Response Surface Methodology RSM

1
Response Surface Methodology (RSM)

• RSM is a statistical technique that is useful
  for developing, improving, and optimizing
  processes.
• It is an extension of other statistical
  approaches, including Regression, and Design of
  Experiments.
• It should be applied after initial phases of
  experimentation, where the vital few factors have
  been identified.
• The area of interest can be previously
  identified, or a box method can be used to find
  optimum values in different regions, if your map
  is complex.

2
Getting Started

• The first step to RSM is that you must have or
  generate a large number of data points.
• The second step is to assume a response equation.
  The most common equations are linear and
  quadratic. Interaction effects can also be
  included.
• The objective is to generate a map of response,
  either in the form of contours, or as a
  3-dimensional graph.

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Example Contour Map - Water Flows
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Method - Continued

• Take the given response equation and data, and
  solve for the regression coefficients.
• Plot the surface contour. This will give a
  visual reference of the data.
• Use Path of Steepest Ascent or other RSM
  technique method to find the optimum of the
  surface.
• Calculate the R2 and the adjusted R2 values.

5
Example - Bone Strength Study

• The objective of the current study is to model
  the strength of a treated human bone, given the
  following factors
• cement injected into the bone
• Ability to achieve desired compressive strength
  and stiffness.

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Vertebroplasty Study

• Vertebroplasty is a procedure which injects
  acrylic bone cement into the trabecular core of
  the vertebral body.
• The study was done with 51 specimens from 5
  cadavers.
• The amount of cement was 10, 20, and no fill
  randomly assigned to each vertebra. Each
  vertebra was then subjected to a compression test
  and the maximum compressive strength and
  stiffness were recorded.
• Higgins, et al., The Biomechanical Effects of
  Unipedicular Vertebroplasty on Intact Vertebrae,
  SPINE, Vol. 28, No.14, 2003.

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Experimental Data Points
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• Quadratic equation was fitted to the data
  points. The R2 value is 0.7588 and the adjusted
  R2 value is 0.5865.
• The current quadratic fit is reasonable. More
  accuracy is desirable therefore, more data is
  needed.

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Summary

• RSM can help to find global optimums when
  non-linear terms are used
• RSM can help to find equivalence of different
  strategies to achieve optimal results.
• RSM is slick it can generate impressive
  3-dimensional color graphs that can wow an
  audience however, it is complex, data intensive,
  and limited to few variables