Statistics Toolbox

Augmenting D-Optimal Designs

In practice, experimentation is an iterative process. You often want to add runs to a completed experiment to learn more about the system. The function daugment allows you choose these extra runs optimally.

Suppose you execute the eight-run design below for fitting a linear model to four input variables.

• settings = cordexch(4,8)
  settings =
       1    -1     1     1
      -1    -1     1    -1
      -1     1     1     1
       1     1     1    -1
      -1     1    -1     1
       1    -1    -1     1
      -1    -1    -1    -1
       1     1    -1    -1
  

This design is adequate to fit the linear model for four inputs, but cannot fit the six cross-product (interaction) terms. Suppose you are willing to do eight more runs to fit these extra terms. The following code show how to do so.

• [augmented, X] = daugment(settings,8,'i');
  
  augmented
  augmented =
       1    -1     1     1
      -1    -1     1    -1
      -1     1     1     1
       1     1     1    -1
      -1     1    -1     1
       1    -1    -1     1
      -1    -1    -1    -1
       1     1    -1    -1
      -1    -1    -1     1
       1     1     1     1
      -1    -1     1     1
      -1     1     1    -1
       1    -1     1    -1
       1    -1    -1    -1
      -1     1    -1    -1
       1     1    -1     1
  info = X'*X
  info =
      16     0     0     0     0     0     0     0     0     0     0
       0    16     0     0     0     0     0     0     0     0     0
       0     0    16     0     0     0     0     0     0     0     0
       0     0     0    16     0     0     0     0     0     0     0
       0     0     0     0    16     0     0     0     0     0     0
       0     0     0     0     0    16     0     0     0     0     0
       0     0     0     0     0     0    16     0     0     0     0
       0     0     0     0     0     0     0    16     0     0     0
       0     0     0     0     0     0     0     0    16     0     0
       0     0     0     0     0     0     0     0     0    16     0
       0     0     0     0     0     0     0     0     0     0    16
  

The augmented design is orthogonal, since X'*X is a multiple of the identity matrix. In fact, this design is the same as a 2⁴ factorial design.

Generating D-Optimal Designs

Designing Experiments with Uncontrolled Inputs