What is folding?

When a Plackett-Burman design or a fractional factorial design is folded, the data in the worksheet are duplicated and put at the bottom of the original data set. Then, the sign on each value in the second set that is for a factor on which the design was folded is changed. Folding is a way to reduce confounding. Confounding occurs when you have a fractional factorial design and one or more effects cannot be estimated separately. The effects that cannot be separated are said to be aliased.

Resolution IV designs may be obtained from resolution III designs by folding. If you fold on one factor, then the factor and all its 2-factor interactions are unconfounded from other main effects and 2-factor interactions. If you fold on all factors, then all main effects will be free from each other and from all 2-factor interactions.

For example, suppose you are creating a three-factor design in four runs:

Original fraction

A	B	C
–	–	+
+	–	–
–	+	–
+	+	+

Folded on all factors

When you fold on all factors, Minitab adds four runs to the design and reverses the signs of each factor in the additional runs.

A	B	C
–	–	+
+	–	–
–	+	–
+	+	+
+	+	–
–	+	+
+	–	+
–	–	–

Folded on factor A

When you fold on one factor, Minitab adds four runs to the design, but only reverses the signs of the specified factor. The signs of the other factors remain the same. These rows are then appended to the end of the data matrix.

A	B	C
–	–	+
+	–	–
–	+	–
+	+	+
+	–	+
–	–	–
+	+	–
–	+	+

Defining relation and folding

When you fold a design, the defining relation or alias structure of the design is usually shortened because fewer terms are confounded with each other. Specifically, when you fold on all factors, any word in the defining relation that has an odd number of the letters is omitted. When you fold on one factor, any word containing that factor is omitted from the defining relation. For example, you have a design with five factors. The defining relation for the unfolded and folded designs (both folded on all factors and folded on factor A) are:

Unfolded design: I + ABD + ACE + BCDE
Folded design: I + BCDE

If you fold a design and the defining relation is not shortened, then the folding adds replicates. It does not reduce confounding. In this case, Minitab gives you an error message.

If you fold a design that is blocked, the same block generators are used for the folded design as for the unfolded design.