## 7 Summary and Conclusions  
The article presented a framework for condition prediction of existing concrete bridges, using a combination of the semi-Markov process as a statistical model and carbonation-induced corrosion as an analytical model. As such, the framework should assist engineers and operators in condition assessment of large number of bridges in infrastructural networks, as well as in optimizing the scheduling of interventions. In the framework, the condition is forecasted in the form of the probability that the bridge (process) will assume one of condition states \(i\) in a given subsequent period, by using the sojourn times derived from analytical deterioration models. The distinctiveness of the presented framework and its contribution to the state-of-the-art in bridge management and condition prediction are that:  
* the framework takes into account the probabilistic nature of the deterioration process, as well as the historic deterioration path, through PDFs and SFs of the sum of sojourn times presented in Equation (6). In this way, the framework does not just consider the present condition, but rather the sequence of events that preceded it. In other words, the semi-Markov process does not exhibit the'memoryless' assumption, which is an important property of the Markov chain model;
* by estimating the transition probabilities in the transition matrix \(P^{l,t+1}\) based on analytical models of deterioration, the framework is suitable for bridge inventory where reliable data on condition states are lacking, which is very often the case for condition data related to advanced deterioration [63];
* the framework overcomes other shortcomings of the homogeneous Markov chain, such as discrete transition time intervals, constant bridge population, and stationary transition probabilities;
* it is a holistic framework in the sense that it utilizes all the available data, such as environmental loading, material properties, structural parameters, etc., and not just condition ratings from visual inspections. This data can be acquired from literature survey, standards valid at the time of  
Figure 11: Probability that the process will assume one of the condition states \(i\) at the age of 50 years, dependent on different corrosion rate \(v_{corr}\). design and construction, design documents, inspection documents, test and monitoring reports, empirical knowledge of experts, and so on;
* although the article concentrates on concrete bridges and the process of carbonation-induced corrosion, it is flexible to implementation on any structural or material type, as well as any deterioration process for which an adequate deterioration model exists;
* by considering both deterioration path and bridge properties, the framework can highlight groups of structures with similar properties, and in this way differentiate those with a high rate of deterioration from those deteriorating at a slower pace. Altogether, it can be concluded that the enclosed framework presents a suitable alternative to presently implemented frameworks for condition prediction used in Bridge Management Systems. Conceptualization, I.Z., A.V., A.S. and J.M. ; methodology, I.Z., A.V., A.S. and J.M. ; software, I.Z. and A.V. ; validation, I.Z., A.V., A.S. and J.M. ; formal analysis, I.Z. and A.V. ; investigation, I.Z. and A.V. ; resources, A.S. and J.M. ; data curation, I.Z. and A.V. ; writing--original draft preparation, I.Z. and A.V. ; writing--review and editing, I.Z. ; visualization, I.Z. and A.V. ; supervision, A.S. and J.M. ; project administration, A.S.; funding acquisition, A.S. This research was funded by OBB-Infrastruktur Bau AG, Vienna, through the project 'Life-Cycle Assessment for Railway Structures'. The authors would like to extend their appreciation to their colleagues at the Institute of Structural Engineering, Department of Civil Engineering and Natural Hazards at the University of Natural Resources and Life Sciences in Vienna. The authors declare no conflict of interest.