

(1)

(a)

Geometric view

Assignment of the sixteen

runs to two blocks

(b)

Block 1

bcd abcd

cd

bd

acd

ad

abd

d

(1)

ab

ac

bc

ad

bd

cd

abcd

= 3

= 7

= 6

= 8

= 10

= 4

= 8

= 9

Block 2

a

b

c

d

abc

bcd

acd

abd

= 7

= 5

= 6

= 4

= 6

= 7

= 9

= 12

• D +

Figure 14-26 The 2^4 design in two blocks for Example 14-6. (a) Geometric view. (b) Assignment of the

16 runs to two blocks.

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