*2.4.5 Calculation*

An F statistic is obtained from ANOVA test or a regression analysis to find out if the means between two populations are significantly different [1]. F statistics is used to decide the acceptance or rejection of null hypothesis. F value is calculated from the data, if calculated is larger than F statistics the null hypothesis is rejected. The ANOVA table showing F value is given in **Table 5**.

statistic is sufficiently large. As with other hypothesis tests, we determine whether

*Application of Taguchi Method in Optimization of Pulsed TIG Welding Process Parameter*

In the two-way ANOVA model, there are two factors, each with several levels as

Taguchi DOE is a well-known factual strategy that gives a legitimate and productive technique for process optimization. The Taguchi technique enables us to improve the consistency of production. Taguchi design recognizes that not all factors that cause variability can be controlled. These uncontrollable factors are called noise factor. Taguchi design tries to identify the controllable factor that minimizes the effect of noise factors. During experimentation, you manipulate the control factor to evaluate variability that occurs and then determines the optimal control factor setting, which minimizes the process variability. A process designed with this goal produces more consistent output and performance regardless of the environment in which it is used. It is world widely used for product design and process optimization. As a result, time is reduced considerably. Taguchi DOE methodology uses an orthogonal array that gives different combinations of param-

The following sequence is followed while forming the experiment.

• Calculating the upper and lower limits process parameters.

**4. Selecting base material and their mechanical properties**

AISI 316 stainless steel sheets of dimension 100 75 4 mm are welded autogenously with the butt joint without edge preparation [7]. The chemical

**Grade 316 C Mn Si P S Cr Mo Ni N**

Max. 0.08 2.0 0.75 0.045 0.030 18.0 3.0 14.0 0.10

Min. ——— — — 16.0 2.0 10.0

the F statistic is large by finding a corresponding P-value.

**3. Taguchi design of experiment (DOE)**

*DOI: http://dx.doi.org/10.5772/intechopen.93974*

eters and their levels for each experiment [6].

**3.1 The layout of the experiment**

• Base and filler material selection.

• Selection of process parameters.

• Experiment conducted.

**Table 7.**

**171**

• Selection of standard orthogonal array.

• Calculating optimum condition [6].

*Chemical composition of the base material (wt %).*

*2.4.6 Two-way ANOVA*

shown in **Table 6**.

SS = Sum of Squares (sum of squared deviations):

SST measures the variation of the data around the overall mean x SSG measures the variation of the group means around the overall mean x SSE measures the variation of each observation around its group mean xi

• Degrees of freedom

k � 1 for SSG

n � k for SSE, since it measures the variation of the n observations about k group means. n � 1 for SST, since it measures the variation of all n observations about the overall mean.


It is interesting to note that another formula for MSE is

$$\mathbf{MSE} = \frac{(\mathbf{n}\_1 - \mathbf{1}) + (\mathbf{n}\_2 - \mathbf{1}) + (\mathbf{n}\_3 - \mathbf{1}) + \dots \dots (\mathbf{n}\_k - \mathbf{1})s\_k^2}{(\mathbf{n}\_1 - \mathbf{1}) + (\mathbf{n}\_2 - \mathbf{1}) + \dots \dots + (\mathbf{n}\_k - \mathbf{1})} \times$$

• The F statistic = MSG/MSE

If the null hypothesis is true, the F statistic has an F distribution with k-1 and n-k degrees of freedom in the numerator/denominator respectively. If the alternative hypothesis is true, then F tends to be large. We reject Ho in favor of Ha if the F

