# Risk-Based Selection of Inspection Method for External Post-Tensioning System of Bridges
## 3 Risk-Based Framework and Attributes for Selection of Inspection Method
### Inspection Error in Health Monitoring of Post-Tensioning System Using NDE Methods  
The most important reason for the bridge inspection is to answer whether there is any serious defect that threatens the safety of the whole structure. In the case of a negative answer to the question, there is a possibility of having a false negative answer, representing an inspection error, which is defined in Equation (4):  
\[\mathrm{P}_{\mathrm{error}}=\mathrm{P}(\mathrm{R}>\mathrm{R}_{\mathrm{C}}\,| \mathrm{C}\,\leq\mathrm{R}_{\mathrm{C}}) \tag{4}\]  
where \(\mathrm{P}_{\mathrm{error}}\) is the probability of error (false negative result), \(\mathrm{R}\) is the condition rating that the NDE method will report, \(\mathrm{C}\) is the actual condition rating, and \(\mathrm{R}_{\mathrm{C}}\) is the critical condition rating that the bridge manager aims to avoid that is recommended to be \(\mathrm{R}_{\mathrm{C}}=3\). To elaborate on and solve Equation (4), some clarifications and assumptions are needed that includes:  
Condition rating adapted based on the SNBI ratings per Table 20 of the specifications of national bridge inventory (SNBI) [70] for external post-tensioning system as shown in Table 1.  
It is assumed that \(\mathrm{R}\) fits by \(\mathrm{t}\)-distribution \(\mathrm{R}\,\sim\mathrm{T}(\mu_{\mathrm{R}},\sigma_{\mathrm{R}})\). The structural difference between consecutive SNBI ratings is the same for all. The most critical parameter that influences accuracy of NDE methods is the technology used in the NDE tools. Because of this, NDE methods were classified based on the corresponding technology. The condition of the structure, size of the defects, and environmental parameters might influence the accuracy of the NDE methods; however, these parameters are not named as essential as the NDE technology in the literature [65; 71]. Therefore, proposed accuracy of the NDE method covers the systematic error of the methods and will not cover random error, since the proposed model just considers the technology of the NDE method. The accuracy of the NDE methods discussed in the previous section for evaluating the corrosion and section loss has been reflected qualitatively in Table 2 based on available literature [9; 14; 16; 41; 43]. The proposed model in this paper has four accuracy levels: Very \begin{table}
\begin{tabular}{c c c} \hline \hline
**Rating** & **Condition** & **Description of the Condition** \\ \hline
9 & Excellent & Excellent. \\ \hline
8 & Very Good & No problems were noted with corrosion protection barriers and no sign of water or moisture infiltration. \\ \hline
7 & Good & Some minor problems with corrosion protection barriers. \\ \hline
6 & Satisfactory & Major issues exist with corrosion protection barriers; the potential for water infiltration and steel corrosion initiation exists. Corrective action for restoring the barriers can prevent damage to main steel tension elements. \\ \hline
5 & Fair & Main steel tension elements of the post-tensioning system show minor corrosion. Deterioration is active in post-tensioning elements. \\ \hline
4 & Poor & Advanced corrosion and deterioration of main steel tension elements exist. \\ \hline
3 & Serious & Corrosion, deterioration, and potential breakage of main tension elements have seriously affected external post-tensioning elements. \\ \hline
2 & Critical & Advanced deterioration of external post-tensioning elements is apparent. The integrity of the structure may have been affected and may be necessary to close the bridge until corrective action is taken. \\ \hline
1 & Imminent Failure & Major deterioration or corrosion of the main tension elements of the post-tensioning system, or obvious vertical or horizontal movement affecting structural stability. The bridge is closed to traffic but corrective action may put back the bridge in light service. \\ \hline
0 & Failed & Out of service—beyond corrective action. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Condition rating proposed for external post-tensioning tendons adapted based on SNBI rating.