- Define the boundaries using “
**Optimal**” design:

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.

- Press the “
**Edit Constraints**” button. Enter the inequalities that define the region of operability. Click the “**Constraint Tool**” if you would like assistance writing the inequalities.

- Select the vertex being constrained (excluded) from the design. For this
example it is the low, low combination where
**A = 110**and**B = 17**. Change A from 180 to 110, after you do this the “A <” constraint will change to “A >”. Change B from 23 to 17, after you do this the “B <” constraint will change to “B >”.

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?”

- For this example two statements are necessary to define the constraint:
- When B is 17, A must be at least
**180**; make sure the constraint type is “A >” and enter 180 in the constraint point for A. - When A is 110, B must be at least
**19**; make sure the constraint type is “B >” and enter 19 in the constraint point for B.

- When B is 17, A must be at least

- Click OK and the constraint inequality will be calculated and entered. If there are more constraints they need to be computed one at a time. Use the constraint tool as many times as necessary.

- On the “
**Design Evaluation**”, node look at the contour plot:

- Define the boundaries using an “
**Optimal**” design:

There is a constraint at the all high vertex.

- Click on “
**Edit Constraints**” button and then the “**Constraint Tool**” button for assistance writing the inequalities.

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**.

- When B is 225, and C is 0.7 - A must be no more than

- Click OK after entering the constraint point for each factor. The final OK will produce…

- Define the boundaries using an “
**Optimal**” design:

There are two constraints on this design. One occurs at the all high vertex, on is at the high, high, low vertex.

- Click on the “
**Edit Constraints**” button and then the “**Constraint Tool**” button for assistance writing the inequalities.

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**.

- When B is 225, and C is 0.7 - A must be no more than

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.

- Click OK after entering the constraint points for each constraint. The final OK will produce…

- Define the boundaries using an “
**Optimal**” design:

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.

- Click on the “
**Edit Constraints**” button and then the “**Constraint Tool**” button for assistance writing the inequalities.

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**.

- When C is 100 - A must be no more than

- The final inequality set is…

- Define the boundaries using an “
**Optimal**” design:

There are two constraints on this design, one at the high, low, high vertex, and one at the low, high, low vertex.

- Click on the “
**Edit Constraints**” button and then the “**Constraint Tool**” button for assistance writing the inequalities.

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**.

- When B is 20, and C is 50 - A must be no more than

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.

- The final inequality set is…

- Which condenses down to…

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.

- Define the boundaries using an “
**Optimal**” design:

There are two constraints on this design, one at the all high vertex, and one at the all low vertex.

- Click on the “
**Edit Constraints**” button and then the “**Constraint Tool**” button for assistance writing the inequalities.

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**.

- When B is 40, and C is 50 - A must be no more than

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.

- The final inequality set is…

- Which condenses down to…

Which is the same as the original example 5.