Page 275 - Six Sigma Advanced Tools for Black Belts and Master Black Belts

Char Count= 0
3:5
August 31, 2006
JWBK119-17
260 Strategies for Experimentation under Operational Constraints
Table 17.3 2 4−1 design with 4 =−23.
I X 1 X 2 X 3 X 4
1 − − − −
2 + − − −
3 − + − +
4 + + − +
5 − − + +
6 + − + +
7 − + + −
8 + + + −

4
clearly which eight out of the 16 experimental runs of a full 2 factorial are used for
a particular half-fraction design. Thus, columns A, B, H correspond to Tables 17.1,
17.2, and 17.3, respectively. Such a master table of 2 4−1 designs can be conveniently
used to expressly exclude or include certain factor setting combinations; in many
cases, more than one operational constraint or requirement can be accommodated
simultaneously.

17.4 VARIANTS OF TAGUCHI ORTHOGONAL ARRAYS

The flexibility afforded by the experimental design approach illustrated above is ab-
sent from the usual Taguchi routine which expects an experimenter to obtain his
design from one of the standard orthogonal arrays appended at the end of a Taguchi

Table 17.4 Alternative 2 4−1 designs out of a full design.

X 1 X 2 X 3 X 4 A B C D E F G H
1 − − − − 1 1 1 1
2 + − − − 2 2 2 2
3 − + − − 3 3 3 3
4 + + − − 4 4 4 4
5 − − + − 5 5 5 5
6 + − + − 6 6 6 6
7 − + + − 7 7 7 7
8 + + + − 8 8 8 8
9 − − − + 1 1 1 1
10 + − − + 2 2 2 2
11 − + − + 3 3 3 3
12 + + − + 4 4 4 4
13 − − + + 5 5 5 5
14 + − + + 6 6 6 6
15 − + + + 7 7 7 7
16 + + + + 8 8 8 8