The Bounce Data.jmp sample data file has response surface data inspired by the tire tread data described in Derringer and Suich (1980). The objective of this experiment is to match a standardized target value (450) of tennis ball bounciness. The bounciness varies with amounts of Silica, Silane, and Sulfur used to manufacture the tennis balls. The experimenter wants to collect data over a wide range of values for these variables to see if a response surface can find a combination of factors that matches a specified bounce target. To follow this example:
1.
Select DOE > Response Surface Design.
2.
Load factors by clicking the red triangle icon on the Response Surface Design title bar and selecting Load Factors. Navigate to the sample data folder installed with JMP, and open Bounce Factors.jmp from the Design Experiment folder.
3.
Load the responses by clicking the red triangle icon on the Response Surface Design title bar and selecting Load Responses. Navigate to the sample data folder, and open Bounce Response.jmp from the Design Experiment folder. Response and Factors For Bounce Data shows the completed Response panel and Factors panel.
Response and Factors For Bounce Data
Response Surface Design Selection
1.
Open Bounce Data.jmp from the Design Experiment folder found in the sample data installed with JMP (JMP Table for a Three-Factor Box-Behnken Design).
JMP Table for a Three-Factor Box-Behnken Design
After opening the Bounce Data.jmp data table, run a fit model analysis on the data. The data table contains a script labeled Model, showing in the upper left panel of the table.
2.
Click the red triangle next to Model and select Run Script to start a fit model analysis.
JMP Statistical Reports for a Response Surface Analysis of Bounce Data
See the Fitting Linear Models book for more information about interpretation of the tables in JMP Statistical Reports for a Response Surface Analysis of Bounce Data.
Note: DOE response surface designs are available for up to eight factors only. In the DOE Response Surface Design platform, an error message is generated if more than eight factors are specified with a response surface design. Response surface designs with more than eight factors can be generated using DOE > Custom Design, where either a D-optimal or an I-optimal design can be specified. See Creating Response Surface Experiments for how to use the custom designer to create response surface designs. Curvature analysis is not shown (no error or warning message is given) for response surface designs of more than 20 factors when using the custom designer or the Fit Model platform; all other analyses are valid and are shown.
Statistical Reports for a Response Surface Analysis
See the Fitting Linear Models book for details about the response surface analysis tables in Statistical Reports for a Response Surface Analysis.
The first three plots in the top row of plots in the Prediction Profiler (The Prediction Profiler) display prediction traces for each x variable. A prediction trace is the predicted response as one variable is changed while the others are held constant at the current values (Jones 1991).
The current predicted value of Stretch, 396, is based on the default factor setting. It is represented by the horizontal dotted line that shows slightly below the desirability function target value (The Prediction Profiler). The profiler shows desirability settings for the factors Silica, Silane, and Sulfur that give a value for Stretch of 396, which is quite different from the specified target of 450.
The bottom row has a plot for each factor, showing its desirability trace. The profiler also contains a Desirability column, which graphs desirability on a scale from 0 to 1 and has an adjustable desirability function for each y variable. The overall desirability measure is on the left of the desirability traces.
The Prediction Profiler
2.
To adjust the prediction traces of the factors and find a Stretch value that is closer to the target, click the red triangle on the Prediction Profiler title bar and select Maximize Desirability. This command adjusts the profile traces to produce the response value closest to the specified target (the target given by the desirability function). The range of acceptable values is determined by the positions of the upper and lower handles.
Prediction Profiler with Maximum Desirability Set for a Response Surface Analysis shows the result of the most desirable settings. Finding maximum desirability is an iterative process so your results may differ slightly from those shown below.
Prediction Profiler with Maximum Desirability Set for a Response Surface Analysis
See the Multivariate Methods book for further discussion of the Prediction Profiler.
Contour Profiler for a Response Surface Analysis
Contour Profiler with High and Low Limits
The geometric structure of a design with three effects is seen by using the Scatterplot 3D platform. The plot shown in Scatterplot 3D Rendition of a Box-Behnken Design for Three Effects illustrates the three Box-Behnken design columns. You can clearly see the center points and the 12 points midway between the vertices. For details on how to use the Scatterplot 3D platform, see the Essential Graphing book.
Scatterplot 3D Rendition of a Box-Behnken Design for Three Effects