## 2 Material and Method
### Grey Relational Analysis (GRA)  
GRA [24] is one of the progressive methods for optimizing process parameters, especially when dealing with ambiguous input parameters. It is used to alter responses from multiple targets to single targets using fuzzy social surveys. The dark test, which is based on the unpredictability of the tests, is shaped into an evaluation method to solve obvious structural problems that are jamming with fragmented information. This dark inspection arrangement is divided into two parts. The relative  
Figure 4: (**a**) The delamination and (**b**) the uncut fiber area.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{3}{c}{**Level**} \\ \cline{2-4}  & **1** & **2** & **3** \\ \hline \multirow{2}{*}{\begin{tabular}{c} Spindle speed (S) (rpm) \\ Feed rate (F) (mm/min) \\ Twist angle (T) (Type) \\ Lubrication (L) \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} 228 \\ Triple \\ Dry mode \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} 6100 \\ 589 \\ Low helix \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} 1006 \\ High helix \\ CO\({}_{2}\) \\ \end{tabular} } \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameter of drilling process.  
data that are entirely known are contained in the white frame, and the relatively obscured data are contained in the black frame.  
The quality response targets of the drilling process were the surface roughness, the uncut fiber, and the delamination. The machining parameters, such as cryogenic lubrication, feed rate, and twist angle were used to analyze to minimize the effects of response on bore quality. The grey analysis was grouped into two phases regarding the accompanying progress recorded below. The fundamental ability of GRA standardization for test values in the range 0 to 1 is known as grey relational information.  
The surface roughness, uncut fiber, delamination responses were considered \"lower is better\". The normalized value could be expressed as follows:  
\[x_{i}^{*}(a)=\frac{maxx_{i}^{0}(a)-x_{i}^{0}(a)}{maxx_{i}^{0}(a)-minx_{i}^{0}( a)}, \tag{3}\]  
where \(i=1\),..., \(m\). \(m\) is the number of experimental data items. \(a=1\),..., \(n\). \(n\) is the number of parameters. \(x_{i}^{0}(a)\) denote the original sequence, \(x_{i}^{*}(a)\) is the sequence after the data pre-processing. \(maxx_{i}^{0}(a)\) is the largest value of \(x_{i}^{0}(a)\), \(minx_{i}^{0}(a)\) is the smallest value of \(x_{i}^{0}(a)\).  
The grey relational coefficient (GRC) was estimated for R\({}_{\text{a}}\), U\({}_{\text{c}}\), D\({}_{\text{L}}\) as follows:  
\[\zeta(\text{a})=\frac{\Delta_{min}+\xi\Delta_{max}}{\Delta_{0i}(k)+\xi\Delta_{ max}}, \tag{4}\]  
with  
\[\Delta_{0i}=\|x_{0}^{*}(a)-x_{i}^{*}(a)\|, \tag{5}\]  
\[\Delta_{min}=\min_{\forall j\in i}\min_{\forall k}\|x_{0}^{*}(a)-x_{j}^{*}(a )\|, \tag{6}\]  
\[\Delta_{max}=\max_{\forall j\in i}\max_{\forall k}\|x_{0}^{*}(a)-x_{j}^{*}(a )\|, \tag{7}\]  
where \(x_{0}^{*}(a)\) and \(x_{i}^{*}(a)\) denote the reference sequence and the comparability sequence, respectively. \(\Delta_{0i}\) is the deviation sequence of the \(x_{0}^{*}(a)\) and \(x_{i}^{*}(a)\). \(\xi\) is the distinguishing coefficient, \(\xi\in[0,1]\). Normally, \(\xi\) is general set at 0.5.  
The grey relational grade (GRG) was calculated by averaging the corresponding GRCs.  
\[\gamma_{i}=\frac{1}{n}\sum_{k=1}^{n}\zeta_{i}(a) \tag{8}\]  
However, in a real engineering system, the importance of various factors to the system varies. In the real condition of unequal weight being carried by the various factors, the grey relational grade in Equation (8) was extended and defined as:  
\[\gamma_{i}=\frac{1}{n}\sum_{k=1}^{n}w_{a}\zeta_{i}(a), \tag{9}\]  
where \(w_{a}\) is norm weight of factor \(a\). Given \(\sum_{k=1}^{n}w_{a}=1\) and with same weights, Equations (8) and (9) are equal [37; 38].