# DOE Analysis

A designed experiment is a series of runs, or tests, in which you purposefully make changes to input variables at the same time and observe the responses.

In industry, designed experiments can be used to systematically investigate the process or product variables that affect product quality. After you identify the process conditions and product components that affect product quality, you can direct improvement efforts to enhance a product's manufacturability, reliability, quality, and field performance.

To add output from a DOE, go to Add and complete a form.

## 2k factorial DOE

Use a 2-level factorial design to create a designed experiment to study the effects of 2 − 15 factors. With a 2-level factorial design, you can identify important factors to focus on with further experimentation.

For example, a group of engineers plans an experiment to investigate the effects of three factors on the warping that occurs in a copper plate. They create a 2-level factorial design by specifying the design information, including blocks and center points. To see an example, go to Minitab Help: Example of Create 2-Level Factorial Design.

A 2k factorial DOE has the following types.
2k full factorial design
The experiment uses all possible combinations of factor settings with 8 runs for 3 factors, 16 runs for 4 factors, 32 runs for 5 factors, and so on.
2k fractional factorial design
The experiment uses a fraction (one-half, one-fourth, and so on) of all possible combinations of factor settings, with a smaller number of runs than the 2k full factorial design.
###### Note

Use this form to record the data analysis from your experiment. Use the DOE Planning form to help you design the experiment.

For more information on available designs, go to Minitab Help: Factorial and fractional factorial designs.

### Data considerations

Decide whether you want to run a full-factorial or fractional-factorial DOE.
• If the number of factors is less than 5, run the 2k full factorial design to allow for modeling all 2-factor interactions with only 8 (3 factors) or 16 (4 factors) runs.
• If the number of factors is 5 or more, run the resolution V or higher 2k fractional factorial design to reduce the number of runs while still modeling all 2-factor interactions.

## General full factorial DOE

Use a general full factorial design to create a designed experiment to study factors that can have any number of levels. You can use a general full factorial design to create full resolution, 2-level designs for 8 or more factors.

For example, a marketing manager wants to study the influence that three categorical factors have on the ability of test subjects to recall an online advertisement. Because the experiment includes factors that have 3 levels, the manager uses a general full factorial design. To see an example, go to Minitab Help: Example of Create General Full Factorial Design.

###### Note

Use this form to record the data analysis from your experiment. Use the DOE Planning form to help you design the experiment.

For more information on available designs, go to Minitab Help: Choose a factorial design.

### Data considerations

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 large, and therefore, expensive. Also, for screening purposes, GFF designs provide much more information than you need. You should screen out all possible inputs using two levels, then add inputs needing more than two levels to the screened design.

## Mixture DOE

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. To see an example, go to Minitab Help: Example of Create Mixture Design (Simplex Centroid).

### Data considerations

Before you create a mixture design, first determine which design is most appropriate for your experiment. Minitab provides simplex centroid, simplex lattice, and extreme vertices designs. Consider the following steps.
1. Identify the components, process variables, and mixture amounts that are of interest.
2. Determine the model that you want to fit.
3. Ensure adequate coverage of the experimental region of interest.
4. Determine the impact that other considerations have on your choice of a design. Examples of other considerations include cost, time, availability of facilities, and lower and upper bound constraints.

For more information on available designs, go to Minitab Help: Choose a mixture design.

## Multiple response optimization

Use multiple response optimization to determine the optimal settings in an experiment with a single output, or with multiple competing outputs.

An optimal design uses the "best" group of design points, selected from reducing or augmenting the number of experimental runs in the original design. Optimal design capabilities can be used with general full factorial designs, response surface designs, and mixture designs. To see an example, go to Minitab Help: Example of selecting a D-optimal response surface design.

### Data considerations

The candidate points must be a general full factorial, response surface, or mixture design. The sample size and power should be desirable for a practically important effect size. Usually, you use optimal designs to decrease the number of experimental runs, but smaller sample sizes may not provide a design that can detect small effects with sufficient power. For details, go to Minitab Help: Data considerations for Select Optimal Design.

## Response surface DOE

A response surface design is a set of advanced design of experiments (DOE) techniques that help you better understand and optimize your response.

Response surface design methodology is often used to refine models after you have determined important factors using screening designs or factorial designs; especially if you suspect curvature in the response surface.

For example, an engineer wants to analyze the injection-molding process for a plastic part. First, the engineer performs a fractional factorial design, identifies the important factors (temperature, pressure, cooling rate), and determines that curvature is present in the data. Then, the engineer creates a central composite design to analyze the curvature and find the best factor settings. To see an example, go to Minitab Help: Example of Create Response Surface Design (Central Composite).

### Data considerations

There are two main types of response surface designs.
Central Composite designs
Central Composite designs can fit a full quadratic model. They are often used when the design plan calls for sequential experimentation because these designs can include information from a correctly planned factorial experiment.
Box-Behnken designs
Box-Behnken designs usually have fewer design points than central composite designs; therefore, they are less expensive to run with the same number of factors. They can efficiently estimate the first- and second-order coefficients; however, they cannot include runs from a factorial experiment. Box-Behnken designs always have 3 levels per factor, unlike central composite designs, which can have up to 5. Also, unlike central composite designs, Box-Behnken designs never include runs where all factors are at their extreme setting, such as all the low settings.

For more information on available designs, go to Minitab Help: What are response surface designs, central composite designs, and Box-Behnken designs?.