# Surface Plot

## Summary

Provides a three-dimensional view of the predicted process output (usually modeled through a DOE) versus two of the process inputs.

• If I change two process inputs (factors) simultaneously, what is the impact on the process output?
• How robust, or stable, is the optimum solution?
• What settings of the key inputs result in the optimal process output?
When to Use Purpose
Mid-project The three-dimensional surface plot helps to visualize the effects of two process inputs (factors) on the process output. The height of the surface is the predicted process output at various settings of the two factors included in the plot.
Mid-project Surface plots help you locate an optimal solution and assess the region around the optimal solution. If the region around the optimum is relatively flat, the optimum is robust to variation in the two factors. If the region is not relatively flat, any deviation of the one or more of the two factors could have serious consequences on the process output.
Mid-project Used as a graphical aid in regression, ANOVA, or DOE.

### Data

Continuous Y, two continuous X's.

## How-To

1. Enter Y data in one column.
2. Enter factor levels into additional columns, one for each factor.
3. There are two ways to produce a surface plot:
• Choose Graph > 3D Surface Plot, specify the output as the Z-variable, select one factor to be the X-variable, and select a second factor to be the Y-variable. If you are plotting data from a DOE, you should use the second method, below, because it uses the model from the DOE to predict the process output.
• Choose Stat > DOE > Factorial > Contour/Surface Plots or Stat > DOE > Response Surface > Contour/Surface Plots, specify the output as the response, select one factor to be the X-variable, and select a second factor to be the Y-variable. This version of the surface plot uses the DOE model to create the plot; therefore, if your model has additional factors, you must specify the levels at which to hold all other factors. Note that you cannot use this method to create a surface plot if you have a 2K factorial design with center points or a general full factorial (GFF) design.
4. For both methods described above, if you have more than two X-variables, you must specify at what values to hold the additional X-variables. You can set additional variables at their minimum values, maximum values, or means, or you can specify a value.

## Guidelines

• Without significant data points between the high and low settings of the factors, the map may be seriously misleading because no interior data points exist to provide a basis for estimating the shape of the interior.
• The surface plot is often a key tool used to identify optimum process conditions when evaluating a quadratic model derived from a DOE. Quadratic or higher-order models require interior points, thus the surface plots from these models are quite accurate.
• A surface plot is a useful tool to evaluate robustness of an optimum solution for these higher-order models generated from a DOE, provided the experiment does not have many unusual observations. The DOE model uses a quadratic equation to model the surface. The quadratic equation tends to smooth out the abnormalities in the data. If the experiment has a large number of unusual observations, the smoothed-out surface may not accurately depict the Y data. Always check the model for a high r-squared value to be sure that it explains most of the variation in the Y data.
• If you have discrete numeric data from which you can obtain every equally spaced value and you have measured at least 10 possible values, you can evaluate these data as if they are continuous.
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