Abstract
Box-Behnken designs are popular with experimenters who wish to estimate a second-order model, due to their having three levels, their simplicity and their high efficiency for the second-order model. However, there are situations in which the model is inadequate due to lack of fit caused by higher-order terms. These designs have little ability to estimate third-order terms. Using combinations of factorial points, axial points, and complementary design points, we augment these designs and develop catalogues of third-order designs for 3-12 factors. These augmented designs can be used to estimate the parameters of a third-order response surface model. Since the aim is to make the most of a situation in which the experiment was designed for an inadequate model, the designs are clearly suboptimal and not rotatable for the third-order model, but can still provide useful information.
| Original language | English |
|---|---|
| Pages (from-to) | 4225-4239 |
| Number of pages | 15 |
| Journal | Communications In Statistics-Theory And Methods |
| Volume | 41 |
| Issue number | 23 |
| DOIs | |
| Publication status | Published - 1 Dec 2012 |
Keywords
- Alias matrix
- Box-Behnken designs
- G-efficiency
- Lack of fit
- Response surface models
- Second-order designs
- Third-order designs