Create Mixture Design

Mixture experiments are a special class of response surface experiments in which the product under investigation is made up of several components or ingredients. Designs for these experiments are useful because many product design and development activities in industrial situations involve formulations or mixtures. In these situations, the response is a function of the proportions of the different ingredients in the mixture. For example, you might be developing a pancake mixture that is made of flour, baking powder, milk, eggs, and oil. Or, you might be developing an insecticide that blends four chemical ingredients.

In the simplest mixture experiment, the response (the quality or performance of the product based on some criterion) depends on the relative proportions of the components (ingredients). The amount of components, measured in weights, volumes, or some other units, add up to a common total. In contrast, in a factorial design, the response varies depending on the amount of each factor.

Perform the analysis

Complete the following steps to specify the design.

Enter the name of your response variable

The worksheet includes a column with this name where you enter the data from the experiment.

Table of factors

Under Name, enter a descriptive name for each factor.

Enter lower and upper bounds for the components. If all the lower bounds are 0 and all the upper bounds are 1, then some experimental runs consist of only 1 component. When you specify the lower bound of a component but do not change the upper bounds of the other components, the design finds achievable upper bounds for the other components.

Lower bounds are necessary when any of the components must be in the mixture. For example, lemonade must contain lemon juice.
Upper bounds are necessary when the mixture cannot contain more than a specified proportion of an ingredient. For example, a cake mixture cannot contain more than 5% baking powder.

Number of replicates

Select the number of replicates. Replicates are multiple experimental runs with the same factor settings (levels). One replicate is equivalent to the base design, where you conduct each run once. With two replicates, you perform each run twice (in random order), and so on.

Adding replicates can help increase the precision of your model and increase the power to detect effects. To determine how many replicates to include in your design, consider the available resources and the purpose of your design. For example, in a screening design or in sequential experimentation you could begin with the base design (1 replicate) and then consider whether to add replicates after you analyze the data. You can add replicates to your design later with Stat > DOE > Modify Design. For more information on replicates, go to Replicates and repeats in designed experiments.

Example

Researchers want to study how the proportions of three ingredients in an herbal blend household deodorizer affect the acceptance of the product based on scent. The three components are neroli oil, rose oil, and tangerine oil.

Choose Stat > DOE > Quick Designs.
Select Select a Three-Factor Design.
Select Create an experiment with three components of a mixture. Select OK.
Select Understand the effect of changes in the proportions of components of a mixture. Select OK.
In the new dialog, in Enter the name of your response variable, enter Acceptance.

Complete the table with the following settings:

Name	Lower	Upper
Neroli	0	1
Rose	0	1
Tangerine	0	1

In Number of replicates, select None. Select OK.

The design summary table shows that the design has 15 runs. The worksheet contains the 15 runs in run order, which is random.