## 3 Methods
### Integration of the Developed Model into a Cause-Effect Relationship  
To integrate the developed model into a cause-effect relationship between asset condition and financial resources, it must still be linked to the costs that are incurred for single measures. For replacement measures, DB Station&Service AG directly provides these costs. The costs depend on asset size, resulting in larger assets requiring more financial resources than smaller ones of the same asset class. The development of the costs for maintenance measures in collaboration with DB Station&Service AG is described as follows:  
The costs for maintenance measures in the last years were analyzed based on data to obtain an average cost per size of the asset. In this analysis, a distinction is made between preventative and reactive maintenance measures, since costs vary significantly for the two types of maintenance. On average, the cost for reactive maintenance measures in the data analyzed is 46% less compared to the costs for preventative measures. To connect developed costs to the model, it is still necessary to relate them to the effect of a maintenance measure. However, the maintenance costs calculated to this point do not yet include a quality assessment. To establish a correlation, the average quality improvements of an asset up to service life are formed as indicated by the sum of all the improvements in the model and are used to calculate the cost per size of an asset for a maintenance measure. Since improvement is the same for reactive and preventative maintenance measures in the model, but their costs differ, the result is that reactive maintenance measures are the most effective measures. Since they are normally applied to old assets in bad condition, replacement measures tend to be highly effective in terms of score improvement as well, but their cost is of a completely different order of magnitude than those in the maintenance measures. Therefore, the cost-improvement effect is not as high as in reactive maintenance measures. The intended use of the model is not only to describe the score development of average assets but to also estimate the score development of any asset currently in use. Figure 4: Derived model (grey) by means of the condition before (green) and after (red) a maintenance measure is performed. A plausibility check is realized via comparison to the model describing the whole data set (dashed blue curve). The procedure of how the score development of assets can be mapped with the developed model is depicted in Figure 5: first, an adequate degradation slope for the age interval the asset considered is situated in is mapped to the asset. This degradation slope is then used to predict the assets' score development for the next years. As soon as the slope reaches the \"intervention threshold\", which is defined by the dashed blue line indicating the overall average condition of assets, a maintenance measure should be scheduled. This intervention threshold ensures that, in any year, assets are above this threshold so that an improvement is possible. If the financial resources do not allow for the implementation of a maintenance measure in this model at this time, it is assumed that the asset will further degrade with the same degradation slope as before. This is indicated by arrow 1 in Figure 5. In case the maintenance measure can be conducted, the asset condition is improved by the effect of an average maintenance measure at this age; in other words, the difference indicated by the curves, which models the average condition before and after a maintenance measure, is performed (see arrow 2 in Figure 5). Improvement can reach a maximum of the best possible condition, i.e., score 0. If the asset has already exceeded the service life, and its condition is poorer than the one indicated by the intervention threshold, it is listed as a replacement measure.