• Title/Summary/Keyword: four-parameter distributions

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A Study on the Evaluation of Probable Snowfall Depth in Korea (우리나라의 확률적설량 산정에 관한 연구)

  • Lee, Jae-Joon;Jung, Young-Hoon;Lee, Sang-Won
    • Journal of the Korean Society of Hazard Mitigation
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    • v.7 no.2 s.25
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    • pp.53-63
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    • 2007
  • This study is to evaluate the probable snowfall depth by the point frequency analysis and to draw the map of probable snowfall depth in Korea. The 14 probability distributions which has been widely used in hydrologic frequency analysis are applied to the annual maximum depth of snowfall data. The parameters of each probability distribution are estimated by method of moments, maximum likelihood method and method of probability weighted moments. The estimated parameters were checked by parameter validity conditions of each assumed probability distribution. Four tests that are $X^2-test$, Kolmogorov-Smirnov test, Cramer von Mises test and probability plot correlation coefficient test are used in this study to determine the goodness of fit of the distributions. Mostly the 2-parameter gamma distribution was determined as appropriate distribution for the annual maximum new snowfall depth. The probable snowfall depth were obtained from appropriate distribution for the selected return periods and the maps of probable snowfall depth were presented. It will be useful to specify the snowfall load for the design of agricultural facilities such as vinyl house and cattle shed.

Hygro-thermo-mechanical vibration and buckling of exponentially graded nanoplates resting on elastic foundations via nonlocal elasticity theory

  • Sobhy, Mohammed
    • Structural Engineering and Mechanics
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    • v.63 no.3
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    • pp.401-415
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    • 2017
  • In this article, hygro-thermo-mechanical vibration and buckling of exponentially graded (EG) nanoplates resting on two-parameter Pasternak foundations are studied using the four-unknown shear deformation plate theory. The material properties are presumed to change only in the thickness direction of the EG nanoplate according to two exponential laws distribution. The boundary conditions of the nanoplate may be simply supported, clamped, free or combination of them. To consider the small scale effect on forced frequencies and buckling, Eringen's differential form of nonlocal elasticity theory is employed. The accuracy of the present study is investigated considering the available solutions in literature. A detailed analysis is executed to study the influences of the plate aspect ratio, side-to-thickness ratio, temperature rise, moisture concentration and volume fraction distributions on the vibration and buckling of the nanoplates.

Bayesian Model for Cost Estimation of Construction Projects

  • Kim, Sang-Yon
    • Journal of the Korea Institute of Building Construction
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    • v.11 no.1
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    • pp.91-99
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    • 2011
  • Bayesian network is a form of probabilistic graphical model. It incorporates human reasoning to deal with sparse data availability and to determine the probabilities of uncertain cases. In this research, bayesian network is adopted to model the problem of construction project cost. General information, time, cost, and material, the four main factors dominating the characteristic of construction costs, are incorporated into the model. This research presents verify a model that were conducted to illustrate the functionality and application of a decision support system for predicting the costs. The Markov Chain Monte Carlo (MCMC) method is applied to estimate parameter distributions. Furthermore, it is shown that not all the parameters are normally distributed. In addition, cost estimates based on the Gibbs output is performed. It can enhance the decision the decision-making process.

Design of Accelerated Life Tests and Small Sample Study under Continuous and Intermittent Inspections for Lognormal Failure Distribution (수명이 대수정규분포를 따를 때 연속 및 간헐적 검사하에서 가속수명시험의 설계와 소표본 연구)

  • Seo, Sun-Keun;Chung, Won-Kee
    • Journal of Korean Institute of Industrial Engineers
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    • v.23 no.1
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    • pp.177-196
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    • 1997
  • In this paper, statistically optimal accelerated life test(ALT) plans considering statistical efficiency only and new compromise ALT plans to sacrifice some statistical efficiency in return for improved overall properties including estimobility probability and robustness for the model assumptions are developed under the assumptions of constant stress, intermittent inspection, Type I censoring and lognormal failure distribution which has been one of the popular choices of failure distributions in the extensive engineering applications of ALT. Computational experiments are conducted to compare with four ALT plans including two proposed ones under continuous and intermittent inspections over a range of parameter values in terms of asymptotic variance, sensitivities for guessed input values, and proportion of estimable samples, etc. The small and moderate sample properties for the proposed ALT plans designed under asymptotic criterion are also investigated by Monte Carlo simulation.

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New generalized inverse Weibull distribution for lifetime modeling

  • Khan, Muhammad Shuaib;King, Robert
    • Communications for Statistical Applications and Methods
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    • v.23 no.2
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    • pp.147-161
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    • 2016
  • This paper introduces the four parameter new generalized inverse Weibull distribution and investigates the potential usefulness of this model with application to reliability data from engineering studies. The new extended model has upside-down hazard rate function and provides an alternative to existing lifetime distributions. Various structural properties of the new distribution are derived that include explicit expressions for the moments, moment generating function, quantile function and the moments of order statistics. The estimation of model parameters are performed by the method of maximum likelihood and evaluate the performance of maximum likelihood estimation using simulation.

Length-biased Rayleigh distribution: reliability analysis, estimation of the parameter, and applications

  • Kayid, M.;Alshingiti, Arwa M.;Aldossary, H.
    • International Journal of Reliability and Applications
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    • v.14 no.1
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    • pp.27-39
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    • 2013
  • In this article, a new model based on the Rayleigh distribution is introduced. This model is useful and practical in physics, reliability, and life testing. The statistical and reliability properties of this model are presented, including moments, the hazard rate, the reversed hazard rate, and mean residual life functions, among others. In addition, it is shown that the distributions of the new model are ordered regarding the strongest likelihood ratio ordering. Four estimating methods, namely, method of moment, maximum likelihood method, Bayes estimation, and uniformly minimum variance unbiased, are used to estimate the parameters of this model. Simulation is used to calculate the estimates and to study their properties. Finally, the appropriateness of this model for real data sets is shown by using the chi-square goodness of fit test and the Kolmogorov-Smirnov statistic.

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The Influence of Hardwood Interspecific Competition on Stand Structure and Dynamics for Loblolly Pine Plantations

  • Lee, Young-Jin;Cho, Hyun-Je;Kim, Dong-Geun;Bae, Kwan-Ho;Joo, Sung-Hyun;Hong, Sung-Cheon
    • The Korean Journal of Ecology
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    • v.24 no.4
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    • pp.213-217
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    • 2001
  • The purpose of this study is to investigate the effects of hardwood competitions in stand structure and dynamics by applying prediction models for unthinned loblolly pine (Pinus taeda L.) plantations. A parameter recovery procedure for the Weibull distribution function based on four percentile equations was applied to develop diameter distribution prediction models. Four percentiles of the cumulative diameter distribution prediction equations were predicted as a function of quadratic mean diameter plus competin hardwood trees perhectare varibales. According to the results of this study. it was found that as the amount of competing hardwood trees increased, diameter distributions in terms of stand structure dynamics tended to be more skewed to the right. Therefore, the influence of non-planted hardwood trees interspecific competitoin on planted loblolly pines showed negative effects on the stand structure and dynamics.

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Warping and porosity effects on the mechanical response of FG-Beams on non-homogeneous foundations via a Quasi-3D HSDT

  • Mokhtar Nebab;Hassen Ait Atmane;Riadh Bennai;Mouloud Dahmane
    • Structural Engineering and Mechanics
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    • v.90 no.1
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    • pp.83-96
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    • 2024
  • This paper suggests an analytical approach to investigate the free vibration and stability of functionally graded (FG) beams with both perfect and imperfect characteristics using a quasi-3D higher-order shear deformation theory (HSDT) with stretching effect. The study specifically focuses on FG beams resting on variable elastic foundations. In contrast to other shear deformation theories, this particular theory employs only four unknown functions instead of five. Moreover, this theory satisfies the boundary conditions of zero tension on the beam surfaces and facilitates hyperbolic distributions of transverse shear stresses without the necessity of shear correction factors. The elastic medium in consideration assumes the presence of two parameters, specifically Winkler-Pasternak foundations. The Winkler parameter exhibits variable variations in the longitudinal direction, including linear, parabolic, sinusoidal, cosine, exponential, and uniform, while the Pasternak parameter remains constant. The effective material characteristics of the functionally graded (FG) beam are assumed to follow a straightforward power-law distribution along the thickness direction. Additionally, the investigation of porosity includes the consideration of four different types of porosity distribution patterns, allowing for a comprehensive examination of its influence on the behavior of the beam. Using the virtual work principle, equations of motion are derived and solved analytically using Navier's method for simply supported FG beams. The accuracy is verified through comparisons with literature results. Parametric studies explore the impact of different parameters on free vibration and buckling behavior, demonstrating the theory's correctness and simplicity.

Statistical Distribution of Fatigue Life of Composite Materials for Small Wind-Turbine Blades (소형풍력발전 블레이드용 복합재료의 피로수명 분포에 대한 확률론적 평가)

  • Kang, Ki-Weon
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.35 no.10
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    • pp.1281-1289
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    • 2011
  • This paper deals with several statistical distribution functions for the analysis of fatigue life data of composite laminates for small wind-turbine blades. A series of tensile tests was performed on triaxial glass/epoxy laminates for loading directions of $0^{\circ}$, $45^{\circ}$, and $90^{\circ}$. Then, fatigue tests were carried out to determine the fatigue life at the aforementioned loading directions and the fatigue stresses at four levels. Two-parameter Weibull, three-parameter Weibull, normal, and log-normal distributions were used to fit the fatigue life data of the triaxial composite laminates. The three-parameter Weibull distribution most accurately described the fatigue life data measured experimentally for all the cases considered. Furthermore, the variation of fatigue life was simultaneously affected by the loading direction and fatigue stress level.

Development of a novel fatigue damage model for Gaussian wide band stress responses using numerical approximation methods

  • Jun, Seock-Hee;Park, Jun-Bum
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.12 no.1
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    • pp.755-767
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    • 2020
  • A significant development has been made on a new fatigue damage model applicable to Gaussian wide band stress response spectra using numerical approximation methods such as data processing, time simulation, and regression analysis. So far, most of the alternative approximate models provide slightly underestimated or overestimated damage results compared with the rain-flow counting distribution. A more reliable approximate model that can minimize the damage differences between exact and approximate solutions is required for the practical design of ships and offshore structures. The present paper provides a detailed description of the development process of a new fatigue damage model. Based on the principle of the Gaussian wide band model, this study aims to develop the best approximate fatigue damage model. To obtain highly accurate damage distributions, this study deals with some prominent research findings, i.e., the moment of rain-flow range distribution MRR(n), the special bandwidth parameter μk, the empirical closed form model consisting of four probability density functions, and the correction factor QC. Sequential prerequisite data processes, such as creation of various stress spectra, extraction of stress time history, and the rain-flow counting stress process, are conducted so that these research findings provide much better results. Through comparison studies, the proposed model shows more reliable and accurate damage distributions, very close to those of the rain-flow counting solution. Several significant achievements and findings obtained from this study are suggested. Further work is needed to apply the new developed model to crack growth prediction under a random stress process in view of the engineering critical assessment of offshore structures. The present developed formulation and procedure also need to be extended to non-Gaussian wide band processes.