3.1.16 Three Level Factorial Design

For higher order Factorial design the number of design points grows rapidly. In the Three Level Factorial design all possible combinations of the three discrete values of the parameter are used.

In Table 3.9 a comparison between the number of experiments of a full Three Level Factorial design and other designs are shown. The number of design points can be reduced by skipping some higher order interactions between the input parameters.

Table 3.9: Comparison of the number of sample points for several types of experimental designs.

Number of parameters	Full factorial design	Sensitivity analysis design	CCI design	Three level full factorial design
2	4	4	9	6
3	8	6	15	27
4	16	8	25	81
5	32	10	43	243
6	64	12	77	729
7	128	14	143	2187
8	256	16	273	6561
9	512	18	531	19683
10	1024	20	1045	59049
11	2048	22	2071	177147
12	4096	24	4121	531441
n	2n	$2 \cdot n$	$2 \cdot n + 2^n$	3n