Introduction

 

If you started with a Yellow design to identify some key effects, then the half normal plot shows that there are three key main effects: F, E & C; two smaller main effects: A & D; and one 2-factor interaction present. 

 

 

The accompanying aliasing pattern points to main effects being aliased with 3-factor interactions. Since 3-factor interactions are unlikely to be important there is no cause for alarm here. However as 2-Factor Interactions are aliased with other 2-Factor Interactions, the effect labelled AD cannot be separated from the 2-Factor Interaction EF. Since the main effects of E & F and, to a much lesser extent, A & D express themselves it may be difficult to know for certain whether the key interaction is either the displayed default AD, or the hierarchically more likely EF, or the sum of the two.

Rather than run a complete foldover (i.e., double the number of runs) to find out which of a small number of interactions is actually important, a semifold is started like a foldover on one key factor but only half of the runs are completed. In this example, instead of 16-20 additional runs, a semi-fold requires only another 8 or so more runs.

Building the Design: Semi-Fold over a Yellow Design

 

At the Design Layout screen choose Design Tools and Augment Design… Augment. The established method for improving the resolution of Yellow designs is to select Semifold. Click OK.

 

 

In the Semifold dialogue choose a factor to fold on, pick a factor whose interactions are of most interest (e.g. F). Choosing this factor ensures the main effect & all 2-Factor Interactions involving this factor will be clear of other main effects & 2-Factor Interactions.

As you only want half of the runs of a foldover, you are also prompted to Choose the factor and its level to retain for the augmented runs. Here you will most likely want to choose a setting for a factor that was not significant in the original analysis (e.g. D+ high setting of Spray Rate – preferable for more economical or practical reasons. Click OK and design expert will generate half of the foldover runs where D-Spray Rate is at its high setting.

Click Yes when asked Go to Design Evaluation now? In the Design Evaluation click the Results button to view the new aliasing pattern BEFORE you execute the additional runs. A second block of runs is generated where 2-Factor Interactions involving F (including EF) are no longer aliased with other 2-Factor Interactions.

 

A complete fold over on a Yellow design can result in repeating the existing runs!! To avoid this potential pothole simply fold over on a single factor and weigh up the costs\risks\benefits of running half these runs (i.e., a semi-fold).

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

 

The analysis steps for the combined design are the same as those outlined in the 2-Level Designs Tipsheet. Since semi-folding over a Yellow design improves the resolution, particularly of the key 2-Factor Interactions, in the normal plot of effects for this example we are confident that the effects of E, F and their 2-Factor Interactions are statistically significant.

 

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