## 2 Materials and Methods
### Data Analysis Method  
Power spectrum density (PSD) is a way to present the average intensities of vibrations as a function of frequency. In this study, Saver Xware software v.4.2.1.1 (Lansmont Corporation, Monterey, CA, USA) was used to generate PSD for the measured vehicle vibrations. The PSD levels are presented from 1 to 200 Hz. In order to eliminate undesirable events that should not be considered vehicle vibrations, data points under 0.03 Grms (root-mean-square of the acceleration) and equal to or greater than 2 g were excluded from the analysis. This method has been historically used by many previous studies, especially to remove inactive movements of the vehicle, such as idling for pickup and delivery, and shock events that should be treated separately [27; 39; 40].  
An independent \(t\)-test was used to compare the overall Grms values of the vertical vibration levels measured from the Porter 2s and Bongo 3s with a significance level of 0.05. The analysis was performed using SAS JMP Pro 16 software (SAS Enterprises, Raleigh, NC, USA).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Delivery Region** & **Trip** & **Local Delivery Addresses(s)** & **Model** & **Make** & **Year** & \begin{tabular}{c} **Vehicle** \\ **Weight (kg)** \\ \end{tabular} & \
\begin{tabular}{c} **Load Capacity** \\ **(kg)** \\ \end{tabular} &
\begin{tabular}{c} **Duration in** \\ **Motion** \\ \end{tabular} \\ \hline \multirow{2}{*}{Northeast} & NE 1 & Jayang-dong, Gwangjin-gu, Seoul & Bongo 3 & Kia & 2016 & 2895 & 800 & 35 min \\ \cline{2-9}  & NE 2 & Jayang-dong, Gwangjin-gu, Seoul & Porter 2 & Hyundai & 2012 & 2895 & 700 & 42 min \\ \hline \multirow{2}{*}{Southeast} & SE 1 & Gleep-dong, Gangnam-gu, Seoul & Porter 2 & Hyundai & 2013 & 2895 & 700 & 95 min \\ \cline{2-9}  & SE 2 & Ilow-dong, Gangnam-gu, Seoul & Porter 2 & Hyundai & 2020 & 3495 & 1000 & 64 min \\ \hline \multirow{2}{*}{Northwest} & NW 1 & Myeongdong 2g, Jung-gu, Seoul & Porter 2 & Hyundai & 2006 & 2930 & 700 & 93 min \\ \cline{2-9}  & NW 2 & Heungindong, Jung-gu, Seoul & Bongo 3 & Kia & 2014 & 2895 & 800 & 131 min \\ \cline{2-9}  & NW 3 & Yeongong-dong, Jongno-gu, Seoul & Bongo 3 & Kia & 2015 & 2895 & 700 & 159 min \\ \hline \multirow{2}{*}{Southwest} & SW 1 & Dabehang-dong, Dongjak-gu, Seoul & Bongo 3 & Kia & 2015 & 2895 & 700 & 70 min \\ \cline{2-9}  & SW 2 & Sadang-dong, Dongjak-gu, Seoul & Bongo 3 & Kia & 2020 & 3275 & 1000 & 57 min \\ \cline{2-9}  & SW 3 & Sadang-dong, Dongjak-gu, Seoul & Porter 2 & Hyundai & 2022 & 3265 & 700 & 60 min \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specifications and local delivery area information for each investigated vehicle.  
Figure 1: Vehicles measured for last-mile delivery vibration. NE, SE, NW, and SW refer to north-east, southeast, northwest, and southwest, respectively, and the following number indicates the trip number.  
Understanding the distribution characteristics of measured vibration data is also important for proper lab-based simulation tests. Thus, the kurtosis (K) and skewness (S) of probability density functions (confidence interval of 95%) were also computed using Minitab v. 21 (Minitab, LLC, State College, PA, USA). Kurtosis explains the degree of peakedness, and skewness describes the degree of symmetry of measured data distribution compared to the Gaussian distribution. Kurtosis and skewness can be calculated using Equations (2) and (3), respectively, as follows:  
\[S=\frac{1}{N}\sum_{j=1}^{N}\left[\frac{x_{j}-\mu_{x}}{\sigma_{x}}\right]^{3} \tag{2}\]  
\[K=\frac{1}{N}\sum_{j=1}^{N}\left[\frac{x_{j}-\mu_{x}}{\sigma_{x}}\right]^{4} \tag{3}\]  
where \(\mu_{x}\) is the mean and \(\sigma_{x}\) is the standard deviation.