• 107328  Infos

Central composite design

    '''Central Composite Design''' is a [response surface methology] for fitting a second order model to a data set without needing to use a complete 3^k [factorial experiment] After the necessary experiment is created (multiple) linear regression is performed

    Method

    The matrix A for an experiment involving k factors consists of the following three different parts:
    1. The matrix obtained from the 2^k factorial experiment This will be denoted by F
    2. The centre of the system of interest denoted in coded variables as (0000) where there are k zeros This point is often repeated so in order to improve the resolution of the method This part will be denoted by C
    3. A matrix with 2k row where each factor is placed at +-α and all other factors are at zero The α value is determined by the designer and it can have just about any value Thus this part denoted by {cal E} will have the following form:
    [{cal E} = left[ {begin{array}{*{20}c} alpha & 0 & 0 & cdots & cdots & cdots & 0 { - alpha } & 0 & 0 & cdots & cdots & cdots & 0 0 & alpha & 0 & cdots & cdots & cdots & 0 0 & { - alpha } & 0 & cdots & cdots & cdots & 0 vdots & {} & {} & {} & {} & {} & {} 0 & 0 & 0 & 0 & cdots & cdots & alpha 0 & 0 & 0 & 0 & cdots & cdots & { - alpha } end{array}} right

    Determining the value of α

    There are many different methods to determine the value of α Define F = 2k the number of points due to the factorial design and T = 2k + n the number of additional points where n is the number of central points in the design Common values are as follows (Myers 1971):
    1. Orthogonal design: [
    alpha = (025QF)^{025}] where [Q = left( {sqrt {F + T} - sqrt F } right)^2];
    1. Rotatable : [
    alpha = F^{025}] which is the design implemented by MATLAB’s “ccdesign(k)” function

    Reference

    Myers Raymond H. Response Surface Methodology Boston: Allyn and Bacon Inc 1971