How to analize fracfactgen and fracfact results?

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Hi!
I designed an Fractional factorial experiment with:
generators = fracfactgen('a b c d e f g h i j k l m n o p q r',[],3);
[X,confounding] = fracfact(generators);
I have 18 parameters, 2 levels of each one and I choose resolution 3. I got a X matrix of dimensions 32x18 and a array "confounding" of 172x3.
I run the 32 cases and I would like to plot the results in order to represent the influence of each parameters. I try
pareto chart or maineffectsplot but they are for full factorial experiments.
My question is how could I interpret/analize the fractional factorial experiment :)
Thanks in advance

Answers (1)

Abhimenyu
Abhimenyu on 31 Jan 2024
Hi Myriam,
I understand that you want to interpret the results of the fractional factorial design experiment. In a fractional factorial design, especially one with a resolution of III (3), the interpretation of the results can be quite complex due to the confounding of main effects and interactions. In resolution III designs, main effects are confounded with two-way interactions where the effect of a single factor and the interaction of two other factors cannot be distinguished.
Please follow the below mentioned steps to analyze the fractional factorial experiment:
  • Analyze confounding structure: The "confounding array" should be examined to know which effects are confounded with each other. The higher-order interactions should be assumed negligible in order to interpret the main effects and lower-order interactions.
  • Estimate effects: Calculate the effects of each factor. For a resolution III design, the main effects can be estimated by averaging the differences between the high and low levels across all runs for each factor.
  • Main effects plot: Even though "maineffectsplot" MATLAB function is typically used for full factorial designs, it can still be used to visualize the main effects in the fractional factorial design as shown by the code mentoned below. However, these effects may be confounded with two-way interactions.
maineffectsplot(X, response);
%Replace response with your actual response variable from the 32 runs.
  • Interaction plots: If certain interactions are important, these interactions can be plotted using "interactionplot" MATLAB function as shown below in the example MATLAB code. This will help to visualize how the response changes when two factors are varied together.
interactionplot(X, response, 'varnames', {'A', 'B', 'C', ...});
%Replace the varnames with the names of your factors.
  • Statistical analysis: Perform a statistical analysis, such as regression or ANOVA, to determine which factors and interactions are statistically significant. This will involve fitting a statistical model to your data and examining the p-values for each term in the model.
  • Pareto chart: A pareto chart can be used to visualize the standardized effects to see which ones are most influential. However, some of these effects include confounded interactions.
[effects, stdeffects] = fracfactest(X, response);
pareto(stdeffects, names);
%Replace "names" with the names of the effects, and "response" with your response data.
  • Check for negligible interactions: Given the resolution of the design, assumption must be made so that certain interactions are negligible to interpret main effects. If the knowledge of the system suggests that certain two-way interactions are likely to be small, this assumption might be more justifiable.
  • Refine the model: Based on the results of your analysis, you may decide to refine your model by conducting additional experiments, possibly focusing on the factors that appear to be most significant.
If the interactions are suspected to be significant, a higher-resolution design may be necessary for a clear interpretation.
Please follow the below mentioned MATLAB R2023b documentation link to understand about "interactionplot" MATLAB function:
I hope this helps to resolve your query.
Regards,
Abhimenyu

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