## 1 Introduction  
A large number of bridges were constructed in Japan during periods of high economic growth. Fifty years later, performance degradations have been widely found in these bridges. Some bridges may fail without proper maintenance. Parts that have seriously deteriorated threaten the safety of users because of insufficient maintenance. Nowadays, labor fees are continuously increasing, maintenance costs have become a heavy burden on the national budget, and there is a great demand for reduced maintenance costs. Against this background, the Ministry of Land, Infrastructure, Transportation and Tourism (MLIT) announced on 1 July 2014 that close visual bridge inspection would now be required every five years for the approximately 700,000 bridges in Japan. Moreover, private highway companies began to conduct this kind of periodic inspection before the mandatory inspection policy was put in place. This policy has accelerated the data accumulation of inspection results, which now offers an opportunity for statistical analysis. In these circumstances, demands for asset management based on the statistical analysis of bridges are growing. As [PERSON] and [PERSON] (2001) and [PERSON] and [PERSON] (2002) stated, there are two types of models that can be developed and applied to evaluate the deterioration process of infrastructure. The first is a state-based model, which forecasts the possibility that a structure will undergo a decline in condition-state at a given time [1; 2]. A typical example is the Markovian method, which is extensively used in United States (US) bridge management systems ([PERSON] et al. (2006); [PERSON] et al. (2015), [PERSON] et al. (2005)) [3; 4; 5]. However, as [PERSON] et al. (2010) stated, the Markovian method has several limitations. A discrete transition interval is assumed; the future condition of structural elements depends not on their past history, but rather on their current condition, and different bridge component deterioration mechanisms cannot be efficiently considered [6]. Furthermore, the Markovian method cannot evaluate multiple variables, which means that it is difficult to compare the risks of each deterioration factor. The other type of model is time-based, in which the time probability distribution of structural deterioration is computed. A typical example is survival analysis, which is more flexible and expandable than the Markovian method. [PERSON] and [PERSON] (2002) focused on survival analysis and applied it to quantitatively evaluate the effect of several coefficients. However, they indicated that one limitation of their research was that the subsets of bridges were relatively small. [PERSON] and [PERSON] (2015) conducted a survival analysis of concrete bridges in East Japan [7]. Similar to our research, the definition of East Japan only includes Aomori, Akita, Iwate, Yamagata; Miyagi Fukushima Prefecture and the Tokyo region are excluded. The Kaplan-Meier (KM) curve and Cox regression were used to evaluate the deterioration rate of bridge components under different structural features, traffic volume, etc. However, because the analysis was only conducted for one region, it cannot be considered to hold for the entirety of Japan. [PERSON] et al. (2017) also used a semi-parametric multivariate proportional hazards model to characterize the effect of external factors on the deterioration rates of bridge components [8]. As [PERSON] et al. (2013) stated, semi-parametric survival analysis does not assume the distribution of hazard; therefore, it has more flexibility in capturing the features of the original data [9]. In addition, some analyses have tried to establish the relationship between bridge inspection data and environmental information. [PERSON] et al. (2013) classified 2600 bridges according to the years in service, quantity of large vehicle traffic, amount of de-icing salt used, and average ambient temperature in winter in East Japan [10]. In another study, [PERSON] (2013) examined 1662 bridges in Bolzano, which is a mountainous area of Northern Italy.