Applied Statistics and Probability for Engineers

14-7 2kFACTORIAL DESIGNS 523

14-11. The percentage of hardwood concentration in raw

pulp, the freeness, and the cooking time of the pulp are being

investigated for their effects on the strength of paper. The data

from a three-factor factorial experiment are shown in the fol-

lowing table.

Cooking Time 1.5 hours Cooking Time 2.0 hours

Freeness Freeness

350 500 650 350 500 650

10 96.6 97.7 99.4 98.4 99.6 100.6

96.0 96.0 99.8 98.6 100.4 100.9

15 98.5 96.0 98.4 97.5 98.7 99.6

97.2 96.9 97.6 98.1 96.0 99.0

20 97.5 95.6 97.4 97.6 97.0 98.5

96.6 96.2 98.1 98.4 97.8 99.8

Percentage

of Hardwood

Concentration

(a) Analyze the data using the analysis of variance assuming

that all factors are fixed. Use 0.05.

(b) Find P-values for the F-ratios in part (a).

(c) The residuals are found by Graphically

analyze the residuals from this experiment.

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EXERCISES FOR SECTION 14-5

14-6 FACTORIAL EXPERIMENTS WITH RANDOM

FACTORS (CD ONLY)

14-7 2kFACTORIAL DESIGNS

Factorial designs are frequently used in experiments involving several factors where it is

necessary to study the joint effect of the factors on a response. However, several special

cases of the general factorial design are important because they are widely employed

14-12. The quality control department of a fabric finishing

plant is studying the effects of several factors on dyeing for a

blended cotton/synthetic cloth used to manufacture shirts.

Three operators, three cycle times, and two temperatures were

selected, and three small specimens of cloth were dyed under

each set of conditions. The finished cloth was compared to a

standard, and a numerical score was assigned. The results are

shown in the following table.

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

sis of variance with 0.05.

(b) The residuals may be obtained from

Graphically analyze the residuals from this experiment.

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Temperature

300  350 

Operator Operator

Cycle Time 12 31 2 3

23 27 31 24 38 34

40 24 28 32 23 36 36

25 26 28 28 35 39

36 34 33 37 34 34

50 35 38 34 39 38 36

36 39 35 35 36 31

28 35 26 26 36 28

60 24 35 27 29 37 26

27 34 25 25 34 34

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