# Contour Plot

## Summary

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

• If two process inputs (factors) change simultaneously, what is the impact on the process output?
• How robust, or stable, is the optimum solution?
• What is the predicted value of the process output for a particular combination of settings of the two process inputs?
• What settings of the key inputs will result in the optimal process output?
When to Use Purpose
Mid-project Helps to visualize the effects of two process inputs (factors) on the process output. The contours on the graph represent values of the predicted process output at various settings of the two factors on the plot.
Mid-project Helps to assess the region around an 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 both of the two factors could have serious consequences on the process output.
Mid-project Used as a graphical aid when using 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. You can produce a contour plot in two ways:
• Choose Graph > Contour Plot, then specify the output as the z-variable, select one factor to be the x-variable, and a second factor to be the y-variable. If you are plotting data from a DOE, you should use the second method, described below, because it uses the model from the DOE to predict the process output.
• Choose Stat > DOE > Factorial > Contour/Surface Plots or choose Stat > DOE > Response Surface > Contour/Surface Plots, and then specify the output as the response, select one factor to be the x-variable, and a second factor to be the y-variable. This version of the contour plot uses the DOE model to create the plot; therefore, if there are additional factors in the model, you need to specify the levels at which to hold all other factors. It should be noted that you cannot use this method to create a contour 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, means, or other specified value.

## Guidelines

• Without significant data points between the high and low factor settings, the map may be seriously misleading because it will generate contours within the inference space even if no interior data points are provided.
• The Contour 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 contour plot is a useful tool to evaluate robustness of a solution for these higher-order models, provided the experiment has few unusual observations. To model the surface, the DOE model uses a quadratic equation, which tends to smooth the data abnormalities. If the data have a large number of unusual observations, the smoothed 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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