• 품질경영학회지
• /
• 제29권3호
• /
• pp.49-65
• /
• 2001

This paper presents new compromise ALT plan which is applied to situations that true relationship between stress and parameters is not known exactly. The assumed failure distribution of this study is one of location-scale family, i. e., exponential, Weibull, and lognormal distributions which have been ones of the popular choices of failure distributions. The method of applying the stress is constant, and the censoring mechanism is Type I censoring. Compared with existing compromise plans under true simple linear model in terms of statistical efficiency, the efficiency of new compromise plan is better than the corresponding other compromise ones in most cases. For case when true model is quadratic, this plan can be used without any severe loss in statistical efficiency. The proposed new compromise ALT plan is illustrated with a numerical example and sensitivity analyses are conducted to study effects of pre-estimates of design parameters.

• 대한산업공학회지
• /
• 제17권1호
• /
• pp.95-108
• /
• 1991

For the case where the lifetime at a constant stress level has exponential distribution, optimal accelerated life test plans are developed under the assumptions of intermittent inspection and Type I censoring. In a optimal plan, the low and high stress levels, the proportion of test units allocated and the inspection times at each stress are determined such that the asymptotic variance of the maximum likelihood estimator of logarithmic transformed mean at the use condition is minimized. In addition to the optimal plan in which numerical technique to solve the set of nonlinear equations must be employed to determine inspection times at each stress level, we also propose another plans which employ equally-spaced or equal probability inspection schemes at two overstress levels of corresponding optimal one. For both optimal and proposed plans, computational results indicate that the asymptotic variance of the estimated mean at the use stress is insensitive to number of inspections at overstress levels for the range of parameter values considered.

• Structural Engineering and Mechanics
• /
• 제64권1호
• /
• pp.71-79
• /
• 2017

In this study, interaction of several interface cracks located between a functionally graded material (FGM) layer and an elastic layer under anti-plane deformation based on the distributed dislocation technique (DDT) is analyzed. The variation of the shear modulus of the functionally graded coating is modeled by an exponential and linear function along the thickness of the layer. The complex Fourier transform is applied to governing equation to derive a system of singular integral equations with Cauchy type kernel. These equations are solved by a numerical method to obtain the stress intensity factors (SIFs) at the crack tips. The effects of non-homogeneity parameters for exponentially and linearly form of shear modulus, the thickness of the layers and the length of crack on the SIFs for several interface cracks are investigated. The results reveal that the magnitude of SIFs decrease with increasing of FG parameter and thickness of FGM layer. The values of SIFs for FGM layer with exponential form is less than the linear form.

• Kyungpook Mathematical Journal
• /
• 제52권2호
• /
• pp.167-177
• /
• 2012

In this article, we propose exponentially fitted error correction methods(EECM) which originate from the error correction methods recently developed by the authors (see [10, 11] for examples) for solving nonlinear stiff initial value problems. We reduce the computational cost of the error correction method by making a local approximation of exponential type. This exponential local approximation yields an EECM that is exponentially fitted, A-stable and L-stable, independent of the approximation scheme for the error correction. In particular, the classical explicit Runge-Kutta method for the error correction not only saves the computational cost that the error correction method requires but also gives the same convergence order as the error correction method does. Numerical evidence is provided to support the theoretical results.

• 대한수학회지
• /
• 제56권1호
• /
• pp.149-167
• /
• 2019

In this work, we study the existence, uniqueness and stability in the ${\alpha}$-norm of solutions for some stochastic partial functional integrodifferential equations. We suppose that the linear part has an analytic resolvent operator in the sense given in Grimmer [8] and the nonlinear part satisfies a $H{\ddot{o}}lder$ type condition with respect to the ${\alpha}$-norm associated to the linear part. Firstly, we study the existence of the mild solutions. Secondly, we study the exponential stability in pth moment (p > 2). Our results are illustrated by an example. This work extends many previous results on stochastic partial functional differential equations.

• Kyungpook Mathematical Journal
• /
• 제64권1호
• /
• pp.95-111
• /
• 2024

The filled function method is useful in solving unconstrained global optimization problems. However, depending on the type of function, and parameters used, there are limitations that cause difficultiies in implemenations. Exponential and logarithmic functions lead to the overflow effect, requiring iterative adjustment of the parameters. This paper proposes a polynomial-filled function that has a general form, is non-exponential, nonlogarithmic, non-parameteric, and continuously differentiable. With this newly proposed filled function, the aforementioned shortcomings of the filled function method can be overcome. To confirm the superiority of the proposed filled function algorithm, we apply it to a set of unconstrained global optimization problems. The data derived by numerical implementation shows that the proposed filled function can be used as an alternative algorithm when solving unconstrained global optimization problems.

• 응용통계연구
• /
• 제8권2호
• /
• pp.87-97
• /
• 1995

$2 \times 2$ 요인계획법에서 주효과가 전혀 존재하지 않거나 단지 하나만이 존재하는 경우의 교호작용을 위한 일반적인 F 검정과 순위변환을 이용한 F 검정 (FR 검정)의 제1종 오류율과 검정력은 전반적으로 비슷한 수준이나 정규분포보다는 지수분포하에서의 FR 검정의 검정력이 상당히 높은 수준임을 알 수 있다. 반면에 주효과들이 모두 존재하는 경우의 FR 검정의 제1종 오류율은 F 검정에 비하여 효과의 크기가 증가할수록 감소하고 주효과의 구성방법에도 영향을 받으며, 검정력은 효과의 크기와 표본의 크기를 크게할수록 증가하되 FR 검정의 검정력은 F 검정에 비하여 낮은 수준이며 주효과의 구성방법 및 모집단의 분포형태에 따라 민감하게 변화함을 알 수 있다.

• Journal of the Korean Data and Information Science Society
• /
• 제17권4호
• /
• pp.1099-1106
• /
• 2006

This study is an analysis of the stock trading value in terms of investor types in the Korean stock market for recent 12 years. We examined the characteristics in stock trading value variation according to each investor type and the interactive relationship in the trading value between types of investors. The results show that the trading value scale of every investor type increases overall while the proportion of the trading value by each investor type in the market exhibits variation. In addition, a statistically significant interactive relationship in the trading value between types of investors exists: the correlations are formed differently before and after events which largely influence the stock market.

• 대한수학회지
• /
• 제57권3호
• /
• pp.655-668
• /
• 2020

In this paper, we establish the generalized Cameron-Storvick type theorem on function space. We then give relationships involving the generalized Cameron-Storvick type theorem, modified generalized integral transform and modified convolution product. A motivation of studying the generalized Cameron-Storvick type theorem is to generalize formulas and results with respect to the modified generalized integral transform on function space. From the some theories and formulas in the functional analysis, we can obtain some formulas with respect to the translation theorem of exponential functionals.

• Communications for Statistical Applications and Methods
• /
• 제25권5호
• /
• pp.569-575
• /
• 2018

Pareto distribution is important to analyze data in actuarial sciences, reliability, finance, and climatology. In general, unknown parameters of the Pareto distribution are estimated based on the maximum likelihood method that may yield inadequate inference results for small sample sizes and high percent censored data. In this paper, a new approach based on the regression framework is proposed to estimate unknown parameters of the Pareto distribution under the progressive Type-II censoring scheme. The proposed method provides a new regression type estimator that employs the spacings of exponential progressive Type-II censored samples. In addition, the provided estimator is a consistent estimator with superior performance compared to maximum likelihood estimators in terms of the mean squared error and bias. The validity of the proposed method is assessed through Monte Carlo simulations and real data analysis.