In a 2^pdesign with one replicate per treatment, it sometimes happens that the observation for one of the treatments is missing, due to experimental error or to some other cause. When this happens, one approach is to replace the missing value with the value that makes the highest-order interaction equal to 0. Refer to Exercise 7. Assume the observation for the treatment where A, B, and C are all at their low level (ˆ’1) is missing.

a. What value for this observation makes the three-way interaction equal to 0?

b. Using this value, compute estimates for the main effects and the interactions.

Refer to Exercise 7.

The article €œAn Investigation into the Ball Burnishing of Aluminium Alloy 6061-T6€ (M. El-Axir, J Engineering Manufacture, 2007:1733€“1742) presents the results of study that investigated the effects of three burnishing factors on the reduction in diameter of the workpiece (in μm). The factors are A: Burnishing speed, B: Burnishing force, and C: Burnishing feed. The results presented in the following table form a 2³ factorial design (some additional results are omitted).

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Reduction B 570 -1 -1 353 778 769 544 319 651 1 1 1 625