**4. Experiment**

In this section, a summary of Hamzaçebi [21] is given. Hamzaçebi [21] applied the TM to determine the effects of production factors such as adhesive ratio, press pressure, and pressing time on the thermal conductivity (TC) of oriented strand board (OSB). MINITAB 17 statistical software (State College, PA, USA) was used to analyze experiments in the Taguchi design.

#### **4.1 Data**

In the article of Ref [21], adhesive ratio, pressing time, and press pressure were considered as controllable factors. **Table 6** indicates the process parameters and their levels. As deduced from **Table 6**, there are 3 factors, which have 3 levels. After the factor definitions, suitable Taguchi orthogonal array was selected as L9. The L9 design sheet and output of each experiment was given in **Table 7**.


**Table 6.** *The process parameters and their levels.*


level of press pressure (35 kg/cm<sup>2</sup>

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

*=*

where *S=N* is the overall mean of <sup>S</sup>

parameter, and *m* is the number of <sup>S</sup>

mean were calculated by Eqs. (4) and (5), respectively.

the TC of OSB.

<sup>N</sup> *ratio values of TC.*

**Table 8.** S*=*

the overall mean of <sup>S</sup>

contribution results.

**Table 9.**

**125**

) were the optimal values for the minimization of

<sup>N</sup> ratios and the sum of squares due to variation about overall

<sup>N</sup> ratio, ð Þ *S=N <sup>i</sup>* is the <sup>S</sup>

ð Þ *S=N <sup>i</sup>* � *S=N* � � � � <sup>2</sup>

where *SS*Total is the total sum of squares. Secondly, for the ith process parameter, the sum of squares due to variation about overall mean was calculated by Eq. (6).

> ð Þ *S=N ij* � *S=N* � � � � <sup>2</sup>

parameter of jth level, and *ki*mi is the number of levels of ith parameter. Finally, the contribution (Cont) of ith parameter was calculated by Eq. (7). **Table 9** presents the

*SSTotal*

**Process parameter Sum of squares (SSi) % Contribution Rank** Adhesive ratio 0.6667 54.64 1 Press pressure 0.2456 20.13 3 Pressing time 0.3078 25.23 2

*Conti* <sup>¼</sup> *SSi*

*=*

<sup>N</sup> ratio for ith

ð Þ *S=N <sup>i</sup>* (4)

*=*

*=*

<sup>N</sup> )ij is the <sup>S</sup>

*x*100 (7)

*=*

<sup>N</sup> ratio values,

(5)

(6)

<sup>N</sup> ratio of ith

Hamzaçebi [21] applied the Pareto ANOVA to determine the percent contribu-

**Level Adhesive ratio Pressing time Press pressure** 1 16.74 16.77 16.86 2 16.74 16.39 16.14 3 15.74 16.07 16.23 Delta 1.00 0.70 0.72 Rank 1 3 2

tion of each parameter on the TC. To obtain the Pareto ANOVA of <sup>S</sup>

*<sup>S</sup>=<sup>N</sup>* <sup>¼</sup> <sup>1</sup> *m* X*m i*¼1

*=*

*=*<sup>N</sup> ratios.

*i*¼1

*SSTotal* <sup>¼</sup> <sup>X</sup>*<sup>m</sup>*

*SSi* <sup>¼</sup> <sup>X</sup> *ki*

where *SS*<sup>i</sup> is the sum of the square for ith parameter, (S

Total 1.2201 100

*Contribution of process parameters based on Pareto ANOVA.*

*j*¼1

#### **Table 7.**

*The design sheet and output of each experiment.*

In **Table 7**, *y* and *s* present the mean and standard deviation of the TC values, respectively.

#### **4.2 Solution and results**

Hamzaçebi [21] was used the <sup>S</sup>*=*<sup>N</sup> ratio and Pareto ANOVA analysis to evaluate the results of the experiment.

**Figure 3** is the main effect graph of <sup>S</sup>*=*<sup>N</sup> ratios that states the optimal level of the factors. The biggest <sup>S</sup>*=*<sup>N</sup> ratio indicated the optimal combination of parameter values. The ranking of the process parameters was obtained from <sup>S</sup>*=*<sup>N</sup> ratio table which is given in **Table 8**. This order was determined by comparison of delta values. The delta value is equal to the difference between maximum and minimum values for levels of each factor. **Table 8** shows that the order of importance in minimizing the TC of OSB is adhesive ratio, press pressure, and pressing time. **Figure 3** shows the optimal level of the process parameters. As deduced from **Figure 3**, the second level of adhesive ratio (3%), the first level of pressing time (3 min), and the first

**Figure 3.** *Main effect plots for* <sup>S</sup>*=*<sup>N</sup> *ratios of process parameters.*

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


**Table 8.**

In **Table 7**, *y* and *s* present the mean and standard deviation of the TC values,

**Experiment Factors Response**

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

 1 1 1 0.129 0.010 1 2 2 0.153 0.028 1 3 3 0.152 0.025 2 1 2 0.142 0.023 2 2 3 0.143 0.026 2 3 1 0.146 0.025 3 1 3 0.163 0.027 3 2 1 0.154 0.018 3 3 2 0.170 0.019

**Adhesive ratio Pressing time Press pressure** *y s*

*=*

which is given in **Table 8**. This order was determined by comparison of delta values. The delta value is equal to the difference between maximum and minimum values for levels of each factor. **Table 8** shows that the order of importance in minimizing the TC of OSB is adhesive ratio, press pressure, and pressing time. **Figure 3** shows the optimal level of the process parameters. As deduced from **Figure 3**, the second level of adhesive ratio (3%), the first level of pressing time (3 min), and the first

<sup>N</sup> ratio indicated the optimal combination of parameter

<sup>N</sup> ratio and Pareto ANOVA analysis to evaluate

<sup>N</sup> ratios that states the optimal level of the

*=*

<sup>N</sup> ratio table

*=*

values. The ranking of the process parameters was obtained from <sup>S</sup>

respectively.

**Table 7.**

**Figure 3.**

**124**

*Main effect plots for* <sup>S</sup>

*=*

<sup>N</sup> *ratios of process parameters.*

**4.2 Solution and results**

factors. The biggest <sup>S</sup>

the results of the experiment.

Hamzaçebi [21] was used the <sup>S</sup>

*The design sheet and output of each experiment.*

**Figure 3** is the main effect graph of <sup>S</sup>

*=*

S*=*<sup>N</sup> *ratio values of TC.*

level of press pressure (35 kg/cm<sup>2</sup> ) were the optimal values for the minimization of the TC of OSB.

Hamzaçebi [21] applied the Pareto ANOVA to determine the percent contribution of each parameter on the TC. To obtain the Pareto ANOVA of <sup>S</sup>*=*<sup>N</sup> ratio values, the overall mean of <sup>S</sup>*=*<sup>N</sup> ratios and the sum of squares due to variation about overall mean were calculated by Eqs. (4) and (5), respectively.

$$\overline{S/N} = \frac{1}{m} \sum\_{i=1}^{m} \left( \mathbf{S}/N \right)\_i \tag{4}$$

where *S=N* is the overall mean of <sup>S</sup>*=*<sup>N</sup> ratio, ð Þ *S=N <sup>i</sup>* is the <sup>S</sup>*=*<sup>N</sup> ratio for ith parameter, and *m* is the number of <sup>S</sup>*=*<sup>N</sup> ratios.

$$\text{SS}\_{\text{Total}} = \sum\_{i=1}^{m} \left( (\text{S/N})\_i - \left( \overline{\text{S/N}} \right) \right)^2 \tag{5}$$

where *SS*Total is the total sum of squares. Secondly, for the ith process parameter, the sum of squares due to variation about overall mean was calculated by Eq. (6).

$$\text{SS}\_{i} = \sum\_{j=1}^{k\_i} \left( (\text{S}/\text{N})\_{ij} - \left( \overline{\text{S}/\text{N}} \right) \right)^2 \tag{6}$$

where *SS*<sup>i</sup> is the sum of the square for ith parameter, (S*=*<sup>N</sup> )ij is the <sup>S</sup>*=*<sup>N</sup> ratio of ith parameter of jth level, and *ki*mi is the number of levels of ith parameter. Finally, the contribution (Cont) of ith parameter was calculated by Eq. (7). **Table 9** presents the contribution results.

$$\text{Cont}\_{i} = \frac{\text{SS}\_{i}}{\text{SS}\_{Total}} \text{x100} \tag{7}$$


**Table 9.**

*Contribution of process parameters based on Pareto ANOVA.*
