• Title/Summary/Keyword: Exponential Type

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Optimal Design of Accelerated Life Tests under Model Uncertainty (불확정 모형하에서 가속수명시험의 최적 설계)

  • 서순근;하천수;김갑석
    • Journal of Korean Society for Quality Management
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    • v.29 no.3
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    • pp.49-65
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    • 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.

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Design of Optimal Accelerated Life Tests for the Exponential Failure Distribution under Intermittent Inspection (지수고장분포(指數故障分布) 및 단속검사하(斷續檢査下)의 최적(最適) 가속수명시험(加速壽命侍險)의 설계(設計))

  • Seo, Sun-Keun;Choi, Jong-Deuk
    • Journal of Korean Institute of Industrial Engineers
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    • v.17 no.1
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    • pp.95-108
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    • 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.

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Mode III SIFs for interface cracks in an FGM coating-substrate system

  • Monfared, Mojtaba Mahmoudi
    • Structural Engineering and Mechanics
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    • v.64 no.1
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    • pp.71-79
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    • 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.

Exponentially Fitted Error Correction Methods for Solving Initial Value Problems

  • Kim, Sang-Dong;Kim, Phil-Su
    • Kyungpook Mathematical Journal
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    • v.52 no.2
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    • pp.167-177
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    • 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.

STABILITY IN THE α-NORM FOR SOME STOCHASTIC PARTIAL FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS

  • Diop, Mamadou Abdoul;Ezzinbi, Khalil;Lo, Modou
    • Journal of the Korean Mathematical Society
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    • v.56 no.1
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    • pp.149-167
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    • 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.

Polynomial-Filled Function Algorithm for Unconstrained Global Optimization Problems

  • Salmah;Ridwan Pandiya
    • Kyungpook Mathematical Journal
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    • v.64 no.1
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    • pp.95-111
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    • 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.

Simulation analysis of type I error and power for F test and rank transformed F test in $2 times 2$ factorial ANOVA ($2 times 2$ 요인 계획법의 F 검정과 순위 F 검정에 따른 제1종 오류와 검정력 분석에 대한 의태 연구)

  • 최영훈
    • The Korean Journal of Applied Statistics
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    • v.8 no.2
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    • pp.87-97
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    • 1995
  • When there is no main effcts or only one main effect in a $2 \times 2$ factorial design, Type I error rates and power for the rank transformed F test (FR test) for interaction are nearly equal to those of the classical F test. However the power of FR test is quite superior under the exponential distribution rather than the of FR test is quite superior under the exponential distribution rather than the normal distribution. Meanwhile when both main effects are in the model, Type I error rates of FR test, compared with those of F test, decrease as the effect size increases and are dependent on the fashion in which main effects are constructed. In addition, the power of FR test increases as the effect size and the sample size increase and is highly dependent on the manner in which main effects are constructed and the type of population distribution.

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An Empirical Study on Stock Trading Value of Each Investor Type in the Korean Stock Market

  • Shin, Yang-Kyu
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.4
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    • pp.1099-1106
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    • 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.

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GENERALIZED CAMERON-STORVICK TYPE THEOREM VIA THE BOUNDED LINEAR OPERATORS

  • Chang, Seung Jun;Chung, Hyun Soo
    • Journal of the Korean Mathematical Society
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    • v.57 no.3
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    • pp.655-668
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    • 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.

New approach for analysis of progressive Type-II censored data from the Pareto distribution

  • Seo, Jung-In;Kang, Suk-Bok;Kim, Ho-Yong
    • Communications for Statistical Applications and Methods
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    • v.25 no.5
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    • pp.569-575
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    • 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.