Generating a mixture design and analysing the results with XLSTAT-DOE

How can I generate a mixture design and how to do the corresponding analysis of the results?

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

 An Excel sheet with both the data and the results can be downloaded by clicking here. Data are based on the example described by Phan Tan Luu. It is an experimental design to study the hardness of a mixture. This mixture has 3 components: lactose, CACO3 and cellulose. We would like to generate the mixture design using a Scheffé's simplex of degree 2. 

A design (3; 2) is generated, it has 6 experiments. There is no constraint on the components.

The quantity of mixture is set equal to 1 and we decide to make 2 repetitions to have enough data to run a quadratic model.

 1. Step: Generate an experimental design

 After opening XLSTAT, click the DOE button in the ribbon and select “Mixture designs” (see below).

 Once you've clicked on the button, the dialog box appears. Select the data on the Excel sheet.

 Enter the model Name (mixture), select the number of factors (3 in this example), the experimental design is a simplex, the number of degrees of the model is 2 and the total quantity of mixture is one. We only have one response and select 2 repetitions.

dialog box mixture model

 In the “factors” tab, select the corresponding columns in the Excel sheet “Data” as shown in the screenshot in order to enter the information about the factors:

dialog box mixture design

 In the “responses” tab enter the information about the response variable.

dialog box mixture design

 Once you have clicked on the “Ok” button, the computation starts.

 The design table itself is displayed in the Excel sheet mixture.

result design

 2. Step: Carrying out the experiments.

Now the 12 experiments are carried out and the resulting distance is written in the corresponding Excel cell in the generated experimental design.

In the attached file, the results are already entered in order to be able to continue with the analysis. The results are on a yellow background in the file to find them easier.

result design

 3. Step: Analysis of the experiments

 After opening XLSTAT, click the DOE button in the ribbon and select “Analysis of a surface response design” (see below).

 Once you've clicked on the button, the dialog box appears. Select the data on the Excel sheet.

 Now you are able to select the data in the Excel sheet. Select the name of the model by selection the corresponding cell B27 in the Excel sheet of the experimental design (here mixture!$B$27). By the help of this selection XLSTAT can find information about the chosen experimental planning in the hidden Excel sheet and will use this information during the analysis. Select the result column as shown in the screenshot below.

dialog box analyse mixture design

Once you have clicked on the “Ok” button, the computation starts.

The results are classical ANOVA results. The analysis of variance table shows a significant effect of one of the component.

doe mixture anova

Further details about the model are available in the two following sections with the model parameters and the model equation.

 doe mixture parameter

Then the experimental design is represented using a ternary diagram.

mixture design ternary diagram

The optimum can be located with the ternary diagram with a combination (1, 0, 0), with only the lactose product.

Click here for other tutorials.

About KCS

Kovach Computing Services (KCS) was founded in 1993 by Dr. Warren Kovach. The company specializes in the development and marketing of inexpensive and easy-to-use statistical software for scientists, as well as in data analysis consulting.

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