Chaughule, Thorat - Statistical Analysis/Design of Experiments
A number of statistical methods available for effective designs of the experiments
are as follows:
8.6.1. Full factorial design
A factorial design is an experimental strategy in which design variables are varied
together, instead of one at a time. The factorial experiments in which all combination of
levels of the factors is run are referred as full factorial experiments. In the full factorial
design it is prerequisite to define the lower and upper bounds of each N design variables.
The allowable range is then discretized at different levels. To construct an approxima-
tion model that can capture interactions between N design variables, a full factorial ap-
proach (Montgomery, 1997) may be necessary to investigate all possible combinations.
If each of the variables is defined at only the lower and upper bounds (two levels), the
experimental design is called 2N full factorial. Two level factorial experiments are those
in which each factor is investigated at only two levels. The early stages of experimenta-
tion usually involve scrutinizing the vital factors from a large number of potential fac-
tors. Two level factorial experiments are used during this stage to quickly filter out un-
wanted effects so that attention can then be focused on the more important ones. The
design matrix for 2^2 designs is shown in Figure 8.2. Full factorial two level experiments
are also referred to as 2k designs where k denotes the number of factors being investi-
gated in the experiment. A full factorial two level design with k factors requires 2 k runs
for a single replicate.
Figure 8.2. 2N Factorial DesignFor example, a two level experiment with three factors will require 2^3 = 8 runs. The
choice of the two levels of factors used here depends on the factor itself. Some factors
naturally have two levels. For example, if gender is a factor, then male and female are
the two levels. For other factors, the limits of the range of interest are usually used. For
example, if drying temperature is a factor that varies from 45°C to 65°C then the two
levels used in the 2k design for this factor would be 45°C to 65°C. The two levels of the
factor in the 2k design are usually represented as -1 (for the first level) and 1 (for the
second level).
The 2^3 design is a two level factorial experiment design with three factors (say fac-
tors A, B and C). This design tests three (k = 3) main effects A, B and C; three two factor
interaction effects AB, BC, AC and one three factor interaction effect, ABC. The design