Following the brainstorming sessions, an estimate of sample size was
rendered on the basis of a two-level design model. The sample size was
computed using a type I (alpha) and type II (beta) error probability of 5%. It
should be noted that the error term used in the sample size calculation was
based on the outcomes of the initial process capability study. Test
sensitivity was tentatively established at one standard deviation.

Given the required levels of decision confidence and test sensitivity, the
team discovered they would not be able to execute a screening experiment and
then follow on with a higher-resolution design because of excessive testing
costs. Consequently, trade-offs were made. In this case, test sensitivity and
beta risk were adjusted to reduce total sample size (N). After making all
required compromises, it was determined that 16 experimental runs could be
made with minimum replication. The primary objective at this point was to test
as many variables as possible.

After some general discussion, the team decided to employ a 2^{8-4}
design (resolution IV fractional factorial). This particular design ensured
that second-order and higher interactions were clear of the main effects;
however, the second-order effects were aliased together in certain
combinations. The potential interactive effects were carefully evaluated.
After such evaluation, the experimental factors were assigned to the
appropriate design matrix columns. This process provided an experiment design
which represented the practical balance between items such as experimental
precision, decision risk, manufacturing objectives, and cost, to mention a
few. The design matrix is located in Figure B-28.