Introduction

 

If you started with a Yellow design to identify some key effects, the likelihood is that there is at least one key interaction present. Consider the case on the left where the half normal plot identifies 5 key effects from the 6 factors were explored in 16 runs + 4 centre points (a quarter fraction yellow design).

 

 

Click Alias List on the Effects Tool to inspect the accompanying aliasing pattern. We see the main effects are aliased with 3-Factor Interactions and the 2-Factor Interactions are aliased with at least one other 2-Factor Ineractions. In particular the AB interaction standing out on the effects plot is aliased with CE. It is difficult to know whether it is AB, or CE, or both that are significant with the current amount of information. A semi-fold would employ at least 8 additional runs to determine which effect is real.  This seems an excessive number of runs to de-alias just two effects. Alternatively, the most resource efficient approach to resolving this ambiguity is to use a D-optimal augmentation, which in theory needs only 2 extra experiments to estimate the one additional effect, CE.

Building the Design: Augmenting using a Factorial D-optimal approach

 

At the Design Layout screen choose Design Tools and Augment Design… Augment. Select Factorial D-optimal. The next screen provides the menu for generating factorial D-Optimal designs. Click OK.

 

 

Click Edit model and in the model list locate and double click the additional term(s) you wish to include in the Model (CE in this case). Note: Minimum model points & Total Experiments will increase to 2.

In practice however we recommend additional runs. If you increase the Minimum model points to estimate the additional effects and add more centre points (by duplicating existing ones in the design layout) this will improve the robustness of your design & test the stability of your system over time.
 

Once the design is generated you should go to Design Evaluation & double-check the new alias structure to make sure you will get the information you want (i.e., that AB and CE are no longer aliased). Note: even though this minimal augmentation has achieved the desired result – AB and CE are no longer aliased – their aliasing patterns look complicated. This is the result of running so few additional runs.

 

To be safe, you should always assess the impact an augmentation strategy has on aliasing patterns & discuss these with a statistician or lead user.

 

Run the Experiments and Enter the Data

 

For each additional run, enter the results for each response into the Design (Actual) sheet.

 

 

Analysing your Results

 

After running the additional combinations suggested by the D-optimal feature and entering the responses, the analysis steps are the same as those outlined in the 2-Level Designs Tipsheet.  We produced a similar plot of effects to the one shown before, except now we are more confident that the effect is due to the interaction AB.

When you augment a design it is unlikely that all the effects will be completely de-aliased or independent. You will therefore see a message that This design is not orthogonal After you select your effects on the Normal plots or from the Effects List, do as Design Expert requests and click Recalculate to see how the effects change in light of what effects you selected.

Recalculated.

 

 

 

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