Suppose an engineer wants to study the effects of seven fact

Suppose an engineer wants to study the effects of seven factors and is willing to make 32 runs. He elects to perform a 2^7-2 fractional factorial design with generators G = ABC and F = AB. The main effect A is confounded with what other effects? Suggest an alternative plan that produces less confounding of low-order terms.

Solution

In a 2^7-2 fraction factorial experiment

Generators are G=ABC and F = AB

i.e I = ABCG anf I = ABF

Now the generalized interaction of the generator ABCG and ABF is CFG

Therefore teh complete defining relation for this design is

I = ABCG = ABF = CFG

The alised structure of effect A is

A = BCG = BF = ACFG

The effect A is comfounded with these effects

An alternative plan is to use a resolution IV or resolution V design in which no main effect is confounded with any other main effect or two factor interaction