# Generation of a mixture design

Use this tool to generate a mixture design with multiple factors. Available in Excel with the XLSTAT software.

## Mixture design description

Mixture designs are used to model the results of experiments where these relate to the optimization of formulation. The resulting model is called "mixture distribution"

Mixture designs differ from factorial designs by the following characteristics:

• The factors studied are proportions which sum is equal to 1.

• Construction of the design of experiments is subjected to constraints because the factors may not evolve independently of each other (the sum of the proportions being 1).

## Mixture design options in XLSTAT

Design of experiments: Choose the experiment plan you want to use. Depending on the number of factors, different plans are offered.

Degree of the model: In the case of a simplex design, you have the possibility to choose the number of degrees of the model.

Total quantity of mixture: Enter the total quantity of mixture. It is the quantity of mixture used in the experiment.

Display experiments sheets: Activate this option if you want to display individual Excel sheets for each experience. This can be useful in order to print them out and carry out the experiments.

## Mixture design results in XLSTAT

Variables information: This table shows the information about the factors. For each factor the short name, long name, unit and physical unit are displayed.

Experimental design: This table displays the complete experimental design. Additional columns include information on the factors and on the responses, a label for each experiment, the sort order, the run order and the repetition.

Responses optimization: The responses optimization table of is displayed after the experimental design. You must then select the following parameters:

• Objective: Choose the objective of the optimization. You have the choice between minimum, optimum and maximum.

If the selected objective is the optimum or the maximum, the following fields are activated:

• Lower: Enter for each answer the value of the lower bound below which the desirability is 0.

• Target (left): Enter the value of the lower bound above which desirability is 1 for each response.

If the selected objective is the optimum or the minimum, the following fields are activated:

• Target (right): Enter for each response the value of the upper bound below which the desirability is equal to 1.

• Lower: Enter for each answer the value of the upper limit above which the desirability is 0.

• s: Activate this option if the increasing desirability function must be non-linear. Then enter the value of the shape parameter which must be between 0.01 and 100.

• t: Activate this option if the decreasing desirability function must be non-linear. Then enter the value of the shape parameter which must be between 0.01 and 100.

• Weight: Activate this option if the answers must have an exponential value different from 1 when calculating desirability. Then enter the value of the shape parameter which must be between 0.01 and 100.  ### analyze your data with xlstat

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