Use FrF2 to create a quarter fraction 25−2 design.

(a) Use the design.info function to examine the aliases and determine the generators used by FrF2 to create the design.

(b) Determine the dening relation.

(c) Verify that the alias structure for this design can be obtained from the dening relation you found in (b).

(d) Suppose that after analysis of data from this experiment that two main eects A and D appear to be signicant. Because of the confounding between main eects and two-factor interactions, interpreting the results to mean that these two main eects are the only signicant eects could be misleading. Using the eect heredity principle, suggest two alternate plausible models that could explain the data.

(e) List the experiments in a foldover fraction that you could use to augment the original eight experiments in order to remove the aliasing between main eects and two-factor interactions.