experiment. In these conditions, fractional factorials (2kp) are
used that ‘‘sacrifice” interaction effects so that main effects may
still be computed correctly [15]. This exploratory phase is repeated
until significant interaction effects exist. A significant
interaction effect indicates that the response surface will be
curved in that region, i.e. a second-order polynomial function.
Provided that the experimenter has defined factor limits appropriately
and/or taken advantage of all available tools in multiple
regression analysis, then a higher-order model is generally unusual.
Then, a three-level factorial or composite design is used to
fit response surface to a second-order polynomial metamodel.
At last, canonical analysis is employed to investigate the response
surface in order to determine whether the estimated stationary
point is a maximum, a minimum, or a saddle-point. In case, the
estimated surface is determined not to have a simple optimum
well within the range of experimentation, then ridge analysis is
performed to aid in the interpretation of the existing response
system [19,20].