• Title/Summary/Keyword: Normal Distribution

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Variable Sampling Interval Control Charts for Number of Defectives

  • Cho, Gyo-Young;Ahn, Young-Seon;Kim, Youn-Jin
    • Journal of Korean Society for Quality Management
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    • v.25 no.3
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    • pp.62-73
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    • 1997
  • Previous VSI control chart works have been done on quality variable whose distribution is normal. But there are many situations in which hte assumption of not a, pp.opriate. Also, in many industrial processes, the interest is to monitor the number of defectives. In this paper, we will take the existing properties of VSI control chart developed for the normal distribution and a, pp.y them to the np-chart based on the discrete binomial distribution. We will consider the CUSUM chart for the number of defectives. Here, the interesting object is to compute the VSI ATS for CUSUM control chart using Markov chain a, pp.oach and to compare FSI ATS and VSI ATS.

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Bootstrap Confidence Intervals of the Process Capability Index Based on the EDF Expected Loss (EDF 기대손실에 기초한 공정능력지수의 붓스트랩 신뢰구간)

  • 임태진;송현석
    • Journal of Korean Society for Quality Management
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    • v.31 no.4
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    • pp.164-175
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    • 2003
  • This paper investigates bootstrap confidence intervals of the process capability index(PCI) based on the expected loss derived from the empirical distribution function(EDF). The PCI based on the expected loss is too complex to derive its confidence interval analytically, so the bootstrap method is a good alternative. We propose three types of the bootstrap confidence interval; the standard bootstrap(SB), the percentile bootstrap(PB), and the acceleration biased­corrected percentile bootstrap(ABC). We also perform a comprehensive simulation study under various process distributions, in order to compare the accuracy of the coverage probability of the bootstrap confidence intervals. In most cases, the coverage probabilities of the bootstrap confidence intervals from the EDF PCI turned out to be more accurate than those from the PCI based on the normal distribution. It is expected that the bootstrap confidence intervals from the EDF PCI can be utilized in real processes where the true distribution family may not be known.

The Limit Distribution of an Invariant Test Statistic for Multivariate Normality

  • Kim Namhyun
    • Communications for Statistical Applications and Methods
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    • v.12 no.1
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    • pp.71-86
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    • 2005
  • Testing for normality has always been an important part of statistical methodology. In this paper a test statistic for multivariate normality is proposed. The underlying idea is to investigate all the possible linear combinations that reduce to the standard normal distribution under the null hypothesis and compare the order statistics of them with the theoretical normal quantiles. The suggested statistic is invariant with respect to nonsingular matrix multiplication and vector addition. We show that the limit distribution of an approximation to the suggested statistic is representable as the supremum over an index set of the integral of a suitable Gaussian process.

Evaluation of Fatigue Life Characteristic of a Real Waterwork Pipe Using the Probability Density Function (확률밀도함수를 이용한 상수도 실 배관의 피로수명 특성 평가)

  • Choi, Jung-Hun;Koo, Jae-Mean;Seok, Chang-Sung;Song, Weon-Keyu
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.32 no.9
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    • pp.707-712
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    • 2008
  • The fatigue characteristics of a material or a structure are generally derived from fatigue tests of standard specimens. However, test results of standard specimens are different from those of real structures or components. Therefore, to calculate more accurate fatigue life, the geometrical effect and surface condition must be considered by comparing test results of standard specimens with those of real structures or components. Thus the object of this paper is to evaluate the fatigue characteristics of a real waterwork pipe. Also, to evaluate fatigue characteristic based on life distribution, the statistical fatigue characteristics were analyzed by the normal distribution and related data of P-S-N curve.

The Defensive Effect of Samooltang on Injury of Gastric Mucous Membrane of Mouse by Ethanol (알코올로 유발된 생쥐의 위점막손상에 대한 사물탕의 보호효과)

  • Lee Seong-Hwan;Lim Seong-Woo
    • The Journal of Korean Medicine
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    • v.25 no.3
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    • pp.1-11
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    • 2004
  • Objectives : This study was carried out to investigate the effect of Samooltang (SMT) on the injury of gastric mucous membrane by ethanol in mice. Methods : The normal group was mice with no inflammation. The control group was mice with gastro-inflammation elicited by ethanol. The sample group was SMT-administered mice before gastro-inflammation elicitation. Results : In the immunohistochemical change, the distribution of SBA and COX-1 treated with SMT noticeably increased over the control group (p<0.05). The distribution of NF-κB P50, COX-2, and TUNEL treated with SMT noticeably decreased over the control group (p<0.05). The distribution of SMT was the same as the normal group. Conclusions : According to the above results, it is supposed that SMT would be helpful against gastritis and gastric ulcer caused by alcoholic drinks.

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Adaptive Iterative Depeckling of SAR Imagery

  • Lee, Sang-Hoon
    • Korean Journal of Remote Sensing
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    • v.23 no.5
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    • pp.455-464
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    • 2007
  • Lee(2007) suggested the Point-Jacobian iteration MAP estimation(PJIMAP) for noise removal of the images that are corrupted by multiplicative speckle noise. It is to find a MAP estimation of noisy-free imagery based on a Bayesian model using the lognormal distribution for image intensity and an MRF for image texture. When the image intensity is logarithmically transformed, the speckle noise is approximately Gaussian additive noise, and it tends to a normal probability much faster than the intensity distribution. The MRF is incorporated into digital image analysis by viewing pixel types as states of molecules in a lattice-like physical system. In this study, the MAP estimation is computed by the Point-Jacobian iteration using adaptive parameters. At each iteration, the parameters related to the Bayesian model are adaptively estimated using the updated information. The results of the proposed scheme were compared to them of PJIMAP with SAR simulation data generated by the Monte Carlo method. The experiments demonstrated an improvement in relaxing speckle noise and estimating noise-free intensity by using the adaptive parameters for the Ponit-Jacobian iteration.

Effect of Flow Inlet or Outlet Direction on Air-Water Two-Phase Distribution in a Parallel Flow Heat Exchanger Header

  • Kim, Nae-Hyun;Kim, Do-Young;Cho, Jin-Pyo;Kim, Jung-Oh;Park, Tae-Kyun
    • International Journal of Air-Conditioning and Refrigeration
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    • v.16 no.2
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    • pp.37-43
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    • 2008
  • The air and water flow distributions are experimentally studied for a round header - ten flat tube configuration. Three different inlet orientation modes (parallel, normal, vertical) were investigated. Tests were conducted with downward flow configuration for the mass flux from 70 to $130kg/m^2s$, quality from 0.2 to 0.6, non-dimensional protrusion depth (h/D) from 0,0 to 0.5. It is shown that, for almost all the test conditions, vertical inlet yielded the best flow distribution, followed by normal and parallel inlet. Possible explanation is provided using flow visualization results.

The skew-t censored regression model: parameter estimation via an EM-type algorithm

  • Lachos, Victor H.;Bazan, Jorge L.;Castro, Luis M.;Park, Jiwon
    • Communications for Statistical Applications and Methods
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    • v.29 no.3
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    • pp.333-351
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    • 2022
  • The skew-t distribution is an attractive family of asymmetrical heavy-tailed densities that includes the normal, skew-normal and Student's-t distributions as special cases. In this work, we propose an EM-type algorithm for computing the maximum likelihood estimates for skew-t linear regression models with censored response. In contrast with previous proposals, this algorithm uses analytical expressions at the E-step, as opposed to Monte Carlo simulations. These expressions rely on formulas for the mean and variance of a truncated skew-t distribution, and can be computed using the R library MomTrunc. The standard errors, the prediction of unobserved values of the response and the log-likelihood function are obtained as a by-product. The proposed methodology is illustrated through the analyses of simulated and a real data application on Letter-Name Fluency test in Peruvian students.

Uncertainty Assessment of Emission Factors for Pinus densiflora using Monte Carlo Simulation Technique (몬테 카를로 시뮬레이션을 이용한 소나무 탄소배출계수의 불확도 평가)

  • Pyo, Jung Kee;Son, Yeong Mo;Jang, Gwang Min;Lee, Young Jin
    • Journal of Korean Society of Forest Science
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    • v.102 no.4
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    • pp.477-483
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    • 2013
  • The purpose of this study was to calculate uncertainty of emission factor collected data and to evaluate the applicability of Monte Carlo simulation technique. To estimate the distribution of emission factors (Such as Basic wood density, Biomass expansion factor, and Root-to-shoot ratio), four probability density functions (Normal, Lognormal, Gamma, and Weibull) were used. The two sample Kolmogorov-Smirnov test and cumulative density figure were used to compare the optimal probability density function. It was observed that the basic wood density showed the gamma distribution, the biomass expansion factor results the log-normal distribution, and root-shoot ratio showd the normal distribution for Pinus densiflora in the Gangwon region; the basic wood density was the normal distribution, the biomass expansion factor was the gamma distribution, and root-shoot ratio was the gamma distribution for Pinus densiflora in the central region, respectively. The uncertainty assessment of emission factor were upper 62.1%, lower -52.6% for Pinus densiflora in the Gangwon region and upper 43.9%, lower -34.5% for Pinus densiflora in the central region, respectively.

Analysis of Soil Erosion Hazard Zone by R Factor Frequency (빈도별 R인자에 의한 토양침식 위험지역 분석)

  • Kim, Joo-Hun;Oh, Deuk-Keun
    • Journal of the Korean Association of Geographic Information Studies
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    • v.7 no.2
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    • pp.47-56
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    • 2004
  • The purpose of this study is to estimate soil loss amount according to the rainfall-runoff erosivity factor frequency and to analyze the hazard zone that has high possibilities of soil erosion in the watershed. RUSLE was used to analyze soil loss quantity. The study area is Gwanchon that is part of Seomjin river basin. To obtain the frequency rainfall-runoff erosivity factor, the daily maximum rainfall data for 39 years was used. The probability rainfall was calculated by using the Normal distribution, Log-normal distribution, Pearson type III distribution, Log-Pearson type III distribution and Extreme-I distribution. Log-Pearson type III was considered to be the most accurate of all, and used to estimate 24 hours probabilistic rainfall, and the rainfall-runoff erosivity factor by frequency was estimated by adapting the Huff distribution ratio. As a result of estimating soil erosion quantity, the average soil quantity shows 12.8 and $68.0ton/ha{\cdot}yr$, respectively from 2 years to 200 years frequency. The distribution of soil loss quantity within a watershed was classified into 4 classes, and the hazard zone that has high possibilities of soil erosion was analyzed on the basis of these 4 classes. The hazard zone represents class IV. The land use area of class IV shows $0.01-5.28km^2$, it ranges 0.02-9.06% of total farming area. Especially, in the case of a frequency of 200 years, the field area occupies 77.1% of total fanning area. Accordingly, it is considered that soil loss can be influenced by land cover and cultivation practices.

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