Three-Level orthogonal design is a fractional
factorial of 
. For 
, the 
fractional design first generates
full factorials for
factors. Then, the
remaining 
columns are
determined from the pre-generated columns. To do these, a defining relation
is introduced as 
. The
component of the
column is
determined as
where, 
.
As an example, we generate 
fractional factorial design with 
and 
. From the rules, the 3rd and 4th columns
are
and 
. These results are listed side by side in
Table 1.
Table 1 A fractional factorials of with and
The above factorial design of is only one of the 
fractions of 
full factorial designs. Among those
fractions, only the
cases that are orthogonal between columns are the three-level orthogonal array
for 
. Hence, the
defining relation for factors
is very important to maintain the orthogonal characteristics in the columns.
We support the automatic generator for the three-level
orthogonal array design. If one define the number of factors 
, the
RecurDyn/AutoDesign automatically generates the fractional factorials, where
is internally
determined as possible as minimize the trials.
Reference
1. Peter W.M. John, 1998, Statistical Design and Analysis of Experiments, SIAM, Philadelphia.
2. Douglas C Montgomery, 2000, Design and Analysis of Experiments, John Wiley & Sons, New York.