## 1 Introduction  
### Background  
Featured Application: The methodology provided in this article can be used for probabilistic assessment of service life of bridge superstructures based on survival analysis of long-term field inspection data from various geographic locations. The effects of various parameters on the probability of survival at different ages can be explicitly  
Long-term reliability is one of the most important issues in bridge engineering and preservation. There is substantial interest in seeking better design, maintenance and rehabilitation methods to achieve longer service lives. Bridges deteriorate due to long-term effects of environmental exposure and loading. Durability-based design, preventive maintenance, and structural health monitoring can provide important long-term benefits in a variety of bridge types [1; 2; 3; 4]. Optimal bridge management strategies require effective probabilistic assessment of future bridge conditions based on reliability analyses. Such reliability analyses benefit from understanding and quantifying the existing field performance data as influenced by various parameters. The strength-based reliability approach (based on a probabilistic assessment of resistance versus load) is commonly utilized for prediction of maintenance requirements or remaining service life. The reliability index (\(\beta\)) provides a measure of the likelihood of failure (loads exceeding resistance) for various structural elements. [PERSON] and [PERSON] [5] used time-dependent reliability index profiles to optimize life-cycle maintenance and evaluate the reliability of deteriorating structures. [PERSON] [6] evaluated safety and approximate remaining service life of a reinforced concrete bridge deck strengthened with FRP using the reliability index in a time-dependent approach. [PERSON] et al. [7] conducted time-dependent reliability assessments of deteriorated reinforced concrete bridges under service load. [PERSON] and [PERSON] [8] performed time-dependent reliability research on the effect of corrosion on strength-based reliability of bridge girders. [PERSON] and [PERSON] [9] investigated strength-based reliability approaches based on the annual reliability index to determine the optimized maintenance time for aging structures. [PERSON] and [PERSON] [10] conducted a study on time-dependent reliability of deteriorating reinforced concrete bridge decks. They used a reliability model to assess the probability of flexural failure of a concrete slab bridge under corrosion. Monte Carlo simulation was used to simulate 75 years of service life. It should be noted that the end of service life for almost all bridges comes about because of serviceability issues such as corrosion, and not because of a local or global structural failure (load exceeding resistance). Therefore, serviceability-based reliability models have also been developed [11; 12; 13]. For example, theoretical models to assess the service life of bridge decks due to corrosion consider factors such as penetration of chlorides, initiation and progression of corrosion, cracking, and progressive delamination. Effects of concrete properties, cover depth, diffusion coefficient, surface chloride concentration, aggregate type, bar layout, etc. can be considered in an analytical model. Assuming availability of such an effective serviceability-based theoretical model, Monte Carlo simulations or other approaches can then be performed to assess the service life in a probabilistic manner. The primary challenge, however, is effective verification and calibration of such theoretical models against field performance data in a meaningful probabilistic approach. To do so, large-scale observation-based (phenomenological) reliability models are needed based on field performance data. Survival analysis techniques can provide such a global probabilistic model given availability of large-scale data. The National Bridge Inventory (NBI) records can be the source of such large-scale data.