Box-Behnken Design

3-level response-surface design without corner points — for processes where extreme combinations of all factors simultaneously are not permitted.

Also known as: Box-Behnken, BBD

The Box-Behnken design (Box & Behnken, 1960) is a rotatable 3-level design for 3 or more factors. It avoids the corner points of the factor cube — no run drives all factors to their extremes simultaneously — and is the first choice when simultaneous extreme conditions would be undesirable or unsafe.

  • 3 levels per factor (−1, 0, +1); all runs lie on edges or the central plane, never at corners
  • Rotatable or near-rotatable — constant prediction accuracy at equal distance from the centre
  • Efficient: fewer runs than a CCD of the same order; e.g. 15 runs for 3 factors vs. 20 (CCC) or 20 (CCF)

See also

Used in

In the Algorithm Lab

Sources

  • Box, G. E. P. & Behnken, D. W. — Some New Three Level Designs for the Study of Quantitative Variables, Technometrics, 2(4), 1960
  • Myers, Montgomery & Anderson-Cook — Response Surface Methodology, 4th Edition