Design-Expert 8.0使用指南-Multifactor RSM-Optimal design(2)

Handy New Design or Open Design options Click the yellow

Response Surface folder tab, select Optimal as the design, and enter the L[1] (lower) and L[2] (upper) limits as shown below.

Entering factor levels for optimal design

Create the multilinear constraint

Press the Edit Constraints button at the bottom of the screen.

Edit constraints fields for entering equations

At this stage, if you know the multilinear constraint(s), you can enter them directly by doing some math.

Multifactor constraints like that pictured above must be entered as an equation taking the form of:

βL ≤ β1A+ β1B…≤ βU

where βL and βU are lower and upper limits, respectively.

2 D-Optimal RSM Tutorial Design-Expert 8 User’s Guide

DX8-04F-MultifactorRSM-IVopt.docx Rev. 5/17/10

Anderson and Whitcomb provide guidelines for developing constraint equations in Appendix 7A of their book RSM Simplified. If, as in this case for both A and B, you want factors to exceed their constraint points (CP), this equation describes the boundary for the experimental region:

1 A LLAB LLB CPA LLACPB LLB

where LL is the lower level. In this case, lower levels are 110 for factor A and 17 for factor B. These factors’ CPs are 180 for factor A and 19 for factor B (the endpoints on the diagonal constraint line shown in the figure below).

Constraint points

Plugging in these values produces this equation:

1 A 110B 17 180 11019 17

However, the software requires formatting as a linear equation. This is

accomplished using simple arithmetic as shown below.

1 A 110B 17 702

70 2 1 2 A 110 70 B 17

140 2A 220 70B 1190

1550 2A 70B

Dividing both sides by 2 simplifies the equation to 775 A 35B

This last equation can be entered directly, or it can be derived by Design-Expert from the constraint points while setting up a RSM design.

Rather than entering this in directly, let’s make Design-Expert do the math. Click the Add Constraint Tool button. It’s already set up with the appropriate defaults based on what you’ve entered so far for the design constraints.

Design-Expert 8 User’s Guide D-Optimal RSM Tutorial 3

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