# Metal Color, Marbling, and the Evaluation of Defects in Beef and Port at the Point of Purchase
## 3 Results and Discussion
### Taguchi Loss Function for Color
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Characteristic**} & \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**TLF**} & \multirow{2}{*}{**Target Value m \({}^{*}\)**} & \multicolumn{2}{c}{**Consumers’ Tolerance**} & \multicolumn{1}{c}{**Cost**} & \multirow{2}{*}{**Coefficient**} \\  & & & & & **(A\({}_{\text{a}}\) \% of Unsatisfied & (\(\text{k}=\text{A}_{\text{a}}/\text{D}_{\text{a}}^{2}\) \\ \hline \multirow{2}{*}{Color of beef} & \multirow{2}{*}{\(\Delta\)E} & Smaller is better & \multirow{2}{*}{3.61} & \(\text{D}_{\text{d}}=6.32-3.61=2.71\) & \multirow{2}{*}{\(\text{A}_{\text{d}}=10\%\)} & \multirow{2}{*}{\(\text{k}_{\text{d}}=10/2.71^{2}=1.36\)} \\  & & \(\text{L(x)}=\text{k}\cdot\text{x}^{2}\) & & & \(\text{D}_{\text{d}}=8.95-3.61=5.34\) & \multirow{2}{*}{\(\text{A}_{\text{d}}=20\%\)} \\ \hline \multirow{2}{*}{Color of pork} & \multirow{2}{*}{\(\Delta\)E} & Smaller is better & \multirow{2}{*}{2.00} & \(\text{D}_{\text{d}}=6.32-2.00+4.32\) & \multirow{2}{*}{\(\text{A}_{\text{d}}=10\%\)} & \multirow{2}{*}{\(\text{k}_{\text{d}}=10/4.32^{2}=0.54\)} \\  & & \(\text{L(x)}=\text{k}\cdot\text{x}^{2}\) & & & \(\text{D}_{\text{d}}=8.94-2.00+6.94\) & \multirow{2}{*}{\(\text{A}_{\text{d}}=20\%\)} \\ \hline \multirow{2}{*}{Marbling of beef} & \multirow{2}{*}{\(\begin{tabular}{c} Markling score \\ (\%) of beef \\ \end{tabular} } & Smaller is better & \multirow{2}{*}{/} & \(\text{D}_{\text{d}}=32.0-1.00-2.20\) & \multirow{2}{*}{\(\text{A}_{\text{d}}=10\%\text{A}_{\text{d}}=20\%\)} & \multirow{2}{*}{\(\text{k}_{\text{d}}=10/2.52\)} \\  & & \(\text{L(x)}=\text{k}\cdot\text{x}^{2}\) & & & \(\text{D}_{\text{d}}=4.50-1.00-3.50\) & \multirow{2}{*}{\(\text{A}_{\text{d}}=10\%\text{A}_{\text{d}}=20\%\)} \\  & & \(\text{The nominal value,}\) & & & \(\text{D}_{\text{d}}=27.40-21.00-6.40\) & \multirow{2}{*}{\(\text{A}_{\text{d}}=10\%\text{A}_{\text{d}}=20\%\)} \\  & & \(\text{L(x)}=\text{k}\cdot\text{(x}-\text{m})^{2}\) & & & \(\text{D}_{\text{d}}=30.00-21.00-9.00\) & \multirow{2}{*}{\(\text{A}_{\text{d}}=10\%\text{A}_{\text{d}}=20\%\)} \\ \hline \multirow{2}{*}{Marbling of pork} & \multirow{2}{*}{\(\begin{tabular}{c} Markling score \\ (\%) of pork \\ \end{tabular} } & The nominal value, & \multirow{2}{*}{\(\text{D}_{\text{d}}=11.40-5.74=5.66\)} & \multirow{2}{*}{\(\text{A}_{\text{d}}=10\%\text{A}_{\text{d}}=20\%\)} & \multirow{2}{*}{\(\text{k}_{\text{d}}=10/5.66^{2}=0.31\)} \\  & & & & \(\text{L(x)}=\text{k}\cdot\text{(x}-\text{m})^{2}\) & \\ \hline \multirow{2}{*}{\begin{tabular}{c} Markling of pork \\ \end{tabular} } & \multirow{2}{*}{\(\begin{tabular}{c} Markling score \\ (\%) of pork \\ \end{tabular} } & The nominal value, & \multirow{2}{*}{\(\text{D}_{\text{d}}=11.40-5.74=5.66\)} & \multirow{2}{*}{\(\text{A}_{\text{d}}=10\%\text{A}_{\text{d}}=20\%\)} & \multirow{2}{*}{\(\text{k}_{\text{d}}=10/5.66^{2}=0.31\)} \\  & & & & \(\text{L(x)}=\text{k}\cdot\text{(x}-\text{m})^{2}\) & \\ \hline \multirow{2}{*}{\begin{tabular}{c} Markling of pork \\ \end{tabular} } & \multirow{2}{*}{\(\
\begin{tabular}{c} Markling score \\ (\%) of pork \\ \end{tabular} } & \multicolumn{2}{c}{\(\text{D}_{\text{d}}=11.40-5.74=5.66\)} & \multirow{2}{*}{\(\text{A}_{\text{d}}=10\%\text{A}_{\text{d}}=20\%\)} & \multirow{2}{*}{\(\text{k}_{\text{d}}=10/5.66^{2}=0.31\)} \\  & & \(\text{L(x)}=\text{k}\cdot\text{(x}-\text{m})^{2}\) & & \(\text{S}.74\%\) & \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Markling of pork \\ \end{tabular} } & \multicolumn{2}{c}{* Determination of targets based on survey responses. ** Values provided by image analysis, where x\({}_{\text{o}}\) represents measured value for certain percentage of tolerance A\({}_{\text{o}}\).} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The main inputs for TLFs for color and marbling of beef and pork. Figure 3: **The nominal value, the best value” TLF adopted from [24]. Note: LSL represents the lower specification limit; USL represents the upper specification limit.