**2.3 Signal to noise ratio**

Taguchi method stresses the necessity of studying the response variable using the signal-to-noise ratio, resulting to decrease the effect of quality characteristic


*2.4.2 ANOVA table*

as a one-way ANOVA.

n = the total sample <sup>¼</sup> <sup>P</sup><sup>k</sup>

*2.4.4 Parting the total variability*

Sources of variability:

SSG = P<sup>k</sup>

3. SSE = Pni

**Table 4.**

**169**

j¼1*:* Pni

N = total number of observations SSf = sum of squares of a factor K = number of levels of the factor SSe = sum of squares of error Fo = computed value of F Vf = variance of the factor Ve = variance of the error

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

*2.4.3 One-way ANOVA and their notation*

k = the number of groups/populations/

x = the mean of all responses ¼ 1*=*n

Where,

A detail of all analysis of variance computations is given **Table 4**.

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

When there is just one explanatory variable, we refer to the analysis of variance

ni P<sup>n</sup> j¼i xij

<sup>j</sup>¼<sup>1</sup>ð Þ xij � <sup>x</sup> <sup>2</sup>

<sup>j</sup>¼<sup>1</sup>ð Þ xij‐xi <sup>2</sup>

Here is a key to symbols you may see as you read through this section.

si = the sample standard deviation from the ith group <sup>¼</sup> <sup>1</sup>*=*ð Þ ni � <sup>1</sup> <sup>P</sup>ni

P*:* ij xij

Viewed as one sample one might measure the total amount of variability among observations by summing the squares of the differences between each xi j and x:

<sup>i</sup>¼<sup>1</sup>ð Þ ni � <sup>1</sup> s2

**Source of variation Sum of squares Degree of freedom Mean square variance Fo** Factor SSf K � 1 Vf = SSf/K � 1 Vf/Ve

Error SSe N � K Ve = SSe/N � K

i

j¼1*:* Pni

xi j = the jth response sampled from the ith group/population. xi = the sample mean of responses from the ith group <sup>¼</sup> <sup>1</sup>

<sup>i</sup>¼<sup>0</sup>xi

1.SST (stands for the sum of squares total)Pni

Sum of Square Group within groups means

<sup>j</sup>¼<sup>1</sup>ð Þ xij � <sup>x</sup> <sup>2</sup> <sup>¼</sup> <sup>P</sup><sup>k</sup>

2. Sum of Square Group between group

It is the case that SST = SSG + SSE.

Total SStotal N � 1

*Analysis of Variance Computations (ANOVA).*

<sup>i</sup>¼<sup>0</sup>ni xij ð Þ � <sup>x</sup> <sup>2</sup>

#### **Table 3.**

*Standard L8 orthogonal array.*

variation due to the uncontrollable parameter. The S/N ratio can be used in three types:

i. Larger the better:

S/N Ratio = �10log. 1/a [<sup>P</sup> <sup>i</sup>¼<sup>0</sup>1*=*yi2]

ii. Smaller the better:

S/N Ratio = �10log.1/a [<sup>P</sup> <sup>i</sup>¼<sup>0</sup>yi2]

iii. Nominal the best:

S/N Ratio = �10log. [<sup>P</sup> <sup>i</sup>¼<sup>0</sup>̄yi 2/s2]

Where,

a = Number of trials

yi = measured value


Parameters that affect the output can be divided into two parts: controllable (or design) factors and uncontrollable (or noise) factors. Uncontrollable factors cannot be controlled but its effect can be minimized by varying the controllable factors.

#### **2.4 Analysis of variance**

ANOVA were first introduced by Sir Ronald A, Fisher, the British biologist. ANOVA is a method of partitioning total variation into accountable sources of variation in an experiment. It is a statistical method used to interpret experimented data and make decisions about the parameters under study. ANOVA is a statistical method used to test differences between two or more means [1].

#### *2.4.1 Hypotheses of ANOVA*

H0: The (population) means of all groups under consideration are equal. Ha: The (pop.) means are not all equal. (Note: This is different than saying. they are all unequal.)

*Application of Taguchi Method in Optimization of Pulsed TIG Welding Process Parameter DOI: http://dx.doi.org/10.5772/intechopen.93974*

## *2.4.2 ANOVA table*

variation due to the uncontrollable parameter. The S/N ratio can be used in three

1 1111111 2 1112222 3 1221122 4 1222211 5 2121212 6 2122121 7 2211221 8 2212112

**1234567**

<sup>i</sup>¼<sup>0</sup>1*=*yi2]

<sup>i</sup>¼<sup>0</sup>yi2]

<sup>i</sup>¼<sup>0</sup>̄yi 2/s2]

Parameters that affect the output can be divided into two parts: controllable (or design) factors and uncontrollable (or noise) factors. Uncontrollable factors cannot be controlled but its effect can be minimized by varying the controllable factors.

ANOVA were first introduced by Sir Ronald A, Fisher, the British biologist. ANOVA is a method of partitioning total variation into accountable sources of variation in an experiment. It is a statistical method used to interpret experimented data and make decisions about the parameters under study. ANOVA is a statistical

H0: The (population) means of all groups under consideration are equal.

Ha: The (pop.) means are not all equal. (Note: This is different than saying. they

method used to test differences between two or more means [1].

types:

**Table 3.**

i. Larger the better:

*Standard L8 orthogonal array.*

ii. Smaller the better:

iii. Nominal the best:

a = Number of trials yi = measured value

s = standard deviation

**2.4 Analysis of variance**

*2.4.1 Hypotheses of ANOVA*

are all unequal.)

**168**

Where,

S/N Ratio = �10log. 1/a [<sup>P</sup>

**Trial no. Column**

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

S/N Ratio = �10log.1/a [<sup>P</sup>

S/N Ratio = �10log. [<sup>P</sup>

ȳ = mean of the measured value

A detail of all analysis of variance computations is given **Table 4**. Where,

N = total number of observations

SSf = sum of squares of a factor K = number of levels of the factor

SSe = sum of squares of error

Fo = computed value of F

Vf = variance of the factor

Ve = variance of the error
