The need for a constraint arises because low A and low B at the same time will not work. At the lowest level of A factor B must be at least 19. At the lowest level of B factor A must be at least 180.
To define the constraint points, answer the following question for each factor at the excluded vertex. “What are the acceptable values for a given factor when all other factors are forced to the excluded vertex values?”
There is a constraint at the all high vertex.
Select the vertex being excluded (in this case the all high vertex) and enter the constraint points. (This constraint excludes two vertices.)
- When B is 225, and C is 0.7 - A must be no more than 700.
- When A is 1700, and C is 0.7 - B must be no more than 210.
- When A is 1700, and B is 225 - C must be no more than 0.3.
There are two constraints on this design. One occurs at the all high vertex, on is at the high, high, low vertex.
Select the first vertex, in this case all high, and write the defining statements. For the first constraint enter the Constraint tool…
- When B is 225, and C is 0.7 - A must be no more than 1400.
- When A is 1700, and C is 0.7 - B must be no more than 208.
- When A is 1700, and B is 225 - C must be no more than 0.3.
Click OK.
For the second constraint, we are at a new vertex on the Constraint tool… Change Vertex C to 0.2, after you do this the “C <” constraint will change to “C >”.
Enter the constraint point:
- When B is 225, and C is 0.2 - A must be no more than 1350.
- When A is 1700, and C is 0.2 - B must be no more than 200.
- When A is 1700, and B is 225 - C must be at least 0.45.
There is a single constraint, it is impossible to run experiments when both A and C are at their high levels. B is not involved in this relationship.
Define the constraint. For the constraint where A is 100, B is skipped, and C is 100.
- When C is 100 - A must be no more than 75.
- B is skipped.
- When A is 100 - C must be no more than 25.
There are two constraints on this design, one at the high, low, high vertex, and one at the low, high, low vertex.
Define the constraints. For the first constraint where A is 70, B is 20, and C is 50.
- When B is 20, and C is 50 - A must be no more than 30.
- When A is 30, and C is 10 - B must be at least 60.
- When A is 30, and B is 20 - C must be no more than 10.
For the second constraint where A is 30, B is 40 and C is 10.
- When B is 40, and C is 10 - A must at least 60.
- When A is 30, and C is 10 - B must be no more than 10.
- When A is 30, and B is 40 - C must be at least 40.
Note
Both of these constraints exclude two vertices. Either excluded vertex can be used as a basis for the constraint. Using the other vertices the constraint tool settings can change as can the final inequality, but with a little bit of algebra the inequalities are found to be equivalent. The next example is the same problem but done from the perspective of the other vertices.
There are two constraints on this design, one at the all high vertex, and one at the all low vertex.
Define the constraints. For the first constraint where A is 70, B is 40 and C is 50…
- When B is 40, and C is 50 - A must be no more than 50.
- When A is 70, and C is 50 - B must be at least 60.
- When A is 70, and B is 40 - C must be no more than 30.
The default constraint type at a high factor setting is less than, but B needs to be changed to greater than to accomodate this double exclusion.
For the second constraint where A is 30, B is 20 and C is 10…
- When B is 20, and C is 10 - A must be at least 40.
- When A is 30, and C is 10 - B must be no more than 10.
- When A is 30, and B is 20 - C must be at least 20.
The default constraint type at a low factor setting is greater than, but B needs to be changed to less than to accomodate this double exclusion.
Which is the same as the original example 5.