[in Japanese]

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The application of B-spline surface to the estimation of lake bottom topography is described. Using the analysis of bivariate B-spline the shape of the lake bottom is approximated. According to the validity of the estimation by bivariate B-spline function the method is applied to the actual observation point of the lake depth. A survey over the water area has more difficulties than that on the land, and the measurement observation point are distributed quite irregularly. The locations of the measured observation point don't exist regularly over the lake. Those locations were distributed along with the wake of the boat on which the sample observation point were collected. The density of the observation point is quite high in some small region and quite low in another wide region. Based on such irregular observation point we tried the statistical estimation. The regularized term with a penalty coefficient make the proper approximation of the parameters of B-spline functions. There are many factors such that the number of the knots, the locations of those knots, the number of B-spline functions and the coefficient of the penalized term. Appropriate information criterion which has sufficient accuracy and small amount of computation is applied to the determination of the optimal model.

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[in Japanese]

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The Arrhenius-log-normal model has been used, in general, for the deterioration model due to the thermal stress. The Arrhenius law is based on the chemical reaction theory between the absolute temperature and the activity of materials. In the International Electrotechnical Commission 60216-1, the deterioration due to the thermal stress is represented by using the mechanical strength, and the time showing 50% mechanical strength to the initial strength is defined as the failure time. We assume here the generalized Pareto distribution model for such a model. Combining the Arrhenius law with the generalized Pareto distribution model, we have discussed the optimal allocation of test specimens using simulation study.

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