## 3 Results  
### Data Analysis  
Increasing the value of the loss function (S/N, \(\eta\)) and reducing the radiation dose are very important to improve the quality of brain images. The optimal experiments in the Taguchi design are those that yield the maximum S/N values. The definition of \(\eta\) (Equation (1)) herein can be revised to satisfy various requirements. However, the definition of \(\eta\) involved not only the averaged grades in each experiment but also the consistency of the grades given by the well-trained radiologists in a real optimization process. The recalculated S/N values for experiments 1 to 18 were 33.06, 34.30, 33.36, 32.98, 33.66, 34.89, 33.50, 34.00, 33.98, 22.92, 33.74, 33.11, 26.12, 33.00, 33.54, 26.67, 32.51, and 33.76, respectively.  
Table 3 presents the \(\eta\) values for the L\({}_{18}\) orthogonal array. Experiment 6 yielded the highest average grade of 55.56, converted into an \(\eta\) value of 34.89 dB, which was the highest for any experiment. That experiment therefore involved the optimal acquisitions of A1 (2.5 mm thickness), B2 (350 mAs), C3 (140 kVp), D3 (smooth filter), and E1 (200 mm\({}^{2}\) FOV). Accordingly, a high \(\eta\) does not depend on a high averaged grade (Equation (1)). Table 3 based on the Taguchi design shows that the optimal experiment for CT was experiment 6. Experiment 10 yielded the worst grade of 14.00, with a standard deviation of 7.50, converted to an \(\eta\) value of 22.92 dB.  
Figure 3 plots the averaged grades, the standard deviations of the grades, and \(\eta\) values against the corresponding operating parameters of the 128-slice CT. However, neglecting cross-interactions of the five parameters may produce an erroneous optimization analysis because over-intensifying the \(\eta\) of an individual parameter might reduce the overall performance [7,14].  
Table 4 presents a Taguchi experiment with A1 (2.5 mm thickness), B3 (400 mAs), C3 (140 kVp), D1 (sharp filter), and E1 (200 mm\({}^{2}\) FOV) such that the parameters are set to yield the highest S/N obtained in any of the experiments because the variable \(\eta\) is of the \"the-higher-the-better\" type according to the Taguchi design (Equation (1)). Variations in the other parameters caused only minor fluctuations.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameter** & **SS\({}_{\mathbf{x}}\)1** & **DoF** & **Var\({}_{\mathbf{x}}\)2** & **F** & **Contribution** & **Confidence** & **Confidence** \\  & & & & & **(\%)** & **Level (\%)3** & **Significance** \\ \hline Thickness & 5653.39 & 1 & 5653.39 & 224.97 & 23.12 & 100.00 & Yes \\ mAs & 82.46 & 2 & 41.23 & 1.64 & 0.34 & 80.25 & No \\ kVp & 9466.46 & 2 & 4733.23 & 188.35 & 38.71 & 100.00 & Yes \\ Filter & 1598.01 & 2 & 799.01 & 31.80 & 6.53 & 100.00 & Yes \\ FOV & 3575.64 & 2 & 1787.82 & 71.14 & 14.6 & 100.00 & Yes \\ Others & 462.59 & 8 & 57.82 & 2.30 & 1.89 & 97.62 & No \\ \hline Error & 3618.67 & 144 & 25.13 & & & & \\ Total & 24,457.22 & 161 & & & & & \\ \hline \hline \end{tabular}  
* \({}^{1}\) SS\({}_{\mathbf{x}}\): The sum of the square of a specific parameter. 2 Var\({}_{\mathbf{x}}\): The variance of a specific parameter. 3 At least 99% confidence level.  
\end{table}
Table 4: Parameter confidence levels attributed to the effectiveness of the 128-slice CT acquisition experiment. A parameter was considered significant if the corresponding confidence level exceeded 95%.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Experiment**} & \multicolumn{4}{c}{**Radiologist 1**} & \multicolumn{4}{c}{**Radiologists 2**} & \multicolumn{4}{c}{**Radiologist 3**} & \multirow{2}{*}{**Ave.**} & \multirow{2}{*}{**SD.**} & \multirow{2}{*}{**S/N *} \\ \cline{2-2} \cline{6-13}  & & **Score 1** & **Score 2** & **Score 3** & **Score 1** & **Score 2** & **Score 3** & **Score 1** & **Score 2** & **Score 3** & \\ \hline
**1** & 47 & 36 & 42 & 52 & 47 & 49 & 46 & 43 & 43 & 45.00 & 4.60 & 33.06 \\
**2** & 49 & 48 & 51 & 56 & 52 & 53 & 55 & 51 & 52 & 51.90 & 2.60 & 34.30 \\
**3** & 46 & 45 &