MANE 6313

Week 10, Module A

Describe fractional factorial designs, generators, defining relation and aliasing schemes for a one-half fraction.

As the number of factors grows in a \(2^k\) experiment, the number of runs often exceeds our ability to conduct the experiments. e.g. \(2^6\) experiment requires 64 runs.
Often we are only interested in a few effects. E.g. in the \(2^6\) experiment, there are 6 main effects and 15 two-factor interactions. The remaining 42 degrees of freedom are associated with three-factor or higher interactions.
Often we can get the information we need by running only a fraction of the factorial experiment
Fractional factorials are often used as screening experiments.

The sparsity of effects principle. The system or process is likely to be primarily driven by some of the main effects and low-order interactions.
The projection property. When we identify unimportant variables and remove them from the model, the resulting model is stronger (larger) designs.
Sequential Experimentation. It is possible to combine the runs of two (or more) fractional factorials to assemble sequentially a larger design to estimate the factor effects and interactions of interest.

This design results in a \(2^{k-1}\) experiment, a half-fraction.
You must select an effect to generate the two fractions. This effect is called the generator. E.g. in a \(2^3\) design select \(ABC\) as the generator. The other fraction is \(-ABC\).
We always associate \(I\) with the positive fraction. Thus, \(I=ABC\) and we call this quantity the defining relation for the fractional factorial experiment.
The fraction containing the positive generator is called the principal fraction. The other fraction is called the alternate or complementary fraction.