Orthogonal Arrays

The simulation procedure is described by orthogonal arrays called Taguchi matrices. Such an array is based on the number of variables and their interactions (columns) plus the number of levels which yield the number of lines. Usually a pre-defined matrix is chosen, but it is also possible to design a new matrix or to adapt an existing matrix. In Figure 1a L9 matrix is shown, which is suitable for the evaluation of the influence of 4 parameters with 3 levels each. The first column shows the number of the simulation. The following 4 columns (A-D) describe the settings for the 4 parameters. The results of the 9 simulations are recorded in the last column. The matrix describes the setting for each parameter. For example in simulation number 4 the parameter A is set to level 2, parameter B to level 1, parameter C to level 2 and parameter D is set to level 3. Several pre-defined matrices exist, shown in Figure 2 for different numbers of parameters and levels.

A modification of these matrices is possible. For example, the number of levels of a chosen parameter can be increased or reduced. But it has to be kept in mind that the sum of the degrees of freedom for all columns is not higher than the degree of freedom of the whole matrix. The degree of freedom of one column is equal to the number of levels minus 1 while the degree of freedom of the matrix is the number of simulations minus 1.

After all simulations have been done, the influence of each parameter is determ­ined by an statistical ANOVA-Analysis (Analysis of Variances).