• 산업경영시스템학회지
• /
• 제10권16호
• /
• pp.101-106
• /
• 1987

Statistical control charts are useful tools to monitor and control the manufacturing processes and are widely used in most Korean industries. Many Korean companies, however, do not always obtain desired results from the traditional control charts by Shewhart such as the $\bar{X}$-chart, $\bar{X}$-chart, $\bar{X}$-chart, etc. This is partly because the quality charterstics of the process are not distributed normally but are skewed due to the intermittent production, small lot size, etc. In Shewhart $\bar{X}$-chart. which is the most widely used one in Kora, such skewed distributions make the plots to be inclined below or above the central line or outside the control limits although no assignable causes can be found. To overcome such shortcomings in nonnormally distributed processes, a distribution-free type of confidence interval can be used, which should be based on order statistics. This thesis is concerned with the design of control chart based on a sample median which is easy to use in practical situation and therefore properties for nonnormal distributions may be easily analyzed. Control limits and central lines are given for the more famous nonnormal distributions, such as Gamma, Beta, Lognormal, Weibull, Pareto, Truncated-normal distributions. Robustness of the proposed median control chart is compared with that of the $\bar{X}$-chart; the former tends to be superior to the latter as the probability distribution of the process becomes more skewed. The average run length to detect the assignable cause is also compared when the process has a Normal or a Gamma distribution for which the properties of X are easy to verify, the proposed chart is slightly worse than the $\bar{X}$-chart for the normally distributed product but much better for Gamma-distributed products. Average Run Lengths of the other distributions are also computed. To use the proposed control chart, the probability distribution of the process should be known or estimated. If it is not possible, the results of comparison of the robustness force us to use the proposed median control chart based oh a normal distribution. To estimate the distribution of the process, Sturge's formula is used to graph the histogram and the method of probability plotting, $\chi$$^2$-goodness of fit test and Kolmogorov-Smirnov test, are discussed with real case examples. A comparison of the proposed median chart and the $\bar{X}$ chart was also performed with these examples and the median chart turned out to be superior to the $\bar{X}$-chart.

• 한국물환경학회지
• /
• 제39권5호
• /
• pp.396-412
• /
• 2023

Species from the mayfly genus Ephemera (Order Ephemeroptera) was assessed for their physical microhabitat suitability (namely E. strigata, E. separigata, and E. orientalis-sachalinensis). Probability distribution models (Exponential, Normal, Lognormal, Logistic, Weibull, Gamma, Beta, and Gumbel) based on the data collected from 23,957 sampling units of 6,787 sites in Korea from 2010 to 2021 were used. Mode and standard deviation calculated from the best-fitting models to species distribution along a water depth gradient were 265 cm and 159 cm in E. orientalis-sachalinensis; 10 cm and 83 cm in E. strigata; 20 cm and 15 cm in E. separigata, respectively. The current velocity gradient was 22 cm/s and 40 cm/s in E. orientalis-sachalinensis; 60 cm/s and 53 cm/s in E. strigata; 82 cm/s and 25 cm/s in E. separigata, respectively. The mean diameter (phi scale) of substrate grains were -3.6 and 2.2 in E. orientalis-sachalinensis; -7.4 and 1.5 in E. strigata; -5.8 and 0.9 in E. separigata, respectively. Habitat suitability range of E. orientalis-sachalinensis was estimated to be 161~369 cm (water depth), 5~44 cm/s (current velocity), -5.2~-2.0 (mean diameter); 3~34 cm (water depth), 36~94 cm/s (current velocity), -8.1~-6.3 (mean diameter) for E. strigata; 12~32 cm (water depth), 63~96 cm/s (current velocity), -6.3~-5.2 (mean diameter) for E. separigata. In relative comparison, E. orientalis-sachalinensis was estimated to be rheophobic, eurybathophilic, and eurypsephophilic; E. strigata to be euryrheophilic, bathophobic, and lithophilic; E. separigata to be stenomesorheophilic, stenobathophobic, stenolithophilic.

• Fisheries and Aquatic Sciences
• /
• 제25권5호
• /
• pp.287-297
• /
• 2022

The objective of this study was to evaluate the probability of norovirus foodborne illness by raw oyster consumption. One hundred fifty-six oyster samples were collected to examine the norovirus prevalence. The oyster samples were inoculated with murine norovirus and stored at 4℃-25℃. A plaque assay determined norovirus titers. The norovirus titers were fitted with the Baranyi model to calculate shoulder period (h) and death rate (Log PFU/g/h). These kinetic parameters were fitted to a polynomial model as a function of temperature. Distribution temperature and time were surveyed, and consumption data were surveyed. A dose-response model was also searched through literature. The simulation model was prepared with these data in @RISK to estimate the probability of norovirus foodborne. One sample of 156 samples was norovirus positive. Thus, the initial contamination level was estimated by the Beta distribution (2, 156), and the level was -5.3 Log PFU/g. The developed predictive models showed that the norovirus titers decreased in oysters under the storage conditions simulated with the Uniform distribution (0.325, 1.643) for time and the Pert distribution (10, 18, 25) for temperature. Consumption ratio of raw oyster was 0.98%, and average consumption amount was 1.82 g, calculated by the Pert distribution [Pert {1.8200, 1.8200, 335.30, Truncate (0, 236.8)}]. ₁F₁ hypergeometric dose-response model [1 - (1 + 2.55 × 10^-3 × dose)^-0.086] was appropriate to evaluate dose-response. The simulation showed that the probability of norovirus foodborne illness by raw oyster consumption was 5.90 × 10^-10 per person per day. The annual socioeconomic cost of consuming raw oysters contaminated with norovirus was not very high.

• 대한수학회보
• /
• 제33권1호
• /
• pp.119-126
• /
• 1996

In this paper we study the asymptotic behavior of the edge independence number of a random (n,n)-tree. The tools we use include the matrix-tree theorem, the probabilistic method and Hall's theorem. We begin with some definitions. An (n,n)_tree T is a connected, acyclic, bipartite graph with n light and n dark vertices (see [Pa92]). A subset M of edges of a graph is called independent(or matching) if no two edges of M are adfacent. A subset S of vertices of a graph is called independent if no two vertices of S are adjacent. The edge independence number of a graph T is the number $\beta_1(T)$ of edges in any largest independent subset of edges of T. Let $\Gamma(n,n)$ denote the set of all (n,n)-tree with n light vertices labeled 1, $\ldots$, n and n dark vertices labeled 1, $\ldots$, n. We give $\Gamma(n,n)$ the uniform probability distribution. Our aim in this paper is to find bounds on $\beta_1$(T) for a random (n,n)-tree T is $\Gamma(n,n)$.

• 한국원자력학회:학술대회논문집
• /
• 한국원자력학회 1997년도 춘계학술발표회논문집(2)
• /
• pp.445-450
• /
• 1997

Self-Powered Neutron Detectors(SPNDs) are currently used to estimate the power generation distribution and fuel burn-up in several nuclear power reactors in Korea. In this paper, Monte Carlo simulation is accomplished to calculate the escape probability of beta particle as a function of their birth position fur the typical geometry of rhodium-based SPNDs. Also, a simple numerical method calculates the initial generation rate of beta particles and the change of generation rate due to rhodium burn-up. Using the simulation and the numerical method, the burn-up profile of rhodium density and the neutron sensitivity are calculated as a function of burn-up time in the reactor. The sensitivity of the SPNDs decreases non-linearly due to the high absorption cross-section and the non-uniform burn-up of rhodium in the emitter rod. In addition, for improvement of some properties of rhodium-based SPNDs which are currently used, this paper presents a new material. The method used here can be applied to the analysis of other types of SPNDs and will be useful in the optimum design of new SPNDs for long term usage.

• 물과 미래
• /
• 제14권4호
• /
• pp.53-72
• /
• 1981

본 연구는 우리나라의 강수빈도 및 강우강도의 시간적. 공간적 분포분석에 관한 것으로 전국을 5개의 권역으로 나누어 분석을 실시하였다. 강수빈도 해석은 39개 지점을 대상지점으로, 강우강도 해석은 36개 지점을 대상지점으로 하여 강수빈도 분포도의 작성과 강수빈도 분포의 시간적, 공간적인 해석 고찰, 각 지점 및 권역별 확률 강우량과 강우 강도식 및 각 강우기간별 회귀직선식을 유도, 제시하였다. 본 연구의 결과는 다음과 같다. (1) 각 권역내의 최다발생빈도 강수량 계급은 여름철을 제외한 모든 기간이 공히 1) 1~5mm, 2) 0.1~1.0mm, 3) 5~10mm 순이었다. (2) 강수량 계급에 따른 최다발생빈도 권역은 연간 20mm 이하의 강수빈도는 II 권역, 30~40mm의 강수빈도는 IV권역, 70mm 이상의 강수빈도는 I권역이었다. (3) 우리나라 전역에 있어서 강수량의 생기확률은 지수함수의 식으로 대표할 수 있음을 알았다.($W(x)=e^{\alpha+\beta}$) (4) 전국의 5개 권역 중 I권역은 자시간 지속, III권역은 단전간 지속 집중 호우지역으로 판단되었다. (5) 강우형태는 10분~40분, 40분~4시간, 4시간~24시간으로 크게 나눌 수 있었으며, 이들 구간에 대해 지점별 확률 강우 강도식을 유도하였다. (6) 각 권역별로 25시간과 10분~18시간 지속시간과의 강우량 상관식을 유도, 도시하였다. (7) 36개 지점에 대한 확률 강우량을 제시하였다.

• 한국항해항만학회지
• /
• 제37권5호
• /
• pp.453-461
• /
• 2013

본 논문에서는 소형 해상 부유체의 위기 평가를 위한 확률기반 위기평가기법(PET)에서 표본 데이터에 최적인 누적분포함수(CDF) 추정에 관한 평가절차와 실험결과를 기술하였다. CDF는 PET에서 부유체의 위기수준을 평가하기 위한 위기허용기준의 참조 값을 제공하기 위한 것으로, 부유체 모델의 롤(Roll), 피치(pitch), 히브(Heave) 등의 운동응답함수에 대한 표본 데이터에서 추정할 수 있다. 본 연구에서는 여덟가지 정형화된 분포함수와 최대우도추정기법을 적용하여 표본 데이터에 대해서 최대우도를 갖는 CDF들을 평가하였다. 분포함수들의 적합도 검정 실험을 통해서, 베타 분포가 롤과 피치 표본 데이터에 대해서 평균 확률오차 $\bar{\delta}(0{\leq}\bar{\delta}{\leq}1.0)$가 가장 작은 0.024와 0.022로 최적임을 나타냈고, 히브 표본 데이터에 대해서는 감마 분포가 $\bar{\delta}$가 가장 작은 0.027로 최적임을 나타냈다. 본 연구에서 제안한 방법은 표본 데이터의 최적분포 추정을 위한 다양한 분야에 적용 가능할 것으로 기대된다.

• Fisheries and Aquatic Sciences
• /
• 제24권6호
• /
• pp.207-218
• /
• 2021

This study evaluated the risk of foodborne illness from highly pathogenic Vibrio spp. (Vibrio vulnificus and V. cholerae) by raw whip-arm octopus (Octopus minor) consumption. In total 180 samples of raw whip-arm octopus were collected from markets and examined for the prevalence of V. vulnificus and V. cholerae. Predictive models describing the kinetic behavior of Vibrio spp. in raw whip-arm octopus were developed, and the data on amounts and frequency of raw whip-arm octopus consumption were collected. Using the collected data, a risk assessment simulation was conducted to estimate the probability of foodborne illness raw whip-arm octopus consumption using @RISK. Initial contamination levels of Vibrio spp. in raw whip-arm octopus were -3.9 Log colony-forming unit/g, as estimated by beta distribution fitting. The developed predictive models were appropriate to describe Vibrio spp. in raw whip-arm octopus during distribution and storage with R² values of 0.946-0.964. The consumption frequency and daily consumption amounts of raw whip-arm octopus per person were 0.47% and 57.65 g, respectively. The probability of foodborne illness from raw whip-arm octopus consumption was estimated to be 8.71 × 10^-15 for V. vulnificus and 7.08 × 10^-13 for V. cholerae. These results suggest that the risk of Vibrio spp. infection from raw whip-arm octopus consumption is low in South Korea.

• 한국물환경학회지
• /
• 제39권6호
• /
• pp.475-490
• /
• 2023

Chemical water quality suitability for species (Ephemera strigata, Ephemera separigata, and Ephemera orientalis-sachalinensis group) of the mayfly genus Ephemera (Order Ephemeroptera) was analyzed with probability distribution models (Exponential, Normal, Lognormal, Logistic, Weibull, Gamma, Beta, Gumbel). Data was collected from 23,957 sampling units of 6,664 sites in Korea from 2010 to 2021. E. orientalis-sachalinensis occurred at the range of BOD₅ 0.3~11.1 mg/L (the best-fit Lognormal model); T-P 0.007~0.769 mg/L (the Gumbel model); TSS 0.4~142.2 mg/L (the Lognormal model). E. strigata occurred at the range of BOD₅ 0.4~7.4 mg/L (the Gumbel model); T-P 0.007~0.254 mg/L (the Lognormal model); TSS 0.4~17.1 mg/L (the Lognormal model). E. separigata occurred at the range of BOD₅ 0.4~2.6 mg/L (the R-Weibull model); T-P 0.007~0.134 mg/L (the Lognormal model); TSS 0.7~10.0 mg/L (the Lognormal model). Habitat suitability range of E. orientalis-sachalinensis was estimated to be 0.4~1.9 mg/L (BOD₅), 0.024~0.086 mg/L (T-P), 2.5~22.4 mg/L (TSS); that of E. strigata was 0.4~0.7 mg/L (BOD₅), 0.007~0.018 mg/L (T-P), 0.0~1.7 mg/L (TSS); that of E. separigata was 0.0~0.4 mg/L (BOD₅), 0.000~0.015 mg/L (T-P), 0.5~3.1 mg/L (TSS). In a relative comparision, E. orientalis-sachalinensis was estimated to be eurysaprobic, and narrowly adapted in high levels of T-P and TSS, E. strigata was estimated to be oligosaprobic and adapted in low levels of T-P and TSS, and E. separigata was estimated to be stenooligosaprobic and widely adapted in low level of T-P and TSS.

• 한국식품위생안전성학회지
• /
• 제35권1호
• /
• pp.37-44
• /
• 2020

패류 중 소비량이 높은 굴에서의 고병원성 Vibrio균(V. vulnificus와 V. cholerae)의 식중독 발생 가능성을 분석하기 위하여 위해평가를 실시하였다. 남해권역, 서해권역, 수도권에서 유통되고 있는 굴 88개를 채취하여 V. vulnificus와 V. cholerae의 오염실태를 조사하고, 생굴에서의 V. vulnificus와 V. cholerae의 생장 경향을 관찰하였다. 2017년의 국민건강영양조사 데이터를 활용하여 생굴의 섭취자 비율 및 섭취량을 조사하였으며, 생굴 섭취로 인한 V. vulnificus와 V. cholerae의 식중독 발생 가능성을 분석하기 위해 @RISK를 통해 위해평가를 실시하였다. 88개의 생굴에서 V. vulnificus와 V. cholerae는 검출되지 않아 Beta distribution과 자연로그를 이용한 식을 통해 초기오염수준을 추정하였다. 그 결과 두 세균 모두 -3.6 Log CFU/g으로 생굴에 오염되어 있는 것으로 추정되었다. 생굴에 bioaccumulation된 V. vulnificus와 V. cholerae는 생장하지 않고 초기 접종 수준을 유지하는 것으로 확인되었다. 생굴을 섭취했다고 응답한 사람은 7,167명 중 25명이었으며, 따라서 섭취자 비율은 0.35%로 나타났다. 섭취량에 대한 최적확률분포는 exponential distribution으로 나타났으며 생굴의 평균 섭취량은 66.8 g으로 확인되었다. V. vulnificus와 V. cholerae의 용량-반응 모델은 Beta-Poisson model을 사용하였다. 이상의 데이터를 이용하여 위해평가 시뮬레이션을 개발하고 분석하였다. 초기오염수준으로 오염된 생굴을 바로 섭취함으로써 발생할 수 있는 식중독발생 가능성은 V. vulnificus의 경우 평균 9.08×10^-15, V. cholerae는 8.16×10^-13이며, 섭취자 비율이 식중독 발생 가능성에 가장 큰 영향을 미치는 것으로 확인되었다.