21.4.3.4. Full Factorial Design

Suppose that three factors such as A, B and C have two-level. Then, the full factorial design is a combination of \({{2}^{3}}\). The sequence of full factorial design is (1), a, b, ab, c, ac, bc and abc. Figure 21.139 shows the geometric view of \({{2}^{3}}\).

In case of four factors (A, B, C and D), their combinations can be made by adding the following combinations to \({{2}^{3}}\): d, ad, bd, abd, cd, acd, bcd and abcd. In these combinations, the trial (1) represents that the levels of all factors are the lower levels, which can be denoted as ‘-’ symbol in the DOE table. The remaining trials denote ‘+’ symbol in the column according to the alphabetic letter.