4. Because the elastometric connector experiments described in Section 12.3 required physical experimentation, Song and Lawson (1988) suggested us-

ing a single array design to save on the number of experiments required.

Table 12.20 shows a resolution IV 27????2 fractional factorial design and the resulting pull-o force. The factor names and levels are the same as those shown in Table 12.3 of Section 12.3. The generators for the design were F = ABC and G = ABD.

(a) What is the dening relation for this design, and how many of the 12 control-by-noise factor interactions can be estimated clear of other main eects or two-factor interactions?

(b) Using the SAS ADX, can you nd a 32-run resolution IV design that has more control-by-noise factor interactions clear? If so, what are the generators?

(c) Calculate a set of 31 saturated eects for this design, and make a normal plot to determine which eects, interactions and confounded strings of two-factor interactions appear to be signicant. Is there a clear interpre-

tation of any confounded strings of interactions?

(d) Make interaction and contour plots of any two-factor interactions be-

tween control factors and noise factors and use them to choose the level of control factors that will minimize the eect of noise factors.

(e) Are there any adjustment factors? If so, what levels should be chosen to maximize the pull-o force?

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Table 12.20 Single Array Experiment for Elastometric Connector A B C D E F G pull-off force Low High High High High High Low 120 150 75 22.0 High 120 150 75 27.6 High High High Low 120 72 25 22.1 High High Low High 120 72 75 20.2 Low Low Low High 120 72 75 18.9 High High High High 24 150 25 13.8 Low High High High 24 72 75 15.2 Low Low Low Low 120 150 25 23.1 High Low High High 24 72 75 16.1 High Low High High 120 72 25 20.1 Low Low High High 120 150 75 21.9 High Low Low Low 24 72 25 17.1 High Low High Low 24 150 25 18.1 Low High Low High 24 150 75 9.6 Low Low High Low 24 72 75 18.3 Low High Low Low 120 72 75 19.1 High Low High Low 120 150 75 27.0 Low Low Low Low 24 150 75 17.3 Low Low High High 24 150 25 17.7 Low Low Low High 24 72 25 14.7 High Low Low Low 120 72 75 22.2 Low High High Low 24 150 25 21.1 Low Low High Low 120 72 25 24.3 Low High Low Low 24 72 25 13.9 High Low Low High 24 150 75 19.4 High Low Low High 120 150 25 22.7 High High Low High 24 72 25 14.6 High High Low Low 120 150 25 23.3 High High High Low 24 72 75 20.4 Low High Low High 120 150 25 22.6 Low High High High 120 72 25 21.0 High High Low Low 24 150 75 17.5