Statistics for Six Sigma Green Belts with Minitab and JMP

Choosing the Treatment Combinations

To choose a subset of the treatment combinations, you can begin with the 2⁴ design. Table 8.16 presents the 16 possible treatment combinations for this full factorial design, along with the pattern of pluses and minuses for the main effects (the columns headed by A, B, C, and D) and the ABCD interaction.

Table 8.16. Treatment Combinations for the 2⁴ Design in Standard Order

Notation	A	B	C	D	ABCD
(1)	–	–	–	–	+
a	+	–	–	–	–
b	–	+	–	–	–
ab	+	+	–	–	+
c	–	–	+	–	–
ac	+	–	+	–	+
bc	–	+	+	–	+
abc	+	+	+	–	–
d	–	–	–	+	–
ad	+	–	–	+	+
bd	–	+	–	+	+
abd	+	+	–	+	–
cd	–	–	+	+	+
acd	+	–	+	+	–
bcd	–	+	+	+	–
abcd	+	+	+	+	+

In a fractional factorial design with four factors in which half the treatment combinations are chosen, only eight treatment combinations are available from the possible 16 combinations. With only eight treatment ...