# A Unified Approach for Risk Assessment of Road Crash Barriers Using Bayesian Statistics
## 5 The Hypothesis Validation
### The Hypothesis III.--Insufficient Minimum Distance behind the Crash Barrier
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Combinations**} & \multicolumn{4}{c}{**Uncorrelated Records**} & \multicolumn{4}{c}{**Correlated Records**} \\ \cline{2-11}  & \multicolumn{2}{c}{**70 km/h**} & \multicolumn{2}{c}{**90 km/h**} & \multicolumn{2}{c}{**70 km/h**} & \multicolumn{2}{c}{**90 km/h**} \\ \cline{2-11}  & **L** & **M** & **H** & **L** & **M** & **H** & **L** & **M** & **H** & **L** & **M** & **H** \\ \hline
1., 2. & 100\% & 0\% & 0\% & 81\% & 7\% & 12\% & 100\% & 0\% & 0\% & 10\% & 30\% & 60\% \\
3, 4. & 100\% & 0\% & 0\% & 84\% & 1\% & 15\% & & & 25\% & 25\% & 50\% \\
5, 6. & 100\% & 0\% & 0\% & 81\% & 7\% & 12\% & & & 22\% & 33\% & 44\% \\
7, 8. & 100\% & 0\% & 0\% & 84\% & 1\% & 15\% & & & & 13\% & 38\% & 50\% \\
9, 10. & 100\% & 0\% & 0\% & 91\% & 0\% & 9\% & & & 75\% & 25\% & 0\% \\
11, 12. & 100\% & 0\% & 0\% & 71\% & 12\% & 18\% & 0\% & 100\% & 0\% & 0\% & 25\% & 75\% \\
13, 14. & 100\% & 0\% & 0\% & 91\% & 0\% & 9\% & 100\% & 0\% & 0\% & & \\
15, 16. & 100\% & 0\% & 0\% & 71\% & 12\% & 18\% & 100\% & 0\% & 0\% & 17\% & 83\% & 0\% \\
17, 18. & 100\% & 0\% & 0\% & 65\% & 18\% & 18\% & 100\% & 0\% & 0\% & & \\
19, 20. & 100\% & 0\% & 0\% & 84\% & 11\% & 5\% & & & & 100\% & 0\% \\
21, 22. & 100\% & 0\% & 0\% & 65\% & 18\% & 18\% & & & & & \\
23, 24. & 100\% & 0\% & 0\% & 84\% & 11\% & 5\% & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Mutual comparison of the probability of each combination for the defect—Insufficient minimum distance behind the crash barrier. (L = Low Risk, M = Medium Risk, H = High Risk). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Combinations**} & \multicolumn{2}{c}{**Uncorrelated Records**} & \multicolumn{2}{c}{**Correlated Records**} \\ \cline{2-5}  & **70 km/h** & **90 km/h** & **70 km/h** & **90 km/h** \\ \hline
1., 2. & 70,000 & 162,922 & 50,000 & 780,550 \\
3., 4. & 63,556 & 247,659 & & 1,598,125 \\
5., 6. & 70,000 & 162,922 & & 577,311 \\
7., 8. & 63  
* **The hypothesis was confirmed--There are not enough records in the datasets for the combinations, but the resulting probability of a small number of data is consistent with the stated assumption. ** The 11 th and 15 th combinations correspond to the severity levels of the hypothesis, i.e., medium (11 th combination) and low (15 th combination) risk. However, only one case was recorded for each of these exposures. * **The hypothesis was not confirmed--There are not enough records in the datasets for the combinations, and at the same time the assumption does not correspond to the resulting probability. ** The following three combinations do not correspond to the hypothesis based on a comparison of the mathematical model outputs. These are the 1 st, 10 th and 20 th combinations. In the case of the 10 th combination, a high risk has been proposed; however, the model output has the highest probability for a low risk, namely 75%. However, there is a slight increase in the medium risk (25%). This is again due to the small number of recorded data--there are only four records for this exposure. A comparable situation applies to the 1 st and 20 th combination, where only one case is recorded for each exposure. These cases then do not belong to the expected severity; their risk level is significantly lower. * **The hypothesis was not confirmed--There is no record for the combinations in the data files, the stated assumption cannot be confirmed. ** The remaining combinations (3 rd, 5 th, 7 th, 9 th, 14 th, 18 th, 19 th, 21 st-24 th) could not be verified due to lack of data in the datasets. The very fact that fewer traffic accidents are recorded for these combinations suggests that they are not very risky combinations. Hypothesis III was confirmed from 24 combinations in 10 cases. A total of 14 exposures of the crash barriers were unconfirmed. Table 15 below shows the resulting confirmed combinations. Hypothesis III is hereby verified and is valid for combinations 2, 4, 6, 8, 11-13, 15-18.