Applied Statistics and Probability for Engineers

14-4 TWO-FACTOR FACTORIAL EXPERIMENTS 519

14-1. In his book (Design and Analysis of Experiments,

5th edition, 2001 John Wiley & Sons), D. C. Montgomery

presents the results of an experiment involving a storage

battery used in the launching mechanism of a shoulder-

fired ground-to-air missile. Three material types can be

used to make the battery plates. The objective is to design a

battery that is relatively unaffected by the ambient temper-

ature. The output response from the battery is effective life

in hours. Three temperature levels are selected, and a fac-

torial experiment with four replicates is run. The data are as

follows:

Temperature (F)

Material Low Medium High

1 130 155 34 40 20 70

74 180 80 75 82 58

2 150 188 136 122 25 70

159 126 106 115 58 45

3 138 110 174 120 96 104

168 160 150 139 82 60

Temperature (C)

Position 800 825 850

1 570 1063 565

565 1080 510

583 1043 590

2 528 988 526

547 1026 538

521 1004 532

EXERCISES FOR SECTION 14-4

(a) Test the appropriate hypotheses and draw conclusions

using the analysis of variance with 0.05.

(b) Graphically analyze the interaction.

(c) Analyze the residuals from this experiment.

14-2. An engineer who suspects that the surface finish of

metal parts is influenced by the type of paint used and the drying

time. He selected three drying times—20, 25, and 30 minutes—

and used two types of paint. Three parts are tested with

each combination of paint type and drying time. The data are

as follows:

(a) State and test the appropriate hypotheses using the analy-

sis of variance with 0.05.

(b) Analyze the residuals from this experiment.

14-3. An article in Industrial Quality Control(1956, pp.

5–8) describes an experiment to investigate the effect of two

factors (glass type and phosphor type) on the brightness of a

television tube. The response variable measured is the current

(in microamps) necessary to obtain a specified brightness

level. The data are shown in the following table:

(a) State the hypotheses of interest in this experiment.

(b) Test the above hypotheses and draw conclusions using the

analysis of variance with = 0.05.

(c) Analyze the residuals from this experiment.

14-4. An experiment was conducted to determine whether ei-

ther firing temperature or furnace position affects the baked

density of a carbon anode. The data are as follows:

Drying Time (min)

Paint 20 25 30

1747378

64 61 85

50 44 92

2929866

86 73 45

68 88 85

Phosphor Type

123

1 280 300 290

290 310 285

285 295 290

2 230 260 220

235 240 225

240 235 230

Glass

Type

(a) State the hypotheses of interest.

(b) Test the above hypotheses using the analysis of variance

with = 0.05. What are your conclusions?

(c) Analyze the residuals from this experiment.

14-5. Continuation of Exercise 14-4. Using Fisher’s LSD

method, investigate the differences between the mean baked

anode density at the three different levels of temperature in

Exercise 14-4. Use = 0.05.

14-6. Johnson and Leone (Statistics and Experimental

Design in Engineering and the Physical Sciences,John Wiley,

1977) describe an experiment conducted to investigate

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