• Structural Engineering and Mechanics
• /
• 제62권3호
• /
• pp.365-372
• /
• 2017

Reliability analysis is a probabilistic approach to determine a safety level of a system. Reliability is defined as a probability of a system (or a structure, in structural engineering) to functionally perform under given conditions. In the 1960s, Basler defined the reliability index as a measure to elucidate the safety level of the system, which until today is a commonly used parameter. However, the reliability index has been formulated based on the pivotal assumption which assumed that the considered limit state function is normally distributed. Nevertheless, it is not guaranteed that the limit state function of systems follow as normal distributions; therefore, there is a need to define a new reliability index for no-normal distributions. The main contribution of this paper is to define a sophisticated reliability index for limit state functions which their distributions are non-normal. To do so, the new definition of reliability index is introduced for non-normal limit state functions according to the probability functions which are calculated based on the convolution theory. Eventually, as the state of the art, this paper introduces a simplified method to calculate the reliability index for non-normal distributions. The simplified method is developed to generate non-normal limit state in terms of normal distributions using series of Gaussian functions.

• 대한수학회지
• /
• 제32권3호
• /
• pp.625-633
• /
• 1995

Classical Fatous' theorem asserts that the non-tangential limit of the Poisson integral of an integrals function on $[\pi, \pi]$ exists a.e.

• 응용통계연구
• /
• 제4권2호
• /
• pp.149-156
• /
• 1991

본 논문에서는 여러 분야에서 중요한 역할을 하는 이차형식의 정확한 밀도함수를 구하는 것 이 어려운 경우에 극소극한정리를 포함하는 문제들에 토레플리트(Toelitz) 형식의 고유값에 대한 점근 이론을 갖고서 이차형식의 점근 밀도함수를 구하였다.

• Journal of the Korean Data and Information Science Society
• /
• 제9권2호
• /
• pp.113-118
• /
• 1998

In this paper we study central limit theorem(C.L.T.) and law of iterated logarithm (L.I.L.) for fuzzy random variables with respect to Hausdorff distance.

• Communications for Statistical Applications and Methods
• /
• 제3권3호
• /
• pp.59-74
• /
• 1996

The properties of the residuals are investigated when K-consecutive observations are interpolated. The central limit theorem is also proved for the LSE for autoregressive parameters when $\kappa4--consecutive observations are contaminated. The performance of the interpolated LSE in small samples is investigated by simulation. And the interpolated with the Yule-Walker type estimator.

• 대한수학회논문집
• /
• 제11권3호
• /
• pp.855-865
• /
• 1996

In this paper, we establish the weak convergences of processes occurring in a generalized Curie-Weiss model and its dual.

• Korean Journal of Mathematics
• /
• 제11권1호
• /
• pp.35-43
• /
• 2003

We study the weak convergence to Fractional Brownian motion and some examples with applications to traffic modeling. Finally, we get loss probability for queue-length distribution related to self-similar process.

• 콘크리트학회지
• /
• 제6권5호
• /
• pp.193-202
• /
• 1994

본 연구에서는 전단스팬비가 작은 철근콘크리트부재를 대상으로, 기존에 주로 실험치에만 의존하여 제안되었던 전단내력식에서 탈피하여 극한해석법중의 하계정리를 이용하여 이론적으로 제안하였다. 본연구에서 제안한 모델에서는 아치기구와 트러스기구를 동시에 고려할 수가 있고 각각의 기구에서 분담하은 힘의 크기를 알 수 있다. 또한, 외부에서 가해진 힘이 어떻게 지검에 전달되고 있는가 시각적으로 이해할 수가 있으며, 전단스팬비(a/b), 전단보강근비, 인장철근비 등의 영향을 정량적으로 고려할 수가 있다. 본 연구에서 유도한 전단내력식을 기존의 실험치와 비교한 결과, 본 연구에서 제안한 식은 실험치와 대체로 일치하며, 다른 연구자에 의해 제안된 전단내력평가식에 손색이 없음을 알았다.

• Geomechanics and Engineering
• /
• 제11권4호
• /
• pp.471-492
• /
• 2016

Underground tunnelling is one of the sustainable construction methods which can facilitate the increasing passenger transportation in the urban areas and benefit the community in the long term. Tunnelling in various ground conditions requires careful consideration of the stability factor. This paper investigates three dimensional stability of a shallow circular tunnel in a layered soil. Upper bound theorem of limit analysis was utilised to solve the tunnel face stability problem. A three dimensional kinematic admissible failure mechanism was improved to model a layered soil and limiting assumptions of the previous studies were resolved. The study includes calculation of the minimum support pressure acting on the face of the excavation in closed-face excavations. The effects of the characteristics of the layers on the minimum support pressure were examined. It was found that the ratio of the thickness of cover layers particularly when a weak layer is overlying a stronger layer, has the most significant influence on the minimum tunnel support pressure. Comparisons have been made with the results of the numerical modelling using FLAC3D software. Results of the current study were in a remarkable agreement with those of numerical modelling.

• Journal of Communications and Networks
• /
• 제11권1호
• /
• pp.47-56
• /
• 2009

We investigate the connectivity of fading wireless ad-hoc networks with a pair of novel connectivity metrics. Our first metric looks at the problem of connectivity relying on the outage capacity of MIMO channels. Our second metric relies on a probabilistic treatment of the symbol error rates for such channels. We relate both capacity and symbol error rates to the characteristics of the underlying communication system such as antenna configuration, modulation, coding, and signal strength measured in terms of signal-to-interference-noise-ratio. For each metric of connectivity, we also provide a simplified treatment in the case of ergodic fading channels. In each case, we assume a pair of nodes are connected if their bi-directional measure of connectivity is better than a given threshold. Our analysis relies on the central limit theorem to approximate the distribution of the combined undesired signal affecting each link of an ad-hoc network as Gaussian. Supported by our simulation results, our analysis shows that (1) a measure of connectivity purely based on signal strength is not capable of accurately capturing the connectivity phenomenon, and (2) employing multiple antenna mobile nodes improves the connectivity of fading ad-hoc networks.