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## Quick reference

### Full Factorial Design of Experiments

The full factorial Design of Experiments (DOE) methodology, is a statistical analysis of the results of a set of experiments or tests. These tests use test samples that vary the factors being analyzed between high and low levels. Each combination of factors is tested.

### When to use

Full factorial DOE is often used to create a statistically valid equation for the system performance based upon the input values of the selected factors being studied. It determines the performance at the edges of the design space and when multiple level factors are used it creates a very accurate model for the entire design space.

### Instructions

The full factorial DOE provides a comprehensive analysis of the design space for the system being analyzed. In the analysis the factors to be studied are selected. A high and low value for each factor is determined. This is often the upper or lower specification or tolerance limit. It is critical that this factor is controllable so that the configuration of each test sample can be established. In some cases, multiple levels of intermediate points are also used, however this will greatly increase the number of experimental tests.

In the full factorial DOE, a test sample representing each combination of high and low factor setting is created. If the DOE is using two-level factors, that means the number of test sample is 2^{N} and if the factors are three-level factors the number of test samples is 3^{N} – where N is the number of factors.

Each sample is tested and the performance is recorded. The results of all the samples testing is statistically analyzed to determine the effect of each factor and the interaction effects between factors with respect to the system level performance. The final result is an equation that can be used to predict performance and the equation can be used to identify the factor settings that will yield optimal performance.

### Hints & tips

- Be certain the factors are controllable. It is critical that you can precisely set each factor at the desired level on each test sample.
- You must do all the tests for the statistics to be valid. So, make sure you have the resources to conduct all tests.
- The basic two-level factors assume a linear response of the system due to the factor. If you know the system response is non-linear, you should consider using multi-level factors.

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