• Title/Summary/Keyword: Inverse Exponential Distribution

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Breakdown Characteristics and Lifetime Estimation of Rubber Insulating Gloves Using Statistical Models

  • Kim, Doo Hyun;Kang, Dong Kyu
    • International Journal of Safety
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    • v.1 no.1
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    • pp.36-42
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    • 2002
  • This paper is aimed at predicting the life of rubber insulating gloves under normal operating stresses from relatively rapid test performed at higher stresses. Specimens of rubber insulating gloves are subject to multiple stress conditions, i.e. combined electrical and thermal stresses. Two modes of electrical stress, step voltage stress and constant voltage stress are used in specimen aging. There are two types of test for electrical stress in this experiment: the one is Breakdown Voltage (BDV) test under step voltage stress and thermal stress and the other is lifetime test under constant voltage stress and temperature stress. The ac breakdown voltage defined as the break-down point of insulation that leakage current excesses a limit value, l0mA in this experiment, is determined. Because the very high variability of aging data requires the application of statistical model, Weibull distribution is used to represent the failure times as the straight line on Weibull probability paper. Weibull parameters are deter-mined by three statistical methods i.e. maximum likelihood method, graphical method and least squares method, which employ SAS package, Weibull probability paper and FORTRAN, respectively. Two chosen models for predicting the life under simultaneous electrical and thermal stresses are inverse power model and exponential model. And the constants of life equation for multistress aging are calculated using numerical method, such as Gauss Jordan method etc.. The completion of life equation enables to estimate the life at normal stress based on the data collected from accelerated aging test. Also the comparison of the calculated lifetimes between the inverse power model and the exponential model is carried out. And the lifetimes calculated by three statistical methods with lower voltage than test voltage are compared. The results obtained from the suggested experimental method are presented and discussed.

Hydrological Studies on the design flood and risk of failure of the Hydraulic Structures( II) (수리구조물의 파괴위험도와 설계홍수량에 관한 수문학적 연구(II) - 비연초과치 계열을 중심으로 -)

  • 이순혁;박명근
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.28 no.3
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    • pp.69-78
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    • 1986
  • This studies were established to find out the characteristics of frequency distributiom for the number of occurrence and magnitude, probable flood flows according to the return periods, design floods, and design frequency factors for the studying basins in relation to the risk levels which can be correlated with design return period and the life of structure in the non-annual exceedance series. Eight watersheds along Han, Geum, Nak Dong and Seom Jin river basin were selected as studying basins. The results were analyzed and summarized as follows. 1. Poisson distribution and Exponential distribution were tested as a good fitted distributions for the number of occurrence and magnitude for exceedance event, respectively,at selected watersheds along Han, Geum, Nak Dong and Seom Jin river basin. 2.Formulas for the probable flood flows and probable flood flows according to the return periods were derivated for the exponential distribution at the selected watersheds along Han, Geum, Nak Dong, and Seom Jin river basin. 3.Analysis for the risk of failure was connected return period with design life of structure in the non-annual exceedance series. 4.Empirical formulas for the design frequency factors were derivated from under the condition of the return periods identify with the life of structure in relation to the different risk levels in the non-annual exceedance series. 5.Design freguency factors were appeared to be increased in proportion to the return periods while those are in inverse proportion to the levels of the risk of failure. Numerical values for the design frequency factors for the non-annual exceedance series ware appeared generally higher than those of annual maximum series already published by the first report. 6. Design floods according to the different risk levels could be derivated by using of formulas of the design frequency factors for all studying watersheds in the nor-annual exceedance series.

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Rain Cell Size Distribution Using Radar Data During Squall Line Episodes (레이더 자료를 이용한 강우입자분포의 통계적 분석 연구)

  • Ricardo S. Tenorio;Kwon, Byung-Hyuk;Lee, Dong-In
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.4 no.5
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    • pp.971-976
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    • 2000
  • The main objective of this paper is to present the rain cell size distribution observed during squall line episodes in the Sudano-Sahelian region. The used data were collected during the EPSAT Program [Etude des Precipitation par SATellite (Satellites Study of Precipitation)] which has been developed since 1958, on an experimental area located near Niamey, Niger (2 10′32"E, 13 28′38"N). The data were obtained with a C-band radar and a network composed of approximately 100 raingages over a 10,000 $\textrm{km}^2$. In this work a culling of the squall line episodes was made for the 1992 rainy season. After radar data calibration using the raingage network a number of PPI (Plan Position Indicator) images were generated. Each image was then treated in order to obtain a series of radar reflectivity (Z) maps. To describe the cell distribution, a contouring program was used to analyze the areas with rain rate greater than or equal to the contour threshold (R$\geq$$\tau$). 24700 contours were generated, where each iso-pleth belongs to a predefined threshold. Computing each cell surface and relating its area to an equi-circle (a circle having the same area as the cell), a statistical analysis was made. The results show that the number of rain cells having a given size is an inverse exponential function of the equivalent radius. The average and median equivalent radii ate 1.4 and 0.69 In respectively. Implications of these results for the precipitation estimation using threshold methods are discussed.

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Thermoelastic interaction in functionally graded nanobeams subjected to time-dependent heat flux

  • Zenkour, Ashraf M.;Abouelregal, Ahmed E.
    • Steel and Composite Structures
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    • v.18 no.4
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    • pp.909-924
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    • 2015
  • This paper investigates the vibration phenomenon of a nanobeam subjected to a time-dependent heat flux. Material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel exponential distribution law in terms of the volume fractions of the metal and ceramic constituents. The upper surface of the functionally graded (FG) nanobeam is pure ceramic whereas the lower surface is pure metal. A nonlocal generalized thermoelasticity theory with dual-phase-lag (DPL) model is used to solve this problem. The theories of coupled thermoelasticity, generalized thermoelasticity with one relaxation time, and without energy dissipation can extracted as limited and special cases of the present model. An analytical technique based on Laplace transform is used to calculate the variation of deflection and temperature. The inverse of Laplace transforms are computed numerically using Fourier expansion techniques. The effects of the phase-lags (PLs), nonlocal parameter and the angular frequency of oscillation of the heat flux on the lateral vibration, the temperature, and the axial displacement of the nanobeam are studied.

A class of accelerated sequential procedures with applications to estimation problems for some distributions useful in reliability theory

  • Joshi, Neeraj;Bapat, Sudeep R.;Shukla, Ashish Kumar
    • Communications for Statistical Applications and Methods
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    • v.28 no.5
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    • pp.563-582
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    • 2021
  • This paper deals with developing a general class of accelerated sequential procedures and obtaining the associated second-order approximations for the expected sample size and 'regret' (difference between the risks of the proposed accelerated sequential procedure and the optimum fixed sample size procedure) function. We establish that the estimation problems based on various lifetime distributions can be tackled with the help of the proposed class of accelerated sequential procedures. Extensive simulation analysis is presented in support of the accuracy of our proposed methodology using the Pareto distribution and a real data set on carbon fibers is also analyzed to demonstrate the practical utility. We also provide the brief details of some other inferential problems which can be seen as the applications of the proposed class of accelerated sequential procedures.

Thermal effects on nonlinear dynamic characteristics of polymer-CNT-fiber multiscale nanocomposite structures

  • Ebrahimi, Farzad;Habibi, Sajjad
    • Structural Engineering and Mechanics
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    • v.67 no.4
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    • pp.403-415
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    • 2018
  • In the present study, nonlinear dynamic response of polymer-CNT-fiber multiscale nanocomposite plate resting on elastic foundations in thermal environments using the finite element method is performed. In this regard, the governing equations are derived based on Inverse Hyperbolic Shear Deformation Theory and von $K{\acute{a}}rm{\acute{a}}n$ geometrical nonlinearity. Three type of distribution of temperature through the thickness of the plate namely, uniform linear and nonlinear are considered. The considered element is C1-continuous with 15 DOF at each node. The effective material properties of the multiscale composite are calculated using Halpin-Tsai equations and fiber micromechanics in hierarchy. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. Five types of impulsive loads are considered, namely the step, sudden, triangular, half-sine and exponential pulses. After examining the validity of the present work, the effects of the weight percentage of SWCNTs and MWCNTs, nanotube aspect ratio, volume fraction of fibers, plate aspect, temperature, elastic foundation parameters, distribution of temperature and shape of impulsive load on nonlinear dynamic response of CNT reinforced multi-phase laminated composite plate are studied in details.

Ruin Probability on Insurance Risk Models (보험위험 확률모형에서의 파산확률)

  • Park, Hyun-Suk;Choi, Jeong-Kyu
    • The Korean Journal of Applied Statistics
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    • v.24 no.4
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    • pp.575-586
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    • 2011
  • In this paper, we study an asymptotic behavior of the finite-time ruin probability of the compound Poisson model in the case that the initial surplus is large. To compare an exact ruin probability with an approximate one, we place the focus on the exact calculation for the ruin probability when the claim size distribution is regularly varying tailed (i.e. exponential claims and inverse Gaussian claims). We estimate an adjustment coefficient in these examples and show the relationship between the adjustment coefficient and the safety premium. The illustration study shows that as the safety premium increases so does the adjustment coefficient. Larger safety premium means lower "long-term risk", which only stands to reason since higher safety premium means a faster rate of safety premium income to offset claims.

Evaluation of Feed Value of IRG in Middle Region Using UAV

  • Na, Sang-Il;Kim, Young-Jin;Park, Chan-Won;So, Kyu-Ho;Park, Jae-Moon;Lee, Kyung-Do
    • Korean Journal of Soil Science and Fertilizer
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    • v.50 no.5
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    • pp.391-400
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    • 2017
  • Italian ryegrass (IRG) is one of the fastest growing grasses available to farmers. It offers rapid establishment and starts growing early in the following spring and has fast regrowth after defoliation. So, IRG can be utilized as the dominant/single species of grass used in a farming system, or to play a role as a large producing pasture and sacrificial paddock. The objective of this study was to develop the use of unmanned aerial vehicle (UAV) for the evaluation of feed value of IRG. For this study, UAV imagery was taken on the Nonsan regions two times during the IRG growing season. We analyzed the relationships between $NDVI_{UAV}$ and feed value parameters such as fresh matter yield, dry matter yield, acid detergent fiber (ADF), neutral detergent fiber (NDF), total digestible nutrient (TDN) and crude protein at the season of harvest. Correlation analysis between $NDVI_{UAV}$ and feed value parameters of IRG revealed that $NDVI_{UAV}$ correlated well with crude protein (r = 0.745), and fresh matter yield (r = 0.655). According to the relationship, the variation of $NDVI_{UAV}$ was significant to interpret feed value parameters of IRG. Eight different regression models such as Linear, Logarithmic, Inverse, Quadratic, Cubic, Power, S, and Exponential model were used to estimate IRG feed value parameters. The S and exponential model provided more accurate results to predict fresh matter yield and crude protein than other models based on coefficient of determination, p- and F-value. The spatial distribution map of feed values in IRG plot was in strong agreement with the field measurements in terms of geographical variation and relative numerical values when $NDVI_{UAV}$ was applied to regression equation. These lead to the result that the characteristics of variations in feed value of IRG according to $NDVI_{UAV}$ were well reflected in the model.

Spatial-Temporal Interpolation of Rainfall Using Rain Gauge and Radar (강우계와 레이더를 이용한 강우의 시공간적인 활용)

  • Hong, Seung-Jin;Kim, Byung-Sik;Hahm, Chang-Hahk
    • Journal of Korean Society for Geospatial Information Science
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    • v.18 no.3
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    • pp.37-48
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    • 2010
  • The purpose of this paper is to evaluate how the rainfall field effect on a runoff simulation using grid radar rainfall data and ground gauge rainfall. The Gwangdeoksan radar and ground-gauge rainfall data were used to estimate a spatial rainfall field, and a hydrologic model was used to evaluate whether the rainfall fields created by each method reproduced a realistically valid spatial and temporal distribution. Pilot basin in this paper was the Naerin stream located in Inje-gun, Gangwondo, 250m grid scale digital elevation data, land cover maps, and soil maps were used to estimate geological parameters for the hydrologic model. For the rainfall input data, quantitative precipitation estimation(QPE), adjusted radar rainfall, and gauge rainfall was used, and then compared with the observed runoff by inputting it into a $Vflo^{TM}$ model. As a result of the simulation, the quantitative precipitation estimation and the ground rainfall were underestimated when compared to the observed runoff, while the adjusted radar rainfall showed a similar runoff simulation with the actual observed runoff. From these results, we suggested that when weather radars and ground rainfall data are combined, they have a greater hydrological usability as input data for a hydrological model than when just radar rainfall or ground rainfall is used separately.

Evaluation for Rock Cleavage Using Distribution of Microcrack Spacings (IV) (미세균열의 간격 분포를 이용한 결의 평가(IV))

  • Park, Deok-Won
    • The Journal of the Petrological Society of Korea
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    • v.26 no.2
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    • pp.127-141
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    • 2017
  • Jurassic granite from Geochang was analysed with respect to the characteristics of the rock cleavage. The multicriteria evaluation for the six directions of rock cleavages was performed using the microcrack spacing-related parameters derived from the enlarged photomicrographs (${\times}6.7$) of the thin section and the spacing-cumulative frequency diagrams. The results of analysis for the representative values of these spacing parameters with respect to the rock cleavage are summarized as follows. First, the analysis for deriving the main parameter indicating the order of arrangement among six diagrams was performed. The values of five parameters with respect to six directions of the rock cleavages were arranged in increasing or decreasing order for the above analysis. The decreasing order of the values of main parameter(mean spacing-median spacing, $S_{mean}-S_{median}$) and mean spacing are consistent with the order of H1, H2, G1, G2, R1 and R2 directions. These sequential arrangements of six directions of the rock cleavages can provide a basis for those of the six diagrams related to spacing. Second, the nine correlation charts between the above main parameter and various parameters were arranged in decreasing order of correlation coefficient ($R^2$). These related charts shows a high correlation of power-law function in common. The values of mean spacing, density (${\rho}$) and length of line oa are directly proportional to the value of main parameter, while the values of constant (a), exponent (${\lambda}$), spacing frequency (N), length of line oa', slope of exponential straight line (${\theta}$) and total length ($1mm{\geq}$) are inverse proportional. Third, the results of correlation analysis between the values of parameters for three planes and those for three rock cleavages are as follows. The values of frequency, total spacing, constant, exponent, slope and length of line oa' for three planes and three rock cleavages show an order of R' < G' < H' and H < G < R, respectively. On the other hand, the values of mean spacing, (mean spacing-median spacing), density and length of line oa show an order of H' < G' < R' and R < G < H, respectively. The correlation of the mutually reverse order of the values of parameters between three planes and three rock cleavages can be drawn. This type of correlation analysis is useful for discriminating three quarrying planes.