## 4 Discussion  
### Verifying the Taguchi Recommendation by Quantified MDD  
Taguchi analysis helps efficiently optimize the gamma camera scanned imaging in the first stage according to the unique eighteen orthogonal arrays. Then, the quantified MDD is provided to verify the optimization process further. The calculated MDD can precisely quantify the performing of scanned images rather than radiologists' visual judgment in the second stage, although the professional judgment based on the double-blinded principle is practically a reliable tool. Figure 5 demonstrates the three derived SPECT and practical images from gamma camera scanned according to (A) group 2 of the original Taguchi's eighteen groups and have the highest \(\mathrm{S/N}\) among eighteen groups, (B) conventional preset, and (C) the combination of the highest \(\mathrm{S/N}\) in every specific factor (cf. Figure 4, beyond the original eighteen groups). As clearly depicted in case (A) or (B), angles 8 and 9 on the right edge are mixed (cf. Figure 1A top-right edge width was 5 mm). Noteworthy is that the acquired images from a practical gamma camera were mirror-reflected, whereas in case (C), angle 9 was barely identified. Nevertheless, if checking the definition of MDD, none of the three cases can fulfill the criteria of MDD to gain a 95% confidence level from angle 8 and angle 7 (cf. Figure 1A, the bottom edge is 29 \(-\) 20 = 9 mm). Thus, we focus  
Figure 4: The fish-bone-plots of average, stdev, or S/N versus six factors of the gamma camera scan protocol. The contribution of each factor can be analyzed and reorganized according to the Taguchi unique orthogonal array.  
on the MDD between angles 7 and 6 (bottom edge is 42 \(-\) 29 = 13 mm) because the slit of this triangle has a deeper depth of 2.8 mm than that between angles 7 and 8 of 2.4 mm (cf. Figure 1A). A deeper depth can deposit comparatively more contrast media solution than a shallow one and become a bright image for calculation. Table 5 shows the correlated calculation of MDD between angles 6 and 7 of three cases in this study. The raw data of each acquired image are saved in the same data matrix. Thus, the cm/pixel values are the same in analyzing the specific MDD. Channel No., as adopted in Equation (7), is obtained from the SPECT of a specific case (cf. Figure 5). The second group in the original L18 has the largest MDD since it cannot separate angles 7 and 8. In contrast, the optimal one has the smallest MDD = 7.1 mm, and the conventional one has a medium MDD = 7.9 mm in reality. While derived MDD values may differ insignificantly, the Taguchi methodology still proves its effective capability in optimizing SPECT resolution of gamma camera images. In addition, the three different protocols of the gamma camera are rearranged in Table 6. As demonstrated, only factors are compromised altogether, and can then minimize the MDD in reality. The quantified MDD provides reliable numerical information to help radiologists in routine quality control rather than visual inspection according to commercial phantom or line pair gauges.  
\begin{table}
\begin{tabular}{l l c c c} \hline \hline  & **Factor** & **2 nd Group** & **Conventional** & **Optimal** \\ \hline (A) & Collimator & LEHR & LEHR & LEHR \\ (B) & Det. to Target Distance & 5 cm & 5 cm & 5 cm \\ (C) & Total Counts & 150 k & 165 k & 150 k \\ (D) & Acquired Energy width & 20\% & 16\% & 16\% \\ (E) & Matrix size & 256 \(\times\) 256 & 256 \(\times\) 256 & 256 \(\times\) 256 \\ (F) & Zoom & 1.28 & 1.28 & 1.28 \\
**MDD** & & **8.4 mm** & **7.9 mm** & **7.1 mm** \\ \hline \hline \end{tabular}
\end{table}
Table 6: The MDD of 2.8 mm deep V-shaped slit obtained from the second group, conventional, and optimal factor settings of the gamma camera scan protocol.  
\begin{table}
\begin{tabular}{l l l} \hline \hline \multicolumn{1}{c}{**Channel No. of the Derived SPECT**} & \multicolumn{1}{c}{\(1\)**X\({}_{1}\)–X\({}_{2}\)** \(\geq\)1.96\(\times\sqrt{\frac{\text{FWM}_{\text{3}}}{2}\)** \(\frac{\text{FWM}_{\text{3}}}{