# Risk-Based Selection of Inspection Method for External Post-Tensioning System of Bridges
## 3 Risk-Based Framework and Attributes for Selection of Inspection Method
### Two-Stage Inspection Methods  
In practice, it may be quite beneficial to inspect the post-tensioning system with an NDE method as the primary inspection, identifying the potential defects for further investigation using a secondary inspection with another NDE method. In this paper, this is called the \"two-stage\" inspection method [72]. The accuracy of the two-stage inspection method is a question to be answered, since only detected defects are investigated in secondary inspection. On one hand, the accuracy of the method in secondary inspection should be more than the primary inspection logically. On the other hand, the error of both the NDE methods are independent of each other, hence the possibility of the error while applying both methods will be achieved using the Bayesian theorem [73]. To investigate the accuracy of the combined method, the ratio of the post-tensioning elements that participate in the secondary inspection is needed. In practice, inspectors put a criterion for sending the detected defects to secondary inspection. Such a criterion is based on the policy at the inspection; however, since the goal of this paper is to propose the model to select the inspection method for structural health monitoring of a post-tensioning system, deterioration of the elements is considered. In practice, in the two-stage inspection method, the inspector sends all the elements with a detected defect with respect to deterioration; any element with sign of corrosion and section loss will be sent to secondary inspection for further investigation. The SNBI rating that the first clues of deterioration are named is R = 6. The probability of having the result of the NDE report equal to or less than the specified criterion regarding the deterioration P(R \(\leq\) 6) is considered as the ratio of the post-tensioning elements that will be sent to secondary inspection. Considering the levels of accuracy in Table 2, it can be shown that with a secondary NDE method more accurate than the primary inspection, the accuracy of the two-stage inspection will be increased. Table 3 shows how the accuracy can be improved when using a two-stage method. The table is arranged for two NDE methods, the second (Column 2) with a better accuracy than the first (Column 1) for the condition of the structure/post-tensioning system being in one of 6, 7, or 8. The table compares the increased accuracy by the proposed model and calculates accuracy with respect to the condition of the post-tensioning system. Nevertheless, the accuracy of the two-stage  
Figure 11: Accuracy Levels of NDE methods. inspection method can be considered one level more than the accuracy of the primary inspection for the cases where the SNBI rating of the post-tensioning system is equal or less than seven (7); for instance, the accuracy of the two-stage inspection method can be considered \"Good\", while it is the combination of a primary inspection method with \"Fair\" accuracy and a secondary inspection method with \"Good/Very Good\" accuracy. This means that if the condition of the post-tensioning system is \"Excellent\" or \"Very Good\", the application of the two-stage inspection cannot increase the accuracy of the whole procedure since the possibility of utilization of the secondary inspection is very low. Additionally, if the accuracy of the primary inspection is \"Good\", the accuracy of the two-stage inspection will be considered \"Good\" for conditions with an SNBI rating of equal or less than seven (7). There are three criteria involved in the calculation of results in Table 3: accuracy of the primary and secondary inspections, condition of the post-tensioning system, and the accuracy in determining this condition. In Table 3, for \"TRUE Diagnosis\", it is assumed that the accuracy of determining the condition is \"Poor\". Further, in this table, the accuracy of the secondary NDE method is better than the primary method. For example, a \"Poor\" primary inspection should be combined with a \"Fair,\" \"Good,\" or \"Very Good\" for the secondary method.