Design of Experiments Guide • Response Surface Designs • Creating a Response Surface Design
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Creating a Response Surface Design
Response Surface Methodology (RSM) is an experimental technique invented to find the optimal response within specified ranges of the factors. These designs are capable of fitting a second-order prediction equation for the response. The quadratic terms in these equations model the curvature in the true response function. If a maximum or minimum exists inside the factor region, RSM can estimate it. In industrial applications, RSM designs usually involve a small number of factors. This is because the required number of runs increases dramatically with the number of factors. Using the response surface designer, you choose to use well-known RSM designs for two to eight continuous factors. Some of these designs also allow blocking.
Response surface designs are useful for modeling and analyzing curved surfaces.
To start a response surface design, select DOE > Response Surface Design, or click the Response Surface Design button on the JMP Starter DOE page. Then, follow the steps described in the following sections.
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Enter Responses and Factors
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Choose a Design
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Specify Axial Value (Central Composite Designs Only)
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Specify Output Options
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View the Design Table
Enter Responses and Factors
The steps for entering responses are outlined in Responses in Custom Designs.
Factors in a response surface design can only be continuous. The Factors panel for a response surface design appears with two default continuous factors. To enter more factors, type the number you want in the Factors panel edit box and click Add, as shown in Enter Factors into a Response Surface Design.
Enter Factors into a Response Surface Design
Click Continue to proceed to the next step.
Choose a Design
Highlight the type of response surface design you want and click Continue. The next sections describe the types of response surface designs shown in Choose a Design Type.
Choose a Design Type
Box-Behnken Designs
The Box-Behnken design has only three levels per factor and has no points at the vertices of the cube defined by the ranges of the factors. This is sometimes useful when it is desirable to avoid extreme points due to engineering considerations. The price of this characteristic is the higher uncertainty of prediction near the vertices compared to the central composite design.
Central Composite Designs
The response surface design list contains two types of central composite designs: uniform precision and orthogonal. These properties of central composite designs relate to the number of center points in the design and to the axial values:
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Uniform precision means that the number of center points is chosen so that the prediction variance near the center of the design space is very flat.
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For orthogonal designs, the number of center points is chosen so that the second order parameter estimates are minimally correlated with the other parameter estimates.
Specify Axial Value (Central Composite Designs Only)
When you select a central composite (CCD-Uniform Precision) design and then click Continue, you see the panel in Display and Modify the Central Composite Design. It supplies default axial scaling information. Entering 1.0 in the text box instructs JMP to place the axial value on the face of the cube defined by the factors, which controls how far out the axial points are. You have the flexibility to enter the values you want to use.
Display and Modify the Central Composite Design
Rotatable
makes the variance of prediction depend only on the scaled distance from the center of the design. This causes the axial points to be more extreme than the range of the factor. If this factor range cannot be practically achieved, it is recommended that you choose On Face or specify your own value.
Orthogonal
makes the effects orthogonal in the analysis. This causes the axial points to be more extreme than the –1 or 1 representing the range of the factor. If this factor range cannot be practically achieved, it is recommended that you choose On Face or specify your own value.
On Face
leaves the axial points at the end of the -1 and 1 ranges.
User Specified
uses the value you enter in the Axial Value text box.
If you want to inscribe the design, click the box beside Inscribe. When checked, JMP rescales the whole design so that the axial points are at the low and high ends of the range (the axials are –1 and 1 and the factorials are shrunken based on that scaling).
Specify Output Options
Use the Output Options panel to specify how you want the output data table to appear. When the options are specified the way you want them, click Make Table. Note that the example shown in Select the Output Options is for a Box-Behnken design. The Box-Behnken design from the design list and the Output Options request 3 center points and no replicates.
Select the Output Options
Run Order provides a menu with options for designating the order you want the runs to appear in the data table when it is created. Menu choices are:
Keep the Same
the rows (runs) in the output table will appear in the standard order.
Sort Left to Right
the rows (runs) in the output table will appear sorted from left to right.
Randomize
the rows (runs) in the output table will appear in a random order.
Sort Right to Left
the rows (runs) in the output table will appear sorted from right to left.
Randomize within Blocks
the rows (runs) in the output table will appear in random order within the blocks you set up.
Add additional points with options given by Make JMP Table from design plus:
Number of Center Points
Specifies how many additional runs to add as center points to the design. A center point is a run that is located in the center of the range of each continuous factor.
Number of Replicates
Specify the number of times to replicate the entire design, including center points. Type the number of times you want to replicate the design in the associated text box. One replicate doubles the number of runs.
View the Design Table
Now you have a data table that outlines your experiment, as described in The Design Data Table.
The Design Data Table
The name of the table is the design type that generated it.
Run the Model script to fit a model using the values in the design table.
The column called Pattern identifies the coding of the factors. It shows all the codings with “+” for high, “–” for low factor, “a” and “A” for low and high axial values, and “0” for midrange. Pattern is suitable to use as a label variable in plots because when you hover over a point in a plot of the factors, the pattern value shows the factor coding of the point.The three rows whose values in the Pattern column are 000 are three center points.
The runs in the Pattern column are in the order you selected from the Run Order menu.
The Y column is for recording experimental results.