Taguchi's approach to parameter design provides the design engineer with a systematic and efficient method for determining near optimum design parameters for performance and any response [
12,
13,
14]. The objective is to select the best combination of control parameters so that the product or process is most robust with respect to noise factors. The Taguchi method utilizes orthogonal arrays from design of experiments theory to study a large number of variables with a small number of experiments. Using orthogonal arrays significantly reduces the number of experimental configurations to be studied. Furthermore, the conclusions drawn from small scale experiments are valid over the entire experimental region spanned by the control factors and their settings [
12]. Orthogonal arrays are not unique to Taguchi, they were discovered considerably earlier [
15]. However, Taguchi has simplified their use by providing tabulated sets of standard orthogonal arrays and corresponding linear graphs to fit specific projects [
16,
17].
2.2. Analysis of Variance (ANOVA)
The first step sequential F-tests were performed using analysis of variance (ANOVA), starting with a linear model and adding terms (linear). As shown in
Table 2, under the "Source" column of the table, the line labeled "Linear" indicates the significance of adding mean terms. The F-value is calculated for each type of model, and the highest order model with significant terms normally would be chosen. Significance is judged by determining if the probability that the F-value calculated from the data exceeds a theoretical value. The probability decreases as the value of the F-value increases. If this probability is less than 0.05 the terms are significant and their inclusion improves the model [
18]. In this study, the “linear” model is the highest order model with significant terms (P-value is less than 0.05); therefore, it would be the recommended model for this data. The 2FI (two factorial) model and higher were found to be aliased. Typically, the selected model will be the highest order polynomial where additional terms are significant and the model is not aliased [
19].
Table 2.
Statistical parameters for sequential models.
Table 2.
Statistical parameters for sequential models.
Source | Sum of Squares | Degree of Freedom | Mean Square | F Value | P Value | Remarks |
---|
Mean | 18751.65 | 1 | 18751.65 | - | - | - |
Linear | 173.61 | 4 | 43.40 | 11.74 | 0.0175 | Suggested |
2FI | 12.22 | 3 | 4.07 | 1.59 | 0.5141 | Aliased |
Residual | 2.56 | 0 | - | - | - | - |
Total | 18940.05 | 9 | 2104.45 | - | - | - |
The regression method was used to fit the” linear” (modified) model to the experimental data and to identify the relevant model terms [
20]. The response function to predict the percentage conversion of ester in the coded variables was as follows:
When a model has been selected, an analysis of variance (ANOVA) is calculated to assess how well the model represented the data [
21]. The values of the coefficients and the analysis of variance (ANOVA) are presented in
Table 3 and
Table 4.
Table 3.
Analysis of Variance (ANOVA) and statistical parameters of TEA-based esterquat cationic surfactant reaction (Linear model).
Table 3.
Analysis of Variance (ANOVA) and statistical parameters of TEA-based esterquat cationic surfactant reaction (Linear model).
Source | Sum of Squares | Degree of Freedom | Mean Square | F Value | P Value |
---|
Model | 184.07 | 5 | 36.81 | 25.54 | 0.0116 |
Residual | 4.32 | 3 | 1.44 | - | - |
Corrected Total | 188.39 | 8 | - | - | - |
R-Squared | 0.9770 | Standard Deviation | 1.20 |
Adjusted R2 | 0.9388 | Coefficient of variation % | 2.63 |
Adequate Precision | 15.872 | Predicted Residual Error of Sum of Squares (PRESS) | 46.41 |
Table 4.
Analysis of Variance (ANOVA) and Regression Coefficients of TEA-based esterquat cationic surfactant reaction (Linear model).
Table 4.
Analysis of Variance (ANOVA) and Regression Coefficients of TEA-based esterquat cationic surfactant reaction (Linear model).
Source | Coefficient Estimate | Sum of Squares | Degree of Freedom | Mean Square | F Value | P Value |
---|
Intercept | 47.17 | - | - | - | - | - |
X1 | −2.40 | 34.66 | 1 | 34.66 | 24.04 | 0.0162 |
X2 | 1.64 | 16.14 | 1 | 16.14 | 11.19 | 0.0442 |
X3 | 2.17 | 28.25 | 1 | 28.25 | 19.60 | 0.0214 |
X4 | 3.97 | 94.57 | 1 | 94.57 | 65.60 | 0.0039 |
X22 | −2.29 | 10.46 | 1 | 10.46 | 7.25 | 0.0742 |
The coefficients of the model were evaluated for significance with a Fisher’s F-test. The ANOVA indicates that the model F-value of 25.54 implied the model was significant. There was only 1.16% chance that the model F-value this large could occur due to noise. In general, the calculated F-value should be several times greater than the tabulated value for the model to be considered good [
22]. The coefficient of determination (R
2) of the model is obtained 0.9770, which indicates 97.70% of the variability in the response could be explained by the model. When R
2 approaches unity, the better empirical model fits the actual data [
22]. Normally, a regression model, having an R
2-value higher than 0.9 is considered as model having a very high correlation [
23]. The present R
2-value, therefore, reflected a very good fit between experimental and predicted values. The adjusted determination coefficient (Adjusted R
2 = 0.9388) was also satisfactory, confirming the significance of the model. The Coefficient of Variation (CV) as the ratio of the standard error of estimate to the mean value of the observed response (as a percentage) is a measure of reproducibility of the model and as a general rule a model can be considered reasonably reproducible if its CV is not greater than 10% [
24]. A lower value of coefficient variation (CV = 2.63%) clearly showed a high degree of precision and a good deal of reliability of the experimental values [
25]. The model also showed adequate precision by the measured the signal to noise ratio. The ratio greater than 4 is desirable. Thus, a ratio of 15.87 indicated an adequate signal. This model can be used to navigate the design space.
The P-values are used as a tool to check significance of each variable, which also indicate the interaction strength between each independent variable [
26]. The smaller P-values show the bigger the significance of the corresponding variable [
18]. P-values in this study less than 0.05 indicate model terms are significant. From the results obtained in
Table 4, all the linear coefficients, and the quadratic term were significant model terms (P-value less than 0.05). The final model to predict the percentage of conversion of TEA-based esterquat cationic surfactant reaction catalyzed by Novozyme 435 is shown in Equation (1).
Negative values of coefficient estimates denote negative influence of parameters on the reaction. It was observed that all the linear coefficients of the model gave positive effect except coefficient estimate for enzyme amount (X
1) in the model of percentage conversion. This may be due to the percentage of conversion was negatively affected by the presence of higher amount of enzyme as the ratio of ester amount/ initial amount of enzyme is lower at higher enzyme amount compared to lower enzyme amount. Besides, it was observed that has significant effect to the reaction. Indeed, despite the negative value, amount of enzyme has one of the biggest effects to response after the effect of molar ratio of substrates.
where
Y = Percentage of Conversion,
X1 = Amount of Enzyme,
X2 = Reaction Time,
X3 = Reaction Temperature and
X4 = Substrate Molar Ratio (OA: TEA)
2.3. Optimization of Reaction and Model Validation
Three solutions with different desirability values were used to predict the optimal conditions for Novozyme-catalyzed production of TEA-based esterquat cationic surfactants and they are presented in
Table 5. Experiments were then carried out under the recommended conditions and the resulting responses were compared to the predicted values. The largest reaction conversion% (49.94%) was obtained in experiment number 3 compared to the other two experiments. The optimum reaction parameters were: enzyme loading of 5.50 wt % of oleic acid, amount of oleic acid of 17.70 mmol, amount of triethanolamine of 8.85 mmol (molar ratio of substrates 1:2), reaction time of 14.44 hours and reaction temperature of 61 °C. The relative deviation of 3.14% is also obtained from the Taguchi experimental design. Comparison of predicted and actual values revealed good correspondence between them, implying that the empirical model derived from Taguchi experimental design can be used to adequately describe the relationship between the factors and the response in Novozyme- catalyzed synthesis of TEA-based esterquat cationic surfactant.
Table 5.
Optimum conditions derived by Taguchi design for TEA-based esterquat cationic surfactant synthesis.
Table 5.
Optimum conditions derived by Taguchi design for TEA-based esterquat cationic surfactant synthesis.
Exp. | Optimal Conditions | Conversion % |
---|
X1 | X2 | X3 | X4 | Actual | Predicted | Relative Deviation |
---|
1 | 5.50 | 14.06 | 61.00 | 2.00 | 47.34 | 48.49 | 2.37 |
2 | 5.50 | 14.00 | 60.83 | 2.00 | 46.27 | 48.44 | 4.48 |
3 | 5.50 | 14.44 | 61.00 | 2.00 | 49.94 | 48.42 | 3.14 |
The lower amount of Novozyme 435 is required to produce the respective amount of product in the aforementioned experiment. From the process point of view, it would be desirable to use lowest enzyme amount to achieve maximum conversion of substrate [
27]. This is because Novozyme 435 is more expensive that the other substrates, thus high reaction conversion obtained by low amount of enzyme. Moreover, shorter reaction time and lower reaction temperature were considered in optimization process because longer reaction time and higher reaction temperature lead to enzyme denaturation and both could resulted in lower reaction conversion especially in longer reaction time.