Multiple Linear Constraints

In some cases simple lower and upper bounds will not properly define your feasible experimental region. Stat-Ease allows you to impose multi-factor constraints in linear form. This feature can be employed for either response surface or mixture designs. It provides considerable flexibility for defining your experimental region. This option is available via the Edit Constraints button; if there is no Edit Constraints button then that design cannot be constrained.

After entering the constraints and building the design, click on Evaluation, Graphs, then switch to the contour plot to review the shape of the constraints.

Allowable entries into the Edit Constraints window include ratios or linear formulas.

Example: ratio constraint

Let’s say that there is a condition such that the ratio of component B to A must be between 1 and 4. This can be written as: 1 ≤ B/A ≤ 4.

Stat-Ease will split it into two parts for the left side and the right side of the constraint.

Left side: 1≤ B/A can be multiplied through by A, resulting in: A≤B

Now subtract A from both sides to get the proper form: 0 ≤ B-A

Right side: B/A ≤ 4 can be multiplied through by A, resulting in B ≤ 4A

Subtract 4A from both sides to get the proper form: B-4A ≤ 0

Example: linear constraint

Let’s say that that the sum of times for a process cannot exceed 30 minutes. If there are three times then the formula needed is A + B+ C ≤ 30.