One Quarter Fraction Design

2k design with four factors/variables requires 16 experiments for the full replication. Therefore, quarter of the 16 experiments will results in only four experiments producing only three degrees of freedoms. Therefore, quarter fraction design is applicable for five or more factors/variables. In the one-half fraction 2k-1 design, only one generator word or the defining relation was required to develop the design. Therefore, in one-quarter fraction 2k-2 design, two generator word (or the defining relation) is required. Therefore, in a 2k-p fractional design, p number of defining relation is required. A one-quarter fraction of five factors of resolution III design is provided in Table 9 using the defining relation I = ABD and I = BCE.

Table 9. One-Quarter Fraction Design of Resolution 3

The Detail Explanations for the one-quarter design is provided in Video 7.

Video 7. Introduction to Basic One Quarter Fractional Factorial 2k Design of Experiments Details Explained

Video 8 shows the process of designing a one-quarter fraction using MS Excel.