Fractional Factorial Design: Screen Many Factors with Fewer Runs
What is a Fractional Factorial Design?
A fractional factorial design runs only a fraction of the full factorial: 2^(k-p) means k two-level factors run 1/2^p of the 2^k full design, for example 2^(5-2) uses 8 of 32 runs. It screens many factors with few runs; the cost is that some effects are confounded, or aliased, with each other, and the degree of confounding is described by the design resolution. Resolution III estimates main effects confounded with two-way interactions, IV keeps main effects clear of three-way interactions while two-way interactions alias each other, and V estimates main effects and two-way interactions clearly.
When to Use It
Use a fractional design in the screening phase when there are 5 or more factors and you suspect only a few are important. Resolution III gives the fewest runs but aliases main effects with two-way interactions, so it is for pure screening; resolution IV is the recommended compromise, with clean main effects and mutually aliased two-way interactions; resolution V is chosen when the factor count is moderate and you want clear two-way interactions. The tool recommends a feasible resolution and generators from your factor count and run budget.
How to Use It (Step by Step)
Enter the number of factors and the acceptable number of runs; the tool recommends a 2^(k-p) design and resolution, then generates the experiment plan with run order, randomization and the alias structure. Execute the runs, fill in the responses, and analyze the main-effect Pareto plot and significance. After screening the key factors, add experiments, such as a fold-over to break the aliases or a full factorial or RSM, to refine the model, and confirm screening conclusions with a confirmation run.
Key Formulas / Example
The design is defined by its defining relation, such as I = ABCD, which determines which effects are aliased. A fold-over reverses all factor signs in a second batch and raises resolution III to IV, separating main effects from two-way interactions. The alias table lists every estimable effect with its aliases, and it is the essential reference for interpreting screening results.