Page 488 - Design for Six Sigma a Roadmap for Product Development

Fundamentals of Experimental Design 447

2
02 12 22

Factor B 1 01 11 21

0
00 10 20

0 1 2
Factor A
2
Figure 12.15 A 3 design.

k-factor interactions have 2 degrees of freedom. The model contains
k
2 2 2 4 4 4 8 26 degrees of freedom. Note that if there
is no replication, the fit is exact and there is no error term (the epsilon
term) in the model. In this nonreplication case, if we assume that there
are no three-factor interactions, then we can use these 8 degrees of
freedom for error estimation.
In this model we see that i 1,2,3, and similarly for j and k, making
27 treatments. These treatments may be tabulated as in Table 12.17,
and the design can be depicted as Fig. 12.16.

3
TABLE 12.17 The 3 Design
Factor A
Factor B Factor C 0 1 2
0 0 000 100 200
0 1 001 101 201
0 2 002 102 202
1 0 010 110 210
1 1 011 111 211
1 2 012 112 212
2 0 020 120 220
2 1 021 121 221
2 2 022 122 222