*Taguchi Method as a Robust Design Tool DOI: http://dx.doi.org/10.5772/intechopen.94908*


#### **Table 3.**

**3.7 Choosing appropriate orthogonal arrays**

*Quality Control - Intelligent Manufacturing, Robust Design and Charts*

characteristic can be studied.

shown in **Table 2**.

**Table 2.**

**118**

*L9 orthogonal Array.*

Orthogonal Arrays (OA) take us all the way to Euler's Greco-Latin squares. But

The idea of using OA in DOE independently of each other is originated in the USA and Japan after World War II [36]. The first use of OA was in the 1930s by Fisher in England. Taguchi added three OAs in 1956. And in the following years, three OAs were added by the American NIST [31]. Taguchi makes use of OA in performing multivariate experiments with a small number of trials. Using OA significantly reduces the size of the experiment to be studied [37]. The use of OA is not exclusive to Taguchi. However, Taguchi simplified their usage. Taguchi developed tabulated standard OA and corresponding linear graphs. A typical OA table is

In this array the columns are bilateral orthogonal. In each column there are all combinations of factor levels with an equal number. There are 4 factors (A, B, C, D) and three levels of each. This design is called the L9 design. The letter L indicates the orthogonal array, and 9 the row number, in other words the number of trials [4]. One point we should pay attention to that how much the OA reduces the

the number of attempts to be made in large numbers. For our example, 3<sup>4</sup> = 81 trials are required, but only 9 trials will be done to achieve the same results. It is obvious that it will provide more convenience in larger series. **Table 3** highlights the conve-

OA allows working economically and simultaneously with many variables that are effective in product mean and variance. Two different OAs can be selected for CV and UCV. Using statistical DOE techniques, suitable subsets for CV and CIA can be demonstrated. Taguchi suggests using OA in planning DOE optimization. The multiplicity of CV and the emergence of interaction require very careful attention in the selection of OA and assignment of CV to columns. Target in establishing CV

11111 21222 31333 4212 3 52231 62312 73132 83213 93321

**ABCD**

), OA significantly reduces

number of trials. Due to the full factorial design (2<sup>k</sup> or 3<sup>k</sup>

nience that OA provides in terms of the number of trials [37].

in Euler's time they were not known as OA. At that time they were known as mathematical games, like 36 office workers' problems. OA is a matrix of numbers arranged in rows and columns. Orthogonal arrays have a balanced property which entails that every factor setting occurs the same number of times for every setting of all other factors considered in the experiment. In an OA, each row represents the levels of the selected factors in a given experiment, and each column represents a specific factor whose effects on the process performance or product quality

*Frequently used OAs and full factorial design comparison.*


#### **Table 4.** *OA information table.*

matrix; It should be to setup a design where the most information can be obtained with the least effort. **Table 4** presents a brief knowledge about the OAs.

Depending on the levels of CV, an appropriate OA is chosen or some changes are made on the selected OA. The assignment of the CV and interaction variables to the columns is achieved by using standard linear graphs suitable for the selected OA. To determine a suitable OA for the experiment, the following procedure should be followed.

