• Title/Summary/Keyword: Non-Normal Distribution

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A Fundamental Study of Probability Functions and Relationship of Wave Heights. -On the Wave Heights of the East Coast of Korea- (파고의 확률분포 및 상관에 관한 기초적 연구 - 동해안의 파고를 중심으로 하여 -)

  • 윤해식;이순탁
    • Water for future
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    • v.7 no.2
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    • pp.99-106
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    • 1974
  • The records of wave heights which were observed at Muk ho and Po hang of the East Coast of Korea were analized by several probility functions. The exponential 2 parameter distribution was found as the best fit probability function to the historical distribution of wave heights by the test of goodness of fit. But log-normal 2 parameter and log-extremal type A distributions were also fit to the historical distribution, especially in the Smirnov-Kolmogorov test. Therefore, it can't be always regarded that those two distributions are not fit to the wave heiht's distribution. In the test of goodness of fit, the Chi-Square test gave very sensitive results and Smirnov-Kolmogorov test, which is a distribution free and non-parametric test, gave more inclusive results. At the next stage, the inter-relationship between the mean and the one-third wave heights, the mean and the one-=tenth wave heights, the one-third and the one-tenth wave heights, the one-third and the highest wave heights were obtained and discussed.

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Study on Within-Wafer Non-uniformity Using Finite Element Method (CMP 공정에서의 웨이퍼 연마 불균일성에 대한 유한요소해석 연구)

  • Yang, Woo Yul;Sung, In-Ha
    • Tribology and Lubricants
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    • v.28 no.6
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    • pp.272-277
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    • 2012
  • Finite element analysis was carried out using wafer-scale and particle-scale models to understand the mechanism of the fast removal rate(edge effect) at wafer edges in the chemical-mechanical polishing process. This is the first to report that a particle-scale model can explain the edge effect well in terms of stress distribution and magnitude. The results also revealed that the mechanism could not be fully understood by using the wafer-scale model, which has been used in many previous studies. The wafer-scale model neither gives the stress magnitude that is sufficient to remove material nor indicates the coincidence between the stress distribution and the removal rate along a wafer surface.

Three-dimensional dynamics of the moving load acting on the interior of the hollow cylinder surrounded by the elastic medium

  • Akbarov, S.D.;Mehdiyev, M.A.;Ozisik, M.
    • Structural Engineering and Mechanics
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    • v.67 no.2
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    • pp.185-206
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    • 2018
  • This paper studies the non-axisymmetric 3D problem on the dynamics of the moving load acting in the interior of the hollow cylinder surrounded with elastic medium and this study is made by utilizing the exact equations of elastodynamics. It is assumed that in the interior of the cylinder the point located with respect to the cylinder axis moving forces act and the distribution of these forces is non-axisymmetric and is located within a certain central angle. The solution to the problem is based on employing the moving coordinate method, on the Fourier transform with respect to the spatial coordinate indicated by the distance of the point on the cylinder axis from the point at which the moving load acts, and on the Fourier series presentation of the Fourier transforms of the sought values. Numerical results on the critical moving velocity and on the distribution of the interface normal and shear stresses are presented and discussed. In particular, it is established that the non-axisymmetricity of the moving load can decrease significantly the values of the critical velocity.

Scanning Electron Microscopic Observation on the Rat Oviductal Epithelium in each Segment during Normal Sexual Cycle (백서난관상피(白鼠卵管上皮)의 주사현미경적(走査電子顯微鏡的) 관찰(觀察))

  • Lee, Jae-Hyun
    • Applied Microscopy
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    • v.10 no.1_2
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    • pp.41-51
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    • 1980
  • Scanning electron microscopic observation of the oviductal epithelium was carried out on the virgin white Wistar rat during normal sexual cycle, and obtained the results as follows; Rat oviductal epithelium during the normal sexual cycle generally consisted of two types of cells: ciliated and non-ciliated cell. The ciliated cells had cilia which was measured $0.2{\mu}$ in width and $3-5{\mu}$ in length. According to the length of microvilli and the distribution in each segment, the non-ciliated cell was further subdivided into four types of cells; NC-I, NC-II, NC-III, and NC-IV. The morphologic characteristics of each type of cells were also ascertained by SEM observations.

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A Comprehensive Measure of Evaluation for Non-Normal Process Capability with Beta Distributions (베타분포를 하는 비정규 공정능력평가의 종합적 측도)

  • 김홍준;김진수;전창희
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.22 no.52
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    • pp.69-79
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    • 1999
  • The main objective of this study are to propose two methods that would be a comprehensive measure of evaluation for non-normal process capability with Beta distributions. First method is introduced using process capability index $C_{psk}$ by the Pearson system and Johnson system. The Pearson system and the Johnson System selected for process capability index calculation have a equivalent result of this study that the ranking of the seven indices in terms of sensitivity to departure of the process median from the target value from the most sensitive one up to the least sensitive are $C^{*}_{pm}$ , $C_{psk}$ , $C_{s}$ , $C_{pmk}$ , $C_{pm}$ , $C_{pk}$ , $C_{p}$ . Second method show using the percentage nonconforming by the Pearson, Johnson and Burr functions. In thus study, we find that the Pearson system and the Burr system are a reasonable method to estimate percentage nonconforming. But, the exact procedure for deriving this estimate will be based on Beta distribution. Accordingly, if a process is not normally distributed , but normal-based techniques are used serious errors can result.

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Cusum Control Chart for Monitoring Process Variance (공정분산 관리를 위한 누적합 관리도)

  • Lee, Yoon-Dong;Kim, Sang-Ik
    • Journal of Korean Society for Quality Management
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    • v.33 no.3
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    • pp.149-155
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    • 2005
  • Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

Statistical Analysis for NDI Results of Aircraft Engine Component for Determining Crack Initiation Period (균열발생시기 결정을 위한 항공기 엔진 구성품의 비파괴검사 결과에 대한 통계적 분석)

  • Choi, Jae-Man;Kwon, Young-Han;Choi, Hwan-Seo;Yang, Seung-Hyo;Woo, Sang-Wook;Cho, Soon-Mi;Lee, Seung-Joo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.33 no.12
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    • pp.1482-1487
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    • 2009
  • In this study statistical analysis was performed for NDI(Non-Destructive Inspection) results of F100 engine front seal support assembly. NDI results can be statistically considered as Quantal Response Data. It is found that the suitable probability distribution to the failure data is normal distribution through MLE(Maximum Likelihood Estimation) of the Quantal Response Data. Moreover, Cumulative Distribution Function, failure rate function and B-Life are calculated on the supposed distribution.

Development of Diagnostic Device for Internal Degradation in Distribution Line Using NDT Mathod (NDT 기법을 이용한 가공배전선로 내부 열화 진단장치 개발)

  • Hyun, Deuk-Chang
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.28 no.8
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    • pp.539-543
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    • 2015
  • At present, the development of a detection device in order to prevent accidents due to wire deterioration in the distribution lines is required. Distribution line is not possible to check the internal state in a normal way because it is covered with the coating. Accordingly, various eddy current techniques that is the non-destructive test (NDT) techniques have been applied to solve this problem. In this paper, we have seen examining the characteristic change of the eddy current sensor according to the simplified shape of the sensor in order to solve the problems for the simplified shape that is generated when the simulation for the shape of the eddy current sensor.

Cusum control chart for monitoring process variance (공정분산 관리를 위한 누적합 관리도)

  • Lee, Yoon-Dong;Kim, Sang-Ik
    • Proceedings of the Korean Society for Quality Management Conference
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    • 2006.04a
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    • pp.135-141
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    • 2006
  • Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

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Probabilistic Simulation for Extraction of Reliability Design Data (설계자료 추출을 위한 확률 시뮬레이션)

  • 김선진
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.29 no.2
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    • pp.152-161
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    • 1993
  • This paper deals with the effect of spatial distribution of material properties on its statistical characteristics and numerical estimation method of reliability of fatigue sensitive structures with respect to the fatigue crack growth. A method is proposed to determine experimentally the probability distribution functions of material parameters of Paris law. da/dN=C(ΔK/K sub(0) ) super(m), using stress intensity factor controlled fatigue tests. The result with a high tensile strength steel shows that the distribution of the parameter m is approximately normal and that of 1/C, is a 3-parameter Weibull. The main result obtained are : (1) The theoretical autocorrelation of the resistance, 1/C, to fatigue crack growth are almost same for different lengths. (2) The variance decreases with the increasing a averaging length. When spatial correlation length is very small. the variane decreases significantly were the averaging length. (3) The probability distribution of load cycles or the number for a crack to reach a certain length can be estimated using these functions by simulation of non-Gaussian(expecially Weibull) Stochastic Process.

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