# Shock Absorption Characteristics and Optimal Design of Corrugated Fiberboard Using Drop Testing
## 3 Experimental Analysis
### In-Package Experiment
The information of the experimental factors is given in Table 3. The experimental fixation factors are described below. The sample pretreatment temperature and humidity were set at 20 \({}^{\circ}\)C \(\pm\) 2 \({}^{\circ}\)C, 65% \(\pm\) 5% relative humidity, and 24 h, according to CNS 14615. The thickness of the Kraft paper was 0.186 mm, with a basis weight of 130 g/m\({}^{2}\). A corrugated flute board with a height of 4.7 mm and a corrugated medium with a basis weight of 100 g/m\({}^{2}\) were used. Experimental Data Analysis  
The analysis procedure started with a least-squares method to estimate the created cubic multiple models. Then, the initial model was obtained by variable filtering. The residual analysis was performed, and if it passed, the model capability was evaluated, and if it failed, the model and residual analysis were recreated after conversion until the residual \begin{table}
\begin{tabular}{c c c} \hline
**Standard** & **Drop Height (cm)** & **Package Weight (kg)** \\ \hline MIL-HDBK-304C [28] & 91.4 & 0–13.6 kg \\
76.2 & 13.6–34.0 kg \\ ASTM D4169 [29] & 61.0 & 0–9.1 kg \\  & 53.3 & 9.1–18.1 kg \\ ASTM D3332 [30] & 106.7 & 0–9.1 kg \\  & 91.4 & 9.1–22.7 kg \\ CNS 10033 [31] & 80.0 & 10 kg or less \\  & 60.0 & 10 kg–20 kg \\ \hline \end{tabular}
\end{table} 
Table 2: Highest and second-highest drop heights of the drop test-related standards. analysis was passed. JMP Pro(r) 16 was used to perform the analysis. Figure 7a shows the results of the effect summary analysis, where the variables with a _p_-value less than 0.05 were filtered out, the model was recreated, and the residual analysis was performed. Figure 7b shows the residual by the predicted plot in the residual analysis; since the plot was extrapolated, the assumption of consistent variance was not passed. Therefore, a transformation was required to recreate the model. The most-used log transformation was used, and then, the model was recreated. Figure 8a-c shows the results of the normality, equal variance, and independence evaluations. The absence of abnormal patterns indicates that the established pattern is consistent with the assumptions. Figure 8: Residual plot for examining the goodness-of-fit in the regression: (**a**) normal probability plot of residuals, (**b**) residuals versus order of data, and (**c**) residuals versus fits. \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Factor**} & \multicolumn{4}{c}{**Level**} \\ \cline{2-5}  & **1** & **2** & **3** & **4** \\ \hline Drop height (cm) & 30 & 60 & 90 & 120 \\ Static stress (g/cm\({}^{2}\)) & 5 & 15 & 25 & 35 \\ Cushion thickness (ply) & 3 & 6 & 9 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental factors of the in-package test. Figure 7: Results of the experimental data analysis: (**a**) effect summary analysis and (**b**) residual by the predicted plot. The optimal model for the established the impact strength \(\hat{y}_{G}\) is as follows:  
\[\hat{y}_{G}=e^{p}\] \[\text{where }\text{p}=6.03 -0.0161x_{\text{{h}}_{\text{{c}}}}+0.00569x_{a}-0.000029x_{\text{{h}} ^{2}c^{2}}+0.0117x_{\text{{h}}^{2}}\] \[\qquad+0.000008x_{\text{{a}}{b}^{2}}-0.000215x_{abc}-0.279x_{b}-0.0 001516x_{\text{{h}}^{3}}\] \[\qquad+0.000443x_{\text{{a}}{b}}+0.00000016x_{\text{{a}}^{2}{b}^{3 }}+0.00186x_{\text{{h}}^{2}}\] \[\qquad-0.0000027x_{\text{{a}}{b}^{2}c^{2}}-0.000432x_{\text{{c}}^{ 3}}+0.00095x_{ac}\] \[\qquad+0.0000038x_{\text{{a}}^{2}{b}^{2}}-0.0000002x_{\text{{a}}^{ 3}{b}}+0.00000362x_{\text{{b}}^{2}{c}}\]  
\(\hat{y}_{G}\) : Predicted value of impact strength \(a\) : Drop height \(b\) : Static stress \(c\) : Cushion thickness Figure 9 shows the results of the model evaluation. Figure 9 shows the results of the actual and predicted models, which are positively correlated. The \(p\)-value in Figure 9 is <0.0001, indicating that the model is appropriate. R\({}^{2}\) = 0.941029 in Figure 9 is very close to the adjusted R\({}^{2}\) = 0.939313 and is greater than 0.9, indicating that the model is representative.