## 2 Materials and Methods
### Morphology and Mechanical Behaviour of the Composite
#### 2.3.6 Statistical Analysis of Responses  
Experimental values obtained from the mechanical tests were analysed for signal to noise (S/N) ratio with the aim of achieving optimization of individual responses. The S/N ratio values were calculated using larger-the better characteristics from Equation (1) and shown in Tables 2 and 3 for both mono-reinforced and hybrid composites. Further optimization of the values was carried out using Grey relational analysis (GRA) to determine the optimum combination in property of the fabricated composites. GRA is part of grey system theory, that was proposed by [PERSON] in 1982 [53] and is usedfor solving problems with complicated interrelationships amid multiple factors and variables [54]. According to [PERSON] et al. [55], this procedure involves utilizing the S/N ratio values obtained to calculate the Grey relational generation (GRG) using the larger-the better attributes with Equation (2) followed by Grey relation coefficient (GRC) using Equation (3) [55] and afterwards Grey relational grade (GR*grade) using Equation (4) [55]. The GRG is the step in GRA that converts the original data into a sequence that can be compared, while GRC is used to identify the elements that influence the system's behaviour. The concluding process of GRA is the determination of optimal factors for the single response by the GR*grade. \[Larger-the\ better:\frac{S}{N}=-10 log\frac{1}{n}\left(\sum_{i=1}^{n}\frac{1}{y^{ 2}}\right) \tag{1}\]  
where \(y\) = number of observations, \(n\) = response value. \[Larger-the\ better\ attributes\ \left(\chi_{ij}\ \right)=\frac{y_{ij}-\underline{y}_{i}}{ \overline{y}_{i}-y_{j}} \tag{2}\]  
(\(i\) = 1, 2, 3, 4...... \(m\) and \(j\) = 1, 2, 3, 4... \(n\)) where, \(y_{i}\) = (\(y_{i1}\), \(y_{i2}\),..., \(y_{ij}\),..., \(y_{in}\)), \(y_{y}\) is the performance value of attribute \(j\) of alternative \(i\) and \(\overline{y}_{i}\) = max{\(y_{ij}\), \(i\) = 1, 2,..., \(m\)} and \(\underline{y}_{i}\) = min{\(y_{ij}\), \(i\) = 1, 2,..., \(m\)}. \[\gamma\left(\chi_{0j},\ \chi_{ij}\right)=\frac{\Delta_{min}+\beta\Delta_{max}}{ \Delta_{ij}+\beta\Delta_{max}}\ \ \ \ (i=1,2,\ \ldots,\ m\ and\ j=1,2,\ldots,n) \tag{3}\]  
where, \(\gamma(x_{0j},\ x_{ij})\) is the GRC between \(x_{ij}\) and \(x_{0j}\). \(\Delta_{ij}=x_{0j}-x_{ij}\), \(\Delta_{min}\) = min (\(\Delta_{ij}\), \(i\) = 1, 2,..., \(m\); \(j\) = 1, 2,..., \(n\)), \(\Delta_{max}\) = max (\(\Delta_{ij}\), \(i\) = 1, 2,..., \(m\); \(j\) = 1, 2,..., \(n\)) and \(\beta\) is the distinguishing coefficient, \(\beta\) \(\in\) [0,1]. The aim of the distinguishing coefficient (\(\beta\)) is to compress or expand the range of the grey relational coefficient and 0.5 is the broadly accepted value [56]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{3}{*}{**Run**} & \multirow{3}{*}{**S/N for**} & **S/N for** & **S/N for** & **S/N for** & **S/N for** & **S/N for** & **S/N for** \\  & & **Flexural** & **Flexural** & **Tensile** & **Tensile** & **Tensile** & **Hardness** \\  & **wt\% UPT** & **Strength** & **Modulus** & **Strength** & **Modulus** & **(HV)** \\  & & **(MPa)** & **(GPa)** & **(MPa)** & **(GPa)** & **(GPa)** & \\ \hline A1 & 39.0849 & 28.0830 & 8.5821 & 23.9373 & 0.6120 & 32.1491 \\ A2 & 38.8897 & 26.7612 & 7.6655 & 20.0563 & 4.1095 & 33.2797 \\ B1 & 38.6900 & 26.8957 & 7.4251 & 19.5224 & 3.5738 & 34.1292 \\ B2 & 38.4856 & 27.8820 & 5.9025 & 20.8279 & 2.5551 & 34.3866 \\ C1 & 38.2763 & 25.0861 & 3.5853 & 21.0884 & 1.8052 & 34.9436 \\ \hline \end{tabular}
\end{table} 
Table 2: Experimental result of the S/N ratio values for mono-reinforced composites.