6.1.11. Taguchi Matrix

The Taguchi methods were developed by Genichi Taguchi in Japan to improve the implementation of total quality control. This method is related to finding the best values to make the system less sensitive to variations in uncontrollable noise factors, i.e. make the product more robust.

Figure 6.20. Taguchi Matrix Sequence Panel

For each input variable, the user should choose between two types of factors: Control Variable and Noise Variable. Control variables are those factors which can easily be controlled, noise variables are factors that are difficult or impossible to control. Examples ofnoise factors are ambient temperature, deterioration of parts or material, humidity etc.Noise factors are primarily response for causing a performance to depart from its target.

The Taguchi experiments are controlled by published orthogonal arrays. The orthogonal arrays are full factorial experiments, where each factor usually has the same number of levels (i.e. the experiment is balanced). The columns in the orthogonal arrays indicate the factor and its corresponding levels, the rows constitute the experiments. The right orthogonal array is chosen according to the number of input variables and the selected level. It is up to the user to establish the appropriate factor levels; typically either 2 or 3 levels are chosen but when the number of factors is limited the number of levels can be increased.

Taguchi DOE uses inner array and outer array method. The inner array is the orthogonal array for the control variables, the outer array is the orthogonal array for the noise variables. The combination of these two arrays consitutes the product array that represents the total set of experiments to be performed. The product array is automatically generated in the DOE Table, the total number of experiments is given by the product of the number of rows of each array.

modeFRONTIER^TM uses the first K columns of the orthogonal array (where K is the number of the input variables), the other columns are automatically deleted from the array.

Example

To evaluate effect of three design variables with two levels modeFRONTIER^TM uses the L4 orthogonal array as follows:

As shown in the above table, the L4 experiment consists of 4 rows and three columns where each row corresponds to a particular experiment and each column identifies settings of a design parameter. In the first design, for instance, the three design variable are set at their low level (level = 0).