## 3 Results and Discussion  
Table 2 displays the overall Grms values, the statistical distribution measurements of the 10 shipments measured in this study, and measurements of common parcel delivery vehicles in the U.S. and Hungary as reported in previous studies [27; 29]. This study first investigated whether the two vehicle models had any significant differences in the overall Grms values for vertical vibration. The mean Grms values of vertical vibration for Porter 2 and Bongo 3 were 0.104 (SD = 0.019) and 0.114 (SD = 0.017), respectively. An independent \(t\)-test result comparing the overall Grms of the two vehicle models showed that there were no statistically significant differences between the two models (t(7.9) = -0.86, \(p>0.42\), Bayes factor = 0.616). It was also clear that the overall Grms values for vertical vibration for the three types of delivery vehicles used in the U.S. and the delivery van in Hungary were significantly higher compared to all shipments measured in Korea. The values of the overall vertical Grms for the Korean last-mile parcel delivery environment were as much as 2.5 times higher than longitudinal and lateral directional vibrations. This confirms multiple historical studies' findings that protective packaging needs to be designed and tested based on vertical vibration levels to resist product damage during transport; vertical vibration is the orientation that transmits the most considerable vibration levels [16; 39; 41; 42]. These findings suggest that establishing a new vibration test profile for Korea in terms of vertical orientation is recommended to better optimize their packaging, but it does not require differentiating between the two most common last-mile delivery vehicle models when establishing the test profile. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & **Overall Grms** & & & \\ \hline
**Model** & **Route** & **Vertical** & **Longitudinal** & **Lateral** & **Kurtosis** & **Skewness** \\ \hline Bongo 3 & NE 1 & 0.087 & 0.050 & 0.073 & 0.64 & 0.96 \\ Porter 2 & NE 2 & 0.083 & 0.048 & 0.052 & 0.26 & 0.22 \\ Porter 2 & SE 1 & 0.114 & 0.059 & 0.055 & \(-\)0.52 & 0.24 \\ Porter 2 & SE 2 & 0.126 & 0.060 & 0.061 & 1.63 & 1.18 \\ Porter 2 & NW 1 & 0.086 & 0.045 & 0.045 & 1.93 & 1.36 \\ Bongo 3 & NW 2 & 0.132 & 0.062 & 0.109 & 0.38 & 0.58 \\ Bongo 3 & NW 3 & 0.112 & 0.076 & 0.117 & 0.29 & 0.53 \\ Bongo 3 & SW 1 & 0.116 & 0.052 & 0.078 & 0.32 & 0.31 \\ Bongo 3 & SW 2 & 0.121 & 0.048 & 0.054 & 1.99 & 1.21 \\ Porter 2 & SW 3 & 0.112 & 0.061 & 0.109 & 0.21 & 0.59 \\ Ford van [29] & 0.207 & - & - & - & - \\ Dodge van [29] & 0.231 & - & - & - & - \\ Freightlmer small truck [29] & 0.377 & - & - & - & - \\ Delivery van in Hungary [27] & Average 0.202 & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Overall Grms values for vertical vibration of last-mile delivery vehicles in Korea, the USA, and Hungary. Figure 2 presents the cumulative distribution functions (CDFs) for the rms of measured vertical vibration events. The CDFs shown in Figure 3 provide the probability of event occurrence at a given the rms level. They show that 95% of the rms levels of vertical vibration events from all measured vehicles were below 0.25. The kurtosis (K) and skewness (S) of PDFs shown in Figure 4 are reported in Table 2. Kurtosis indicates how heavy or light the tail of the distribution is compared to normal distribution. The kurtosis of the normal distribution is 0, the heavy-tailed distribution has positive kurtosis, and the light-tailed distribution has negative kurtosis. The data showed positive kurtosis in most cases, except the SE1 route, which had negative kurtosis. These results show that the rms of recorded vertical vibration events do not follow the normal distribution. Skewness provides information on whether the data distribution is symmetrical. The normal distribution has a skewness value of 0, the right-skewed distribution has a positive skewness value, and the left-skewed distribution has a negative skewness value.