# DOE planning

Use DOE planning to set up and plan experiments. Designed experiments (DOEs) provide a cost-effective methodology for simultaneously testing multiple factors. A DOE consists of a number of experimental runs, or trials. In each trial, the factors to be tested are set at predetermined levels. The type and size of the experiment are determined by the goals of the experimenter and the nature of the factors. Typical goals might include eliminating unimportant factors, developing a full predictive model (Y = f(X)), describing how the process inputs jointly affect the process output, and determining the optimal settings of the inputs.

Use the DOE planning worksheet to set up and plan experiments using two basic types of DOEs.
• General full-factorial experiments
• Factors can have any number of levels
• Always a full-factorial
• Two-level (also called 2K) factorial experiments
• Every factor has exactly two levels
• Either a full-factorial or fractional-factorial
• What factors will be used in the DOE and at what levels?
• Which type of DOE will be used to test the process inputs (factors)?
• What are the goals of the experiment?
• What is the timeline for the experiment?
• Did you have any special considerations when conducting the experiment?
When to Use Purpose
Mid-project Use the DOE planning worksheet before setting up and running any DOE. The planning worksheet is a record of the goals for the experiment and the conditions under which the experiment is to be run. This document is an effective communication tool for explaining the rationale for the experiment to important stakeholders.

## Guidelines

• The first question that must be answered is which type of DOE to use:
• When setting the levels of the factors, you should limit the number of levels for each factor to two. DOEs with two levels for each factor are far more efficient (fewer experimental runs) than those in which some factors have more than two levels.
• 2K factorial DOEs provide a very easy-to-use prediction equation, while General Full Factorial (GFF) DOEs do not. If obtaining a prediction equation is one of the important goals of the experiment, the 2K Factorial DOEs are highly recommended.
• If any factor must be evaluated at more than two levels, use the GFF.
• If you are using a 2K factorial DOE, consider using high-resolution (resolution V or higher) fractional DOEs instead of full-factorial designs. If you use a fractional DOE you can either reduce the size of the experiment or replicate the design with the same number of runs you would have had in the full-factorial design. If 3-way interactions are deemed unlikely and unimportant, the 2K fractional factorial design with a minimum resolution V is the preferred design because it will reduce the sample size while still providing the needed level of analysis.
• For three factors, all at two levels, the 2K full factorial in eight runs is generally recommended.
• For four factors, all at two levels, the 2K full factorial in 16 runs is generally recommended, unless the runs are extremely expensive and it is not important to estimate all 2-factor interactions.
• For five or more factors, all at two levels, 2K fractional factorial designs with resolution V or higher are generally recommended.
• Use the design-selection tables in Minitab to help you select an appropriate DOE (for example, the number of runs, given the number of factors you want to include).
• Whenever possible, the runs in the experiment should be done in random order to prevent confusing a factor effect with the effect of an untested factor (sometimes called a lurking variable).
• Replicating the DOE increases your ability to detect smaller factor effects. If you are not sure how many replicates you need, use the power and sample size calculations in Minitab to determine the number. To use this command, you will need to know (at least approximately) the standard deviation of the output, the size of the effect you want to detect, how much risk you are willing to assume at both missing an effect of interest and wrongly determining an effect is statistically significant.
• The 2K factorial DOE (both full-factorial and fractional-factorial) relies on the assumption that the effects of the factors on the response are reasonably linear (can be modeled adequately with a straight line) in the inference space. You should include center points in your 2K factorial DOE whenever you doubt the linearity of the effects. The center points produce a test for curvature, that is, they test the assumption of linearity. If the curvature is statistically significant, you must still decide whether the amount of curvature present is of concern from a practical standpoint.
• When adding center points to the DOE, the following procedures are often recommended:
• Use the current process settings of the factors as the center point, which gives the operators running the experiment a comfort level with familiar settings of the factors.
• Do not fully randomize the center points in the DOE. Instead, put one or two center points at the start of the experiment, one or two in the middle, and one or two at the end, which provides a check for trends during the running of the experiment.

## How-to

1. State the outputs that will be measured during the experiment.
2. State your factors and their levels of interest.
3. Verify the measurement systems for the Y data and the inputs (factors) are adequate.
4. Develop a data collection strategy. For example, determine who should collect the data, where and when the data should be collected, how many data values are needed, the preciseness of the data, how to record the data, and so on.
5. Select the type of DOE to be used and the number of times the experiment will be replicated.
6. Answer the checklist questions at the end of the worksheet.
7. Obtain approval to proceed with the experiment.