Six Sigma Black Belt Certified Practice Exam

If a full-factorial experiment is cost-prohibitive, which experiment would have fewer runs but the same number of variables?

1. Completely randomized factorial

2. Replicated factorial

3. Multilevel factorial

4. Fractional factorial

The correct answer is: Fractional factorial

In the context of experimentation, a fractional factorial design allows researchers to investigate multiple factors while significantly reducing the number of experimental runs needed compared to a full-factorial design. This approach involves selecting a subset of all possible combinations of the factors and levels, which maintains the ability to estimate main effects and interactions while requiring fewer resources and time. Choosing a fractional factorial design is particularly beneficial when cost constraints make a full-factorial experiment impractical. It retains the same number of variables as a full-factorial design, yet strategically reduces the number of runs. This enables analysts to draw meaningful conclusions without needing to execute an exhaustive number of experiments, making it a cost-effective solution in scenarios where full factorial designs would be too expansive to implement. The other options, while useful in their own contexts, do not effectively meet the need for reducing the number of experimental runs while maintaining the same depth of variable analysis. For instance, replicated factorial designs simply repeat the full set of runs, thereby increasing the total without addressing cost issues, and multilevel factorial designs could alter the number of levels per factor, impacting the number of runs needed. In contrast, fractional factorial specifically targets the need to explore a feasible subset of the experimental space while preserving the same number of variables to analyze.