MANE 6313
Week 9, Module A
Student Learning Outcome
- Select an appropriate experimental design with one or more factors,
- Select an appropriate model with one or more factors,
- Evaluate statistical analyses of experimental designs,
- Assess the model adequacy of any experimental design, and
- Interpret model results.
Module Learning Outcome
Describe fractional factorial designs, generators, defining relation and aliasing schemes for a one-half fraction.
Resources for the Week 9, Module A micro-lecture are:
Fractional Factorial Designs
- 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.
Key Ideas for Fractional Factorial 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.
The one-half fraction of a \(2^k\) design
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This design results in a \(2^{k-1}\) experiment, a half-fraction.
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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 \(-ABC\).
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We always associate \(I\) with the positive fraction. Thus, \(I=ABC\) and we call this quantity the defining relation for the fractional factorial experiment.
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The fraction containing the positive generator is called the principal fraction. The other fraction is called the alternate or complementary fraction.