• Journal of the Korean Statistical Society
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• v.22 no.2
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• pp.307-324
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• 1993

The limiting distribution of the excess over the boundary is determined for the autoregressive process.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.1557-1560
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• 2003

This paper presents the effect of varying boundary conditions such as ground subsidence on failure prediction of buried pipelines. The first order Taylor series expansion of the limit state function is used in order to estimate the probability of failure associated with three cases of ground subsidence. We estimate the distribution of stresses imposed on the buried pipelines by varying boundary conditions and calculate the probability of pipelines with von-Mises failure criterion. The effects of random variables such as pipe diameter, internal pressure, temperature, settlement width, load for unit length of pipelines, material yield stress and thickness of pipeline on the failure probability of the buried pipelines are also systematically studied by using a failure probability model for the pipeline crossing a ground subsidence region.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.1
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• pp.173-180
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• 2004

This paper presents the effect of varying boundary conditions such as ground subsidence, internal pressure and temperature variation for buried pipelines on failure prediction by using a failure probability model. The first order Taylor series expansion of the limit state function incorporating with von-Mises failure criteria is used in order to estimate the probability of failure mainly associated with three cases of ground subsidence. Using stresses on the buried pipelines, we estimate the probability of pipelines with von-Mises failure criterion. The effects of varying random variables such as pipe diameter, internal pressure, temperature, settlement width, load for unit length of pipelines, material yield stress and pipe thickness on the failure probability of the buried pipelines are systematically studied by using a failure probability model for the pipeline crossing ground subsidence regions which have different soil properties.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.475-484
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• 2005

Let W(t) be a Wiener path, let $\xi\;:\;[0,\;{\infty})\;\to\;\mathbb{R}$ be a continuous and increasing function satisfying $\xi$(0) > 0, let $$T_{/xi}=inf\{t{\geq}0\;:\;W(t){\geq}\xi(t)\}$$ be the first-passage time of W over $\xi$, and let F denote the distribution function of $T_{\xi}$. Then the first passage problem has a unique continuous solution as following $$F(t)=u(t)+{\sum_{n=1}^\infty}\int_0^t\;H_n(t,s)u(s)ds$$, where $$u(t)=2\Psi(\xi(t)/\sqrt{t})\;and\;H_1(t,s)=d\Phi\;(\{\xi(t)-\xi(s)\}/\sqrt{t-s})/ds\;for\;0\;{\leq}\;s.