# Path of Steepest Ascent

## Summary

Sequential experimentation is a key component of many DOE endeavors. This is especially true if you have a need to fully optimize the solution using response surface methods involving central composite designs (CCD).

The path of steepest ascent (or descent) defines the most likely path of increasing (or decreasing) response values based on an initial 2K factorial design that contains no evidence of curvature. The points on this path are defined by changing each factor proportionally based on the size and sign of the coded coefficients. These design points are then investigated. The point at which the response changes direction marks the location for a new 2K design. When a 2K design shows significant curvature, axial points are typically added to the design to create a CCD to model the response surface.

• What is the location of the next 2K factorial design?
• What is the direction of the line that will most likely lead to the quickest increase (or decrease) in the response?
• For each point on the path to be investigated, what are the settings for each of the factors?
• At what point does the response fail to continue increasing (or decreasing)?
When to Use Purpose
Mid-project Define a sequential experimentation strategy (DOEs) to quickly find the values of the process inputs that maximize (or minimize) the process output.

### Data

Factor coefficients and settings from a 2K designed experiment (DOE).

## How-To

1. Enter the coded coefficient of the factor you will use as a base.
2. Select whether to evaluate the path of steepest ascent or descent.
3. Enter the names of all factors (including base factor) in your final model.
4. Enter the coded coefficients for the factors. Be sure to include the correct sign.
5. Enter the actual (uncoded) high and low settings for each factor.
6. Enter the increment values. Values of 0 to 5 are provided as default. You can modify the increments or add additional columns as needed to construct your path.
7. Optionally, display a graph of the increment settings versus the response by filling in the first two columns of the graph data table.
8. Optionally, construct a graphical view of your testing plan by filling in the last two columns of the graph data table. Only two factors can be plotted. Select one factor as the X-variable and one as the Y-variable.

## Guidelines

• For each increment of one coded unit of the base factor, all other factors will be adjusted proportionally. It is highly recommended that you use the factor with the largest coefficient (in absolute value) as your base unless you must adjust a different factor by increments of exactly one coded unit.
• The increment defines how large a step will be taken in the direction of the coded coefficient of the base factor. For example, if the coded coefficient is positive, the direction is positive. Conversely, if the coded coefficient is negative, the direction is negative. An increment value of 0 defines the center point of the design.
• When trying to increase the response and you reach a point where the response decreases, you should go back a half step along the path and run a trial. Choose between the full-step and the half-step back (whichever has the higher response value) as the center point of the next factorial design. Use a similar approach to minimize the response.
• Try to limit this approach to two or three factors with a maximum of five factors.
• All factors must be continuous.
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