Foldover Designs in Minitab

The foldover design we discussed in class can be analyzed sequentially in Minitab. Recall that Minitab's foldover command doesn't augment the design matrix in the current worksheet but generates the entire foldover design in a new worksheet--your old responses will have to be re-entered in the new worksheet.

The shot put example was run using the default design for 7 factors in 8 runs so we didn't have to specify the design generators. After analyzing this initial screening design, a foldover was needed to decide whether 3 main effects were active or two main effects and their interaction was active. To generate the foldover design, we selected DOE>Create Factorial Design (as usual), specified 7 factors and then chose the 1/16 fraction (8 runs) under Design.

Under Design, we selected Fold Design>Fold on all factors, deselected Randomize Runs and used the default (principal) fraction. A new worksheet (separate from the earlier analysis) is created and all the responses need to be re-entered. Analysis is similar to analysis of fractional factorial designs though a Block effect, measuring any systemic difference between the two runs in the foldover, is also tested. This Block effect is aliased with three-letter words in the design generator and will be identified by one of those three letter words in the effects plot (e.g., ABD) rather than the Block label.

Another approach

Minitab has another approach that doesn't require the data to be reentered. After generating the initial design, you can select DOE>Modify Design...Select Fold Design, then click OK (do not click on Put Modified Design in a New Worksheet, since that would defeat the purpose of this shortcut); click OK again to fold over on all factors. The additional runs will have been added to the end of your worksheet--you now need to add the responses from the follow-up experiment. When analyzing this design, it seems that only the terms from the initial experiment may be included; you'll have to select the Terms box in Analyze Design... and click the >> to include the terms (this generally includes all the two-way interactions that were aliased with main effects in the initial experiment) from the foldover experiment. The Include Blocks box estimates the Block effect; it does not add the Block effect to the Effects plot, which will only consist of 14 terms rather than 15 terms.