A response surface methodology (RSM) is an advanced experimental design technique used to explore and optimize the relationship between several input variables (factors) and an output variable (response). The main objective is to understand how the response varies with factor levels, and to identify the optimal conditions for the desired response.
Response surface methodology (RSM) is often applied after the completion of screening or factorial designs, which help to identify the factors most influential on response. When there is a suspicion of curvature or non-linearity in the relationship between factors and response, a response surface methodology becomes particularly useful.
The typical process of a response surface methodology (RSM) involves the selection of factor levels, the collection of experimental data at these levels, the construction of a mathematical model that represents the relationship between factors and response, and finally, the optimization of this response to identify optimal conditions.
Response surface methodology (RSM) can take many forms, but generally involve the systematic variation of factor levels to explore different regions of factor space. The use of such designs enables the relationship between factors and response to be modeled more accurately, taking into account interactions and non-linearities.
Ellistat offers a variety of response surface methodologies (RSMs) for different situations. These include the Box-Behnken Design, the Central Composite Design, the Doehlert Experimental Design, D-Optimal Designs, the Hoke Design, Latin Hypercube Sampling, and the NOLH experimental designs. Each of these experimental design methodologies is intended to meet specific needs in terms of experimentation and optimization, offering maximum flexibility and adaptability for Ellistat users.
Centered composite planes
Centered composite designs are a class of Design of Experiments (DOE) that are used to model the relationship between input variables (factors) and the output variable (response) in an experimental environment. These designs are often employed when there is a need to explore and understand a complex response surface while minimizing the number of experimental trials.
A typical centered composite design includes the following elements:
Central points These are points where all factors are set at their central level, often represented by the number zero. These points are used to estimate the linear effects of the factors.
Axial points The "alpha" value is used to determine the distance of the axial points from the center of the factor space. More precisely, the axial points are generally positioned at an "alpha" distance from the central points along the main axes). These points are used to estimate the quadratic effects of the factors.
Axial Cube Points They are used to estimate interactions between factors. These points are located at a distance of ±1 from the origin, but along the main axes (x, y, z) in a three-factor space.
Centered composite designs are particularly useful in situations where non-linear response or significant interaction between factors is suspected. They allow more detailed characterization of the response surface, while keeping the number of trials relatively low compared with exhaustive exploration of the factor space.
Figure 1 Example of a centered composite plane in the case of 3 variables: green points represent the central points, blue points represent the axial points of the cube, orange points represent the axial points.