# General Full Factorial (GFF) DOE

## Summary

Provides a methodology for conducting controlled experiments (DOEs) where the factors (process inputs) can be held at any number of levels (settings). The goals of this type of experiment are usually focused on obtaining a model that definitively selects the vital process inputs, investigating interactions between the vital inputs, and making predictions about the process output.

###### Note

When you insert this tool into the Roadmap, you can use it to record the data analysis from your experiment. Use the DOE Planning Worksheet form to help you design the experiment.

• Which process inputs (factors) have the largest effects on the process output (which inputs are the key inputs)?
• Did important interactions exist between factors?
• How much of the variation in the process output can be explained by varying the process inputs?
• What settings of the key inputs will result in the optimal process output?
When to Use Purpose
Mid-project This type of experiment is the only one that can accommodate categorical factors (process inputs) that must be investigated at more two levels.
Mid-project Models main effects and all possible interactions between factors, which is beneficial for determining the settings for the key inputs resulting in the optimal process output.

### Data

Continuous Y, categorical or numeric X's tested at two or more discrete levels.

## How-To

1. State your factors (Minitab allows up to 15 factors) and their levels of interest (each factor may have up to 100 levels).
2. Verify the measurement systems for the Y data and the inputs (factors) are adequate.
3. Develop a data collection strategy (who should collect the data, as well as where and when; the preciseness of the data; how to record the data, and so on).
4. Run the experiment and reduce to a final model by eliminating terms with high p-values (typically > 0.05). Note: Terms are eliminated in order with the more complex terms evaluated and eliminated first. For example, eliminate all nonsignificant 3-factor interactions before evaluating 2-factor interactions.
5. Use either the response optimizer or interactions and main effects plots to determine optimal settings of significant factors.

## Guidelines

• First, you should develop a sound data collection strategy to ensure that your conclusions are based on truly representative data.
• The residuals of the final model must be independent, reasonably normal, and with reasonably equal variance. The residuals are usually analyzed by a histogram, normal probability plot, and plots of the residuals versus fits and residuals versus order. You can display these graphs at one time using the Four in one option.
• General full factorial (GFF) designs are not recommended for use in screening, or reducing, the number of potentially important inputs. The size of the experiment can be very large, thus the experiment can be very expensive. Also, for screening purposes, GFF designs provide much more information than you need. You should screen out all possible inputs using two levels, and then add inputs needing more than two levels to the screened design.
• If all factors can be evaluated at two levels plus an optional center point, the 2K factorial (fractional or full) DOE is generally preferred as it has the following benefits:
• Provides an efficient means for screening out unimportant factors.
• Provides an easy-to-use prediction equation.
• Provides analysis of saturated designs.
• May be be expanded easily to a central composite design for fitting a quadratic model.
• In the event that 3-way interactions are deemed unlikely and unimportant, the 2K Fractional Factorial design with a minimum resolution V becomes the preferred design.
• When using GFF, strive to reduce the number of levels because the number of runs will quickly grow. For example, 3 X 4 X 5 X 6 = 360 runs. If we can eliminate one level from each factor, 2 X 3 X 4 X 5 = 120 runs.
• Check for possible outliers in the unusual observations table in the Session window output.
• While the discussion here focuses on designed experiments created by Minitab, you can use the Analyze portion of the GFF DOE to analyze any numeric experimental data (for example, two factors each at 10 levels). Do this by entering the Y and X data into Minitab and then use Stat > DOE > Factorial > Define Custom Factorial Design to define the factors. This newly defined custom design can be analyzed in the usual manner.
• If you have discrete numeric data from which you can obtain every equally spaced value and you have measured at least 10 possible values, you can evaluate these data as if they are continuous.
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