## 7 Discussion  
In Figure 2, the examples of the procedure of graphical calculation are depicted with green lines and the obtained values of \(C_{meas,max}\) are shown in the green color. Simply, if a proactive repair costs \(\epsilon\) 15,000 and reactive repair \(\epsilon\) 60,000, then the maximum cost of measurement that would still be cost effective is \(\epsilon\) 3400, \(\epsilon\) 8000, \(\epsilon\) 13,100, and \(\epsilon\) 17,900, given that the initial probabilities of depassivation are \(P_{dep}\) = 0.2, \(P_{dep}\) = 0.4, \(P_{dep}\) = 0.6, and \(P_{dep}\) = 0.8, respectively. As in the graphical example, an analytical calculation can be performed if the lines in Figure 2 that represent the \(C_{meas,max}\) are given as linear equations. These can be written as:  
Figure 2: Maximum cost-effective value of measurement, \(C_{meas,max}\), expressed for different costs of preventive and reactive repair; for probability of depassivation: (**a**) \(P_{dep}\) = 0.2; (**b**) \(P_{dep}\) = 0.4; (**c**) \(P_{dep}\) = 0.6; (**d**) \(P_{dep}\) = 0.8. \[C_{rep,r}=a_{0}*C_{rep,p}+a_{1}*C_{mass} \tag{10}\]  
leading to:  
\[C_{mass,max}=\frac{C_{rep,r}-\ a_{0}*C_{rep,p}}{a_{1}} \tag{11}\]  
The constants \(a_{0}\) and \(a_{1}\) in Equations (10) and (11) can be derived for each different initial probability of depassivation, \(P_{dep}\), as shown in Table 4.  
From Figure 2, it can be seen how with the increase of initial probability of depassivation, \(P_{dep}\), the maximum costs of measurement, \(C_{mass,max}\), become higher. In contrary, at first sight, it would be more expected that with the approaching of \(P_{dep}\) to the value of 1.0, the maximum cost of measurement, \(C_{mass,max}\), would decrease, since the value of information is not that high in the circumstances where depassivation is almost obvious. This can be explained by the fact that several events that reduce the value of measurement were taken into account in the analysis, these being the event of false indication of depassivation, the event of damage not occurring after accurate indication of depassivation, the event of unsuccessful repair, etc. In the analysis, it was presumed that the actual chloride content approximately corresponds to the critical chloride content, and that that their margin (their difference) is relatively low. In this way, it was presumed that a bridge is being almost depassivated, and that the probability of correct measurement is relatively high. However, this does not have to be the case for other bridges. Hence, a further analysis was performed to check the influence of the probabilities of correct measurement on the results. The results of the analysis are presented in Figure 3, for which the parameters presented in Table 3 were used. The exceptions are the probability of depassivation that was set as \(P_{dep}=0.6\) and the probabilities of correct measurement, \(P\) (\(D_{no-dep}\mid T_{no}\)) and \(P\) (\(D_{dep}\mid T_{yes}\)), which varied from 0.5 to 0.9. Furthermore, the analysis was performed for the unit cost of measurement, i.e., \(C_{meas}=1\). The results presented in Figure 3 can be explained as follows: When the probabilities of correct measurement of 0.5 are observed, if, to perform the measurement, the costs are \(\epsilon\) 1000 and the cost of proactive repair is also \(\epsilon\)1000, the cost of reactive repair, \(C_{rep,r}\), has to be above \(\epsilon\)5600 for the measurement to be cost effective. Otherwise, since the probabilities of correct measurement are low, the measurement is not cost effective. As it can be seen, with the increase of the probabilities of correct measurement, the minimum cost of reactive repair decreases, which is as expected. Similar to the probabilities of correct measurement, the influence of the probability of damage given depassivation occurred, \(P\) (\(D_{crack}\mid D_{dep}\)), was analyzed.