## 3 Results and Discussion
The skewness value of data in this study ranged between 0.22 and 1.36, indicating that all measurements had right skewed rms data distribution. Most of the routes had moderately (>0.5) or highly skewed distributions (>1.0). The probability density functions (PDFs) with normal distributions for the individual routes are presented in Figure 3. This confirms that the rms of recorded vertical vibration events do not follow the normal distribution, and vehicle vibration is usually not uniformly excited due to irregular road conditions in the field [27]. However, it is important to consider not only the overall Grms level and data distribution but also the shape of a vibration test spectrum when designing packages to prevent the damages that can occur from vibration. This is because different peak intensities at different forcing frequencies can magnify the vibrations experienced by the product differently in response to its natural frequency, even with the same overall Grms spectrum value. Therefore, the data collected from 10 different small trucks were analyzed to determine PD levels of vibration for the 10 different shipments. Figure 4 shows PSD plots of triaxial vibration for the 10 shipments, the recommended vertical vibration test spectrum for last-mile delivery using the small trucks in Korea, and the ISTA 3A standard [2] vertical vibration test spectrum for pickup and delivery (same as ASTM D7386-16 [3]). Figure 2: Cumulative distribution function on the RMS acceleration of investigated routes in vertical orientation. Figure 3: RMS distribution of investigated routes in the vertical orientation. Figure 4: PSD plots of 10 different small trucks for the lateral, longitudinal, and vertical orientations, recommended composite test spectrum for vertical small truck vibration, and ISTA 3A pickup and delivery vertical vibration test spectrum. A composite (full survey) PSD spectrum (the recommended test spectrum) was developed by smoothing the original small truck spectra using 17 breakpoints. The breakpoints and PD levels of the composite (full survey) spectrum were created by selecting the highest PD levels of vertical vibration data points coming from all 10 shipments between 1 Hz and 200 Hz. These breakpoints were used to ease the input process of the test profile to the testing equipment; testing equipment is usually incapable of following the sharp peaks shown in the original PSD spectrum. Recommended breakpoints in the composite (full survey) spectrum are listed in Table 3.  
The recommended test spectrum developed in this study shows that the vertical vibration levels are consistently lower, in the 1 to 200 Hz frequency range, than those recommended by ISTA 3A [2] and the previous study conducted in Hungary [27]. It was also observed that the peak intensities of the recommended spectrum reside in different frequencies than ISTA 3A [2]. The highest PD levels in the ISTA 3A vibration test profile were located between 3 to 4 Hz and 15 to 24 Hz, whereas intensive ranges in Korea were between 1.5 to 2 Hz and 15 to 19 Hz. This finding encourages Korean packaging engineers to avoid designing protective packaging that has cushioning systems with natural frequencies that overlap the intensive peak frequency range unique to the last-mile delivery environment in Korea rather than aiming to avoid the peak intensity frequency ranges recommended by international standards. Another observation from this study was that lateral and longitudinal orientations do not have intensive peaks of PD levels in the lower frequency range, between 1 and 10 Hz, whereas the vertical direction has the highest PD level peaks in that region. Lateral and longitudinal orientation also lost PD levels quicker in the higher frequency range (over 50 Hz) compared to vertical orientation, which was also observed in Hungary [27]. Table 4 shows a comparison between the overall Grms of ISTA 3A's [2] recommended spectrum and the spectrum recommended from this study for similar bandwidths.