Page 468 - Design for Six Sigma a Roadmap for Product Development

Fundamentals of Experimental Design 427

Run number A(X 1 ) A(X 2 )
1 1 1
2 1 1
3 1 1
4 1 1

The use of 1 and 1 for the factor settings is called coding the data.
This aids in the interpretation of coefficients fit to any experimental
model.

Example 12.5 A router is needed to cut location notches on a printed-
circuit board (PCB). The cutting process creates vibration on the board and
causes the dimensional variation of the notch position. An experimental
study is conducted to identify the cause of vibration. Two factors, bit size (A)
and cutting speed (B), are thought to influence the vibration. Two bit sizes
(1/16 and 1/8 in) and two speeds [40 and 90 rpm (r/min)] are selected, and
four boards are cut at each set of conditions shown in Table 12.6. The
response variable is the vibration measured on each test circuit board.

k
12.3.2 Layout of a general 2 design
If the experiment had more than two factors, there would be an addi-
tional column in the matrix for each additional factor. The number of
k
distinct experimental runs is N 2 . For example, if k 4, then, N
4
2 16.
4
Table 12.7 gives a standard layout for a 2 factorial experiment. The
run number is sequenced by standard order, which is featured by a 1
1 1 1 ... sequence for A, 1 1 11 for B, four 1s and four 1s for C,
and so on. In general, for a two-level full factorial with k factors, the
k
first column starts with 1 and alternates in sign for all 2 runs, and
the second column starts with 1 repeated twice, and then alternates
k
with 2 in a row of the opposite sign until all 2 places are filled. The
third column starts with 1 repeated 4 times, then 4 repeats of 1s

TABLE 12.6 Experiment Layout and Data for Example 12.5

B Y [vibration (four replicates, n 4)]
Run A (cutting
number (bit size) speed) 1 2 3 4

1 1 1 18.2 18.9 12.9 14.4
2 1 1 27.2 24.0 22.4 22.5
3 1 1 15.9 14.5 15.1 14.2
4 1 1 41.0 43.9 36.3 39.9

*Continued in Sec. 12.3.3.