# Fractional Factorial Design

A fractional factorial design is an experimental design (DoE) used to examine the effects of multiple factors (variables) on a response variable. This approach reduces the effort and cost of experiments by analyzing only a subset of the possible combinations of factor levels, instead of testing all combinations as in a full factorial design.

In a full factorial design, all possible combinations of factor levels are tested comprehensively. In contrast, a fractional factorial design deliberately omits specific combinations. This leads to a reduction in the number of required trials, thereby lowering effort and costs, but also results in a reduced amount of information gathered.

### Advantages of Fractional Factorial Designs

**Efficiency:** Significantly fewer experiments are needed to obtain information
about the main effects and important interactions.

**Cost savings:** Less material, time, and resources are required.

**Clarity:** Even in complex experiments with many factors, a fractional factorial
design enables meaningful analysis.

### Disadvantages of Fractional Factorial Designs

**Loss of information:** Due to the reduced number of trials, some higher-order
interactions may not be captured.

**Result distortion:** There is a risk of "aliasing," where effects may be
confounded with each other, potentially leading to misinterpretations.

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