INTRODUCTION TO TAGUCHI METHOD

**2.2.2 A typical orthogonal array**

_{9 } (3^{4}) Orthogonal array | |||||

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Experiment # | |||||

The Table 2.1 shows an L_{9} orthogonal array.There are
totally 9 experiments to be conducted and each experiment is
based on the combination of level values as shown in the table.
For example, the third experiment is conducted by keeping the
independent design variable 1 at level 1, variable 2 at level
3, variable 3 at level 3, and variable 4 at level 3.

**2.2.3 Properties of an orthogonal array**

- The vertical column under each independent variables of the above table has a special combination of level settings. All the level settings appears an equal number of times. For L9 array under variable 4 , level 1 , level 2 and level 3 appears thrice. This is called the balancing property of orthogonal arrays.
- All the level values of independent variables are used for conducting the experiments.
- The sequence of level values for conducting the experiments shall not be changed. This means one can not conduct experiment 1 with variable 1, level 2 setup and experiment 4 with variable 1 , level 1 setup. The reason for this is that the array of each factor columns are mutually orthogonal to any other column of level values. The inner product of vectors corresponding to weights is zero. If the above 3 levels are normalized between -1 and 1, then the weighing factors for level 1, level 2 , level 3 are -1 , 0 , 1 respectively. Hence the inner product of weighing factors of independent variable 1 and independent variable 3 would be

**2.2.4 Minimum number of experiments to be conducted **

**2.3 Assumptions of the Taguchi method**

The design of an experiment involves the following steps

- Selection of independent variables
- Selection of number of level settings for each independent variable
- Selection of orthogonal array
- Assigning the independent variables to each column
- Conducting the experiments
- Analyzing the data
- Inference

The details of the above steps are given below.

**2.4.1 Selection of the independent variables**

**2.4.2 Deciding the number of levels **

**2.4.3 Selection of an orthogonal array**

**2.4.4 Assigning the independent variables to columns**