• Nuclear Engineering and Technology
• /
• v.54 no.6
• /
• pp.2084-2093
• /
• 2022

Probabilistic safety assessment is widely used to quantify the risks of nuclear power plants and their uncertainties. When the lognormal distribution describes the uncertainties of basic events, the uncertainty of the top event in a fault tree is approximated with the sum of lognormal random variables after minimal cutsets are obtained, and rare-event approximation is applied. As handling complicated analytic expressions for the sum of lognormal random variables is challenging, several approximation methods, especially Monte Carlo simulation, are widely used in practice for uncertainty analysis. In this study, a theoretical approach for analyzing the sum of lognormal random variables using an efficient numerical integration method is proposed for uncertainty analysis in probability safety assessments. The change of variables from correlated random variables with a complicated region of integration to independent random variables with a unit hypercube region of integration is applied to obtain an efficient numerical integration. The theoretical advantages of the proposed method over other approximation methods are shown through a benchmark problem. The proposed method provides an accurate and efficient approach to calculate the uncertainty of the top event in probabilistic safety assessment when the uncertainties of basic events are described with lognormal random variables.

• Journal of Institute of Control, Robotics and Systems
• /
• v.8 no.10
• /
• pp.847-850
• /
• 2002

Stochastic process analysis is often based on Monte Carlo simulations. As a more rigorous alternative, a deterministic algorithm based on numerical integration is proposed in this paper. which calculates the probability distributions of dependent random variables using the results of simulation with grid points of independent random variables. For performance evaluation, the proposed algorithm is applied to an example problem which can be analytically solved. and the result is compared with that of Monte Carlo simulation. The proposed algorithm is suitable for general process simulation problems with a few independent random variables, and expected to be applicable to areas such as safety analysis and quality control.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2004.04a
• /
• pp.385-388
• /
• 2004

The present paper establish the improved version of central limit theorem for sums of level-continuous fuzzy random variables as a generalization of central limit theorem for sums of independent and identically distributed random sets.

• Journal of the Korean Mathematical Society
• /
• v.32 no.1
• /
• pp.141-149
• /
• 1995

Let N denote the set of positive integers. Fix $d_1, d_2 \in N with d = d_1 + d_2$. Let X and Y be real random variables and let ${X_i : i \in N^d_1} and {Y_j : j \in N^d_2}$ be independent families of independent identically distributed random variables with $L(X) = L(X_i) and L(Y) = L(Y_j)$, where $L(\cdot)$ denote the law of $\cdot$.

• Journal of the Korean Statistical Society
• /
• v.23 no.2
• /
• pp.239-250
• /
• 1994

In this paper, we prove a strong large deviations theorem for the ratio of independent randoem variables with error rate of $O(n^{-1})$. To obtain our results we use the inversion formula for the tail probability and apply the Chaganty and Sethuraman's (1985) approach.

• Journal of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.441-460
• /
• 2017

In this paper, we establish some conditional versions of the first part of the Borel-Cantelli lemma. As its applications, we study strong limit results of $\mathfrak{F}$-independent random variables sequences, the convergence of sums of $\mathfrak{F}$-independent random variables and the conditional version of strong limit results of the concomitants of order statistics.

• Journal of the Korean Data and Information Science Society
• /
• v.7 no.2
• /
• pp.189-201
• /
• 1996

In this paper, we study the saddlepoint approximations for the ratio of independent random variables. In Section 2, we derive the saddlepoint approximation to the density. And in Section 3, we derive two approximation formulae for the tail probability, one by following Daniels'(1987) method and the other by following Lugannani and Rice's (1980). In Section 4, we represent some numerical examples which show that the errors are small even for small sample size.

• Journal of the Korean Data and Information Science Society
• /
• v.21 no.5
• /
• pp.967-972
• /
• 2010

We shall consider estimations of an exponetiated parameter of the exponentiated Pareto distribution with known scale and threshold parameters. A quotient distribution of two independent exponentiated Pareto random variables is obtained. We also derive the distribution of the ratio of two independent exponentiated Pareto random variables.

• Journal of the Korean Statistical Society
• /
• v.34 no.1
• /
• pp.1-9
• /
• 2005

In this paper we establish the Hajeck-Renyi type inequality for asymptotically quadrant sub-independent random variables and derive the strong law of large numbers by this inequality.

• 한국데이터정보과학회:학술대회논문집
• /
• 2006.11a
• /
• pp.37-42
• /
• 2006

We shall consider an inference of the reliability P(Y