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Response Surface Designs

Response surface designs are covered in the MiC Quality Advanced Design of Experiments course.

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Box Behnken Design

A response surface design that has points at:

  • the center
  • the midpoint of each side

There are no corner points. The design is spherical, all the points (except the center point) lie on a sphere of radius

CCD

See Central Composite Design

Central Composite Design

A response surface design that has points at:

  • the center
  • the corner points
  • axial points at 'a' from the center

The design is usually rotatable, if the correct value of a is selected


Hill Climbing

A technique used in the Design of Experiments to find the maximum or minimum, if it is not contained within the initial parameter settings. It involves:

  • carrying out an initial experiment and, if it does not contain the [maximum/minimum],
  • finding the path of steepest [ascent/descent]
  • carrying out a test at intervals point along the path until it starts to [ascend/descend]
  • carry out an experiment around the highest point on the path to see if it is the [maximum/minimum]
  • if not find the path of steepest ascent, and continue the search

The experiments may be first order designs with center points. If the curvature is non-significant the experimental region does not contain the center point and the path of steepest ascent can be found. If the curvature is large the additional testing required for a second order design is carried out.

 

Response Surface Methods

Response surface design is a types of Experimental Design that investigate curvature of the response surface. They achieve this by using a quadratic regression equation rather than the linear form of the regression equation used in factorial designs.

When the true response surface is approximated by a linear equation the maximum and minimum values at a corner point. Response surface designs can have the maximum or minimum in the interior of the surface. This allows the response to be optimized using hill climbing methods.

There are various types of response surface design including the Central Composite (CCD) and Box Behnken designs.

Steepest Ascent/Descent

See Hill Climbing

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