# Optimal RSM Designs

Optimal is a good design choice when Central Composite and Box-Behnken do not fit your needs. You can specify the model you wish to fit, add multi-linear constraints, add center points, etc. Unlike the CCD and BB designs, where there is a specific pattern to the design points, points in these designs are chosen by an algorithm. Because of this point selection process and the fact that there are often many statistically equivalent sets of design points, it is possible to obtain slightly different designs for the same factor and model information.

Optimal designs are a recommended choice when you have categoric and numeric factors, constraints, need to fit a cubic or higher order model, or are trying to fit a custom model.

Numeric Factors: How many numeric factors are involved in this experiment?

Categoric Factors: How many categoric factors are involved in the experiment?

Note

Unlike CCD’s and BB designs, optimal designs are not automatically replicated for every categoric combination.

Name: (defaults to alphabetically ascending letters) Enter a descriptive name for each factor.

Units: (optional) Enter the units of measure for each factor.

Type:

Numeric Factors (to fit polynomial models)

Continuous: (default) Defines a range for the factor settings. Any value between the low and high level is available for the experiment.

Discrete: Defines the factor settings that available to the experiment for an otherwise continuous factor. Using discrete factor settings can make the experiment more convenient to conduct, while having minimal impact on the strength of the analysis. Check the evaluation node output for a design built with continuous factor settings versus one built with discrete settings to see the impact on the analysis. A discrete factor must have at least one more level than the order of the model needed to fit the response surface. (e.g. three levels are needed for a quadratic model, four levels are needed for a cubic model, etc.)

Only enough levels to fit the design model and provide a lack-of-fit test will be used; there is no requirement or guarantee that all the specified discrete settings will be used.

Categoric Factors (to compare treatments)

Nominal: (default) This type of factor is one that simply uses names or classes to describe the levels, for instance peanut butter types (Creamy, Chunky, SuperChunk).

Ordinal: This type of factor uses numbers that are ordered to show the natural progression, for instance temperature (200, 250, 300 Kelvin), where the baseline is the first level. These will be analyzed using orthogonal polynomial contrasts, which can be broken down into linear, quadratic, cubic, etc. components.

All levels and combinations of levels of categoric factors required to fit the design model will be included in the design.

Note

Instead of using ordinal contrasts you may be better off creating a discrete numeric factor.

Levels: If Type is continuous then only the low and high limits for the factor need to be defined. If Type is discrete then the number of levels (N) allowed needs to be entered. For categoric factors provide the number of levels.

L[i]: Specifies the setting to use in the experiment. L[1] is always the lowest setting for a numeric variable. The value of the level must increase with i. For categoric factors specify the exact spelling and punctuation for each of the treatments.

Edit Constraints button: Click this button to impose constraints on the numeric variables. Use this when some of the extreme combinations of the numeric factors will not produce a useful and/or measurable response. For more details use the help button on the Edit Constraints dialog.