• Bulletin of the Korean Chemical Society
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• v.26 no.11
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• pp.1735-1737
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• 2005

We obtain probabilities at a crossing of two linearly time-dependent potentials that are constantly coupled to the other by solving a time-dependent Schrödinger equation. We find that the system which was initially localized at one state evolves to split into both states at the crossing. The probability splitting depends on the coupling strength $V_0$ such that the system stays at the initial state in its entirety when $V_0$ = 0 while it is divided equally in both states when $V_0 \rightarrow {\infty}$ . For a finite coupling the probability branching at the crossing is not even and thus a complete probability transfer at $t \rightarrow {\infty}$ is not achieved in the linear potential crossing problem. The Landau-Zener formula for transition probability at $t \rightarrow {\infty}$ is expressed in terms of the probabilities at the crossing.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.630-633
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• 2004

Generally, component and FR-4 board are connected by solder joint. Because material properties of components and FR-4 board are different, component and FR-4 board show different coefficients of thermal expansion (CTE) and thus strains in component and board are different when they are heated. That is, the differences in CTE of component and FR-4 board cause the dissimilarity in shear strain and BGA solder joint s failure. The first order Taylor series expansion of the limit state function incorporating with thermal fatigue models is used in order to estimate the failure probability of solder joints under heated condition. A model based on plastic-strain rate such as the Coffin-Manson Fatigue Model is utilized in this study. The effects of random variables such as frequency, maximum temperature, and temperature variations on the failure probability of the BGA solder joint are systematically investigated by using a failure probability model with the first order reliability method(FORM).

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.857-864
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• 2006

Due to the difficulties in numerical generation of random fields that satisfy not only the probabilistic distribution but the spectral characteristics as well. it is relatively hard to find an exact response variability of a structural response with a specific random field which has its features in the spatial and spectral domains. In this study. focusing on the fact that the random field assumes a constant over the domain under consideration when the correlation distance tends to infinity, a semi-theoretical solution of response variability is proposed for in-plane and plate bending structures. In this procedure, the probability density function is used directly resulting in a semi-exact solution for the random field in the state of random variable. It is particularly noteworthy that the proposed methodology provides response variability for virtually any type of probability density functions.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1033-1047
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• 2009

In this paper, we consider a m-type risk model with Markov-modulated premium rate. A integral equation for the conditional ruin probability is obtained. A recursive inequality for the ruin probability with the stationary initial distribution and the upper bound for the ruin probability with no initial reserve are given. A system of Laplace transforms of non-ruin probabilities, given the initial environment state, is established from a system of integro-differential equations. In the two-state model, explicit formulas for non-ruin probabilities are obtained when the initial reserve is zero or when both claim size distributions belong to the $K_n$-family, n $\in$ $N^+$ One example is given with claim sizes that have exponential distributions.

• Magazine of the Korean Society of Agricultural Engineers
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• v.45 no.2
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• pp.35-44
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• 2003

A system reliability method is proposed to decide reliable serviceability of agricultural irrigation system. Even though reliability method is applied to real engineering situations involving actual life environments and maintaining costs, a number of Issues arise as a modeling and analysis level. This article use concepts that can be described the probability of failure with time variant and series-parallel system reliability analysis model. A proposed method use survivor function that can simulate a time-variant performance function for a lifetime before it is required essential maintenance or replacement to define a target probability of failure in agricultural irrigation canal. In the further study, it is required a relationship between a state of probability of failure and current serviceability to make the optimum repair strategy to maintain appropriate serviceability of an irrigation system.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.2
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• pp.714-727
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• 2015

The hierarchical structure in networks is widely applied in many practical scenarios especially in some emergency cases. In this paper, we focus on a tree network with and without packet loss where one source sends data to n destinations, through m relay nodes employing random linear network coding (RLNC) over a Galois field in parallel transmission systems. We derive closed-form probability expressions of successful decoding at a destination node and at all destination nodes in this multicast scenario. For the convenience of computing, we also propose an upper bound for the failure probability. We then investigate the impact of the major parameters, i.e., the size of finite fields, the number of internal nodes, the number of sink nodes and the channel failure probability, on the decoding performance with simulation results. In addition, numerical results show that, under a fixed exact decoding probability, the required field size can be minimized. When failure decoding probabilities are given, the operation is simple and its complexity is low in a small finite field.

• Transactions of the Korean Society of Pressure Vessels and Piping
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• v.6 no.1
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• pp.43-49
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• 2010

The piping failure probability of the reactor coolant system in Kori unit 1 was evaluated considering stress corrosion cracking. The P-PIE program (Probabilistic Piping Integrity Evaluation Program) developed in this study was used in the analysis. The effect of some variables such as oxygen concentration during start up and steady state operation, and operating temperature, which are related with stress corrosion cracking, on the piping failure probabilities was investigated. The effects of leak detection capability, the size of big leak, piping loops, and reactor types on the piping failure probability were also investigated. The results show that (1) LOCA (loss of coolant accident) probability of Kori unit 1 is extremely low, (2) leak probability is sensitive to oxygen concentration during steady state operation and operating temperature, while not sensitive to the oxygen concentration during start up, and (3) the piping thickness and operating temperature play important roles in the leak probabilities of the cold leg in 4 reactor types having same inner diameter.

• Geomechanics and Engineering
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• v.15 no.3
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• pp.879-888
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• 2018

Probability-based design codes have been developed to sufficiently confirm the safety level of structures. One of the most acceptable probability-based approaches is Load Resistance Factor Design (LRFD), which measures the safety level of the structures in terms of the reliability index. The main contribution of this paper is to calibrate the load and resistance factors of the design code for tunnels. The load and resistance factors are calculated using the available statistical models and probability-based procedures. The major steps include selection of representative structures, consideration of the limit state functions, calculation of reliability for the selected structures, selection of the target reliability index and calculation of load factors and resistance factors. The load and resistance models are reviewed. Statistical models of resistance (load carrying capacity) are summarized for strength limit state in bending, shear and compression. The reliability indices are calculated for several segments of a selected circular tunnel designed according to the tunnel manual report (Tunnel Manual). The novelty of this paper is the selection of the target reliability. In doing so, the uniform spectrum of reliability indices is proposed based on the probability paper. The final recommendation is proposed based on the closeness to the target reliability index.

• Wind and Structures
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• v.25 no.3
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• pp.261-282
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• 2017

The probabilistic information of directional extreme wind speeds is important for precisely estimating the design wind loads on structures. A new joint probability distribution model of directional extreme wind speeds is established based on observed wind-speed data using multivariate extreme value theory with the t-Copula function in the present study. At first, the theoretical deficiencies of the Gaussian-Copula and Gumbel-Copula models proposed by previous researchers for the joint probability distribution of directional extreme wind speeds are analysed. Then, the t-Copula model is adopted to solve this deficiency. Next, these three types of Copula models are discussed and evaluated with Spearman's rho, the parametric bootstrap test and the selection criteria based on the empirical Copula. Finally, the extreme wind speeds for a given return period are predicted by the t-Copula model with observed wind-speed records from several areas and the influence of dependence among directional extreme wind speeds on the predicted results is discussed.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.44 no.3
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• pp.22-32
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• 2021

To meet rapidly changing market demands, manufacturers strive to increase both of productivity and diversity at the same time. As a part of those effort, they are applying flexible manufacturing systems that produce multiple types and/or options of products at a single production line. This paper studies such flexible manufacturing system with multiple types of products, multiple Bernoulli reliability machines and dedicated buffers between them for each of product types. As one of the prevalent control policies, priority based policy is applied at each machines to select the product to be processed. To analyze such system and its performance measures exactly, Markov chain models are applied. Because it is too complex to define all relative transient and its probabilities for each state, an algorithm to update transient state probability are introduced. Based on the steady state probability, some performance measures such as production rate, WIP-based measures, blocking probability and starvation probability are derived. Some system properties are also addressed. There is a property of non-conservation of flow, which means the product ratio at the input flow is not conserved at the succeeding flows. In addition, it is also found that increased buffer capacity does not guarantee improved production rate in this system.