Statistics Toolbox

Designing Experiments with Uncontrolled Inputs

Sometimes it is impossible to control every experimental input. But you may know the values of some inputs in advance. An example is the time each run takes place. If a process is experiencing linear drift, you may want to include the time of each test run as a variable in the model.

The function dcovary allows you to choose the settings for each run in order to maximize your information despite a linear drift in the process.

Suppose we want to execute an eight-run experiment with three factors that is optimal with respect to a linear drift in the response over time. First we create our drift input variable. Note, that drift is normalized to have mean zero. Its minimum is -1 and its maximum is 1.

• drift = (linspace(-1,1,8))'
  drift =
     -1.0000
     -0.7143
     -0.4286
     -0.1429
      0.1429
      0.4286
      0.7143
      1.0000
  settings = dcovary(3,drift,'linear')
  settings =
      1.0000    1.0000   -1.0000   -1.0000
     -1.0000   -1.0000   -1.0000   -0.7143
     -1.0000    1.0000    1.0000   -0.4286
      1.0000   -1.0000    1.0000   -0.1429
     -1.0000    1.0000   -1.0000    0.1429
      1.0000    1.0000    1.0000    0.4286
     -1.0000   -1.0000    1.0000    0.7143
      1.0000   -1.0000   -1.0000    1.0000
  

Augmenting D-Optimal Designs

Controlling Candidate Points