Deterioration rates and accelerations of an expressway equipment system vary dependent on its type and installation location. Moreover, in the asset management of the equipment system, it is necessary to quantify the failure process at arbitrary assessment units and decide the optimal management policy. This paper proposes a two dimensional Weibull mixture hazard model in order to estimate heterogeneities among deterioration rates and accelerations of each equipment. And furthermore, the authors develop a Bayesian estimation method of the two dimensional Weibull mixture hazard model. At that time, two kinds of heterogeneities are expressed as Gamma distributions and their correlation can be described using an Archimedean copula. Lastly, the proposed model is applied to the actual inspection data of an expressway equipment system and the usefulness of the model can be discussed as a case study.

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 Risk financing for natural disasters is an important management issue in the railway business because of frequent natural disasters such as typhoons and earthquakes in Japan. In this paper, we propose the mathematical model of ruin probability on natural disaster risk finance in the railway business. The model is the quantitative analytical method of the suitable risk finance according to the financial situation and the natural disaster risk peculiar to the respective railways. Furthermore, we also report the statistical evidence based on the restoration expense of losses by natural disasters.

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