## 5 Summary  
The geometry of railway tracks is a key criterion for the comfort of passengers and the safety of railway operation. Numerous track quality indices (TQIs) have been developed to assess the overall track quality, using measurement signals of track geometry parameters. In this paper a selection of relevant TQIs is discussed and applied on a five kilometer track section. Some indices count the isolated defects, while neglecting the amplitude of these failures. As a result, the overall condition cannot be completely depicted. Most indices rely on standard deviations of the measurement signals, which are combined using different mathematical models. Standard deviations are better suited to assess the general track condition, but can be affected by track elements such as gauge widening and transition ramps. Additionally, combining standard deviations of geometry parameters, which occur in different amplitude ranges (e.g., longitudinal level versus twist, where the respective threshold levels can differ by more than 200% [EN 13848]) over-and underestimates the individual parameters. Some of the analyzed track quality indices rely on adjustment factors which weigh different geometrical parameters or adjust the results for changing line classes. These factors are frequently poorly documented in the literature if they are taken into account at all, which hampers an application in other networks.  
In an attempt to eliminate the above described issues, a new index has been developed, the track quality index of Graz University of Technology (TUG_TQI). It calculates the elongation of a signal triggered by track irregularities--more frequent and more severe track defects yield longer measurement signals and consequently a higher TQI. All incorporated signals are normalized to their respective threshold levels before being processed. This normalization allows combining different geometry parameters without subjective weighting factors. The TUG_TQI offers the following advantages over existing track quality indices:  
* The mathematical model is applicable for every measurement signal and nominal track gauge and thus for any railway network.
* The TUG_TQI can incorporate any measurement signal for which a reliable threshold level is defined.
* The underlying methodology reacts to scattering and peak values of the signals.
* Intended gauge widening in curves and twists in transition elements do not distort the respective indices.
* The gauge signal is split into a positive and a negative part because of differing threshold levels.
* By normalizing the signals, the line speed is implicitly considered.  
The individual indices of the geometry signals enable conclusions to be made regarding the specific maintenance demand. The highest aggregation level--the TUG_TQI--constitutes an optimized assessment of the overall track quality, based on all relevant geometry parameters.  
S.O.: Conceptualization, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing--original draft; J.N.: Conceptualization, Data curation, Formal analysis, Methodology, Validation, Writing--review & editing; P.V.: Resources, Supervision, Writing--review & editing; M.L.: Conceptualization, Formal analysis, Methodology, Project Administration, Resources, Supervision, Validation, Writing--review & editing. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Open Access Funding by the Graz University of Technology.  
The authors declare no conflict of interest.