Chaughule, Thorat - Statistical Analysis/Design of Experiments
three factor or higher order interactions. The full factorial design can prove to be very
inefficient when these higher order interactions can be assumed to be less important.
Instead, a fractional design can be used here to identify the important factors that can be
investigated more thoroughly in subsequent experiments. In unreplicated fractional fac-
torial designs, no degrees of freedom are available to calculate the error sum of squares.
The fractional factorial experimental design is useful for the responses affected by
two significant factors. If the response is influenced by three or more factors at a time
then factorial design is unable to interpret the complex interaction between the factors
affecting the same response. For this, higher order model can be employed.
8.6.3. Response surface methodology
Response surface methodology (RSM) is a collection of mathematical and statistical
techniques that are useful for designing experiments, building models, evaluating the
effects of factors and searching for the optimum conditions, modeling and analysis of
problems in which response of interests is influenced by several variables and objec-
tives (Montgomery, 2003, Kalil et al., 2000). By design of experiments, the objective is to
optimize a response (output variable), which is influenced by several independent va-
riables (factors). RSM can be used to evaluate the relative significance of several affect-
ing factors even in the presence of complex interactions.
Once the important factors have been identified, the next step is to determine the
settings for these factors that result in the optimum value of a response. This optimum
value can either be a maximum value or a minimum value, depending upon the product
or process in consideration. For example, if the response in a drying experiment is the
retention of micronutrients, then the objective would be to find the settings of the fac-
tors for maximum retention of micronutrients. On the other hand, if the response in an
osmotic dewatering experiment is the solid gain, then the goal would be to find the set-
ting that minimizes the solid gain.
The multivariate approach in RSM reduces the number of experiments, improves
statistical interpretation possibilities, and indicates interaction among different parame-
ters. Combinatorial interactions of drying parameters with the quality of dehydrated
product and the optimum processes may be developed using an effective experimental
design procedure. Two steps are necessary, the definition of an approximation function
or response and the design of the plan of experiments. These methods are exclusively
used to examine the "surface" or the relationship between the response and factors af-
fecting the response. RSM can be used for approximation of both experimental and nu-
merical responses. Regression models are used for analysis of the response, as the focus
is on nature of the relationship between the response and the factors, rather than identi-
fication of the important factors.
Response surface methods usually involve the following steps:
I. The experimental design is shifted from the current operating conditions to the
vicinity of the operating conditions where the response can be optimum. This is either
done by the method of steepest ascent (for maximizing the response) or the method of
steepest descent (for minimizing the response).