• Title/Summary/Keyword: Poisson Distribution

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NHPP Software Reliability Model based on Generalized Gamma Distribution (일반화 감마 분포를 이용한 NHPP 소프트웨어 신뢰도 모형에 관한 연구)

  • Kim, Hee-Cheul
    • Journal of the Korea Society of Computer and Information
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    • v.10 no.6 s.38
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    • pp.27-36
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    • 2005
  • Finite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates Per fault. This Paper Proposes reliability model using the generalized gamma distribution, which can capture the monotonic increasing(or monotonic decreasing) nature of the failure occurrence rate per fault. Equations to estimate the parameters of the generalized gamma finite failure NHPP model based on failure data collected in the form of interfailure times are developed. For the sake of proposing shape parameter of the generalized gamma distribution, used to the special pattern. Data set, where the underlying failure process could not be adequately described by the knowing models, which motivated the development of the gamma or Weibull model. Analysis of failure data set for the generalized gamma modell, using arithmetic and Laplace trend tests . goodness-of-fit test, bias tests is presented.

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Microbial Risk Assessment of Non-Enterohemorrhagic Escherichia coli in Natural and Processed Cheeses in Korea

  • Kim, Kyungmi;Lee, Heeyoung;Lee, Soomin;Kim, Sejeong;Lee, Jeeyeon;Ha, Jimyeong;Yoon, Yohan
    • Food Science of Animal Resources
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    • v.37 no.4
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    • pp.579-592
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    • 2017
  • This study assessed the quantitative microbial risk of non-enterohemorrhagic Escherichia coli (EHEC). For hazard identification, hazards of non-EHEC E. coli in natural and processed cheeses were identified by research papers. Regarding exposure assessment, non-EHEC E. coli cell counts in cheese were enumerated, and the developed predictive models were used to describe the fates of non-EHEC E. coli strains in cheese during distribution and storage. In addition, data on the amounts and frequency of cheese consumption were collected from the research report of the Ministry of Food and Drug Safety. For hazard characterization, a doseresponse model for non-EHEC E. coli was used. Using the collected data, simulation models were constructed, using software @RISK to calculate the risk of illness per person per day. Non-EHEC E. coli cells in natural- (n=90) and processed-cheese samples (n=308) from factories and markets were not detected. Thus, we estimated the initial levels of contamination by Uniform distribution ${\times}$ Beta distribution, and the levels were -2.35 and -2.73 Log CFU/g for natural and processed cheese, respectively. The proposed predictive models described properly the fates of non-EHEC E. coli during distribution and storage of cheese. For hazard characterization, we used the Beta-Poisson model (${\alpha}=2.21{\times}10^{-1}$, $N_{50}=6.85{\times}10^7$). The results of risk characterization for non-EHEC E. coli in natural and processed cheese were $1.36{\times}10^{-7}$ and $2.12{\times}10^{-10}$ (the mean probability of illness per person per day), respectively. These results indicate that the risk of non-EHEC E. coli foodborne illness can be considered low in present conditions.

The Comparative Study of Software Optimal Release Time Based on Log-Logistic Distribution (Log-Logistic 분포 모형에 근거한 소프트웨어 최적방출시기에 관한 비교연구)

  • Kim, Hee-Cheul
    • Journal of the Korea Society of Computer and Information
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    • v.13 no.7
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    • pp.1-9
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    • 2008
  • In this paper, make a study decision problem called an optimal release policies after testing a software system in development phase and transfer it to the user. When correcting or modifying the software, because of the possibility of introducing new faults when correcting or modifying the software, infinite failure non-homogeneous Poisson process models presented and propose an optimal release policies of the life distribution applied log-logistic distribution which can capture the increasing! decreasing nature of the failure occurrence rate per fault. In this paper, discuss optimal software release policies which minimize a total average software cost of development and maintenance under the constraint of satisfying a software reliability requirement. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data, make out estimating software optimal release time.

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Various modeling approaches in auto insurance pricing (다양한 모형화를 통한 자동차 보험가격 산출)

  • Kim, Myung-Joon;Kim, Yeong-Hwa
    • Journal of the Korean Data and Information Science Society
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    • v.20 no.3
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    • pp.515-526
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    • 2009
  • Pricing based on proper risk has been one of main issues in auto insurance. In this paper, we review how the techniques of pricing in auto insurance have been developed and suggest a better approach which meets the existing risk statistically by comparison. The generalized linear model (GLM) method is discussed for pricing with different distributions. With GLM approach, the distribution of error assumed plays an main role for the best fit corresponding to the characteristics of dependent variables. Tweedie distribution is considered as one of error distributions in addition to widely used Gamma and Poisson distribution. With these different types of error assumption for estimating the proper premium in auto insurance, various modeling approaches are possible. In this paper, various modeling approaches with different assumptions for estimating proper risk is discussed and also real example is given by assuming different.

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Spatial Distribution Pattern of Ascotis selenaria (Lepidoptera: Geometridae) larvae in a Small-Scale of Citrus Orchard (소규모 감귤원에서 네눈쑥가지나방 유충의 공간분포 특성에 대한 이해)

  • Choi, Kyung San;Kim, Dong-Soon
    • Korean journal of applied entomology
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    • v.52 no.3
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    • pp.243-248
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    • 2013
  • This study was conducted to understand the settlement process of Ascotis selenaria larvae into citrus orchards with respect to oviposition site and analysis of the spatial distribution pattern of the larvae. A. selenaria eggs were not found on citrus trees in field and green house, but not on citrus trees in the field. A. selenaria larvae showed a significant clump distribution in the greenhouse. In the open citrus field, the index of dispersion was around 1.0 in most cases, with a weak clumping degree. However, the d-statistic was between -1.96 and 1.96, indicating a statistically significant random distribution. In addition, the Green's index (a clumping index) was very low in all cases, even though the clump distribution was accepted. for most samples, the probability distribution of larval frequency in the field satisfied the probability distribution functions of Poisson (random pattern) and the negative binomial (clump pattern) distribution. In addition, the temporal distribution of the larvae in the open field showed a pattern which was formed by colonizers from outside oviposition sites. Further, the difference in larval spatial distribution between field and greenhouse orchards was discussed.

Application of Multi-Server Queuing Theory to Estimate Vehicle Travel Times at Freeway Electronic Toll-Collection Systems (고속도로 자동요금징수시스템의 차량 통행시간 산정을 위한 다중서비스 대기행렬이론 연구)

  • Sung, Hyun-Jin;Choi, Jai-Sung;Kim, Sang-Youp
    • The Journal of The Korea Institute of Intelligent Transport Systems
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    • v.10 no.2
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    • pp.22-34
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    • 2011
  • This paper presents the investigation results of a research on how engineers can analyze the economic effect of the ETCS(Electronic Toll Collection System) installed to minimize the vehicle delays on freeway tollgates during toll payments. This research considered this economic effect to occur in the form of vehicle passing time reductions at the ETCS, and the multi-service queuing theory was applied to estimate these values. This research found: 1) When vehicles approaching tollgates show Poisson distribution and the service time of the ETCS shows Exponential distribution, the multi-service queuing theory would be applicable for estimating vehicle passing times at toll-gates, 2) Despite the ETCS placement, exit sections of tollgates give a greater reduction of vehicle passing times than entering sections due to more delays at conventional toll payments, and 3)The ETCS would not guarantee vehicle passing time reductions all the time, because in such a case as many vehicles were queuing at the ETCS, the total delay level for a toll gate would increase greatly. In addition, in order to examine the accuracy of the estimated vehicle passing values, this research compared the values from the multi-service queuing theory with the observed values from a set of field survey values at freeway toll-gates, and found that the two values were in a good agreement with a very low error range of 1-3 seconds per vehicle. Based on this result, the multi-service queuing theory was recommended for practice.

Forensic Decision of Median Filtering by Pixel Value's Gradients of Digital Image (디지털 영상의 픽셀값 경사도에 의한 미디언 필터링 포렌식 판정)

  • RHEE, Kang Hyeon
    • Journal of the Institute of Electronics and Information Engineers
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    • v.52 no.6
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    • pp.79-84
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    • 2015
  • In a distribution of digital image, there is a serious problem that is a distribution of the altered image by a forger. For the problem solution, this paper proposes a median filtering (MF) image forensic decision algorithm using a feature vector according to the pixel value's gradients. In the proposed algorithm, AR (Autoregressive) coefficients are computed from pixel value' gradients of original image then 1th~6th order coefficients to be six feature vector. And the reconstructed image is produced by the solution of Poisson's equation with the gradients. From the difference image between original and its reconstructed image, four feature vector (Average value, Max. value and the coordinate i,j of Max. value) is extracted. Subsequently, Two kinds of the feature vector combined to 10 Dim. feature vector that is used in the learning of a SVM (Support Vector Machine) classification for MF (Median Filtering) detector of the altered image. On the proposed algorithm of the median filtering detection, compare to MFR (Median Filter Residual) scheme that had the same 10 Dim. feature vectors, the performance is excellent at Unaltered, Averaging filtering ($3{\times}3$) and JPEG (QF=90) images, and less at Gaussian filtering ($3{\times}3$) image. However, in the measured performances of all items, AUC (Area Under Curve) by the sensitivity and 1-specificity is approached to 1. Thus, it is confirmed that the grade evaluation of the proposed algorithm is 'Excellent (A)'.

Development of Time-Dependent Reliability-Based Design Method Based on Stochastic Process on Caisson Sliding of Vertical Breakwater (직립방파제의 케이슨 활동에 대한 확률과정에 기반한 시간의존 신뢰성 설계법 개발)

  • Kim, Seung-Woo;Cheon, Sehyeon;Suh, Kyung-Duck
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.24 no.5
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    • pp.305-318
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    • 2012
  • Although the existing performance-based design method for the vertical breakwater evaluates an average sliding distance during an arbitrary time, it does not calculate the probability of the first occurrence of an event exceeding an allowable sliding distance(i.e. the first-passage probability). Designers need information about the probability that the structure is damaged for the first time for not only design but also maintenance and operation of the structure. Therefore, in this study, a time-dependent reliability design method based on a stochastic process is developed to evaluate the first-passage probability of caisson sliding. Caisson sliding can be formulated by the Poisson spike process because both occurrence time and intensity of severe waves causing caisson sliding are random processes. The occurrence rate of severe waves is expressed as a function of the distribution function of sliding distance and mean occurrence rate of severe waves. These values simulated by a performance-based design method are expressed as multivariate regression functions of design variables. As a result, because the distribution function of sliding distance and the mean occurrence rate of severe waves are expressed as functions of significant wave height, caisson width, and water depth, the first-passage probability of caisson sliding can be easily evaluated.

A Study on Calculating Relevant Length of Left Turn Storages Using UAV Spatial Images Considering Arrival Distribution Characteristics at Signalized Intersections in Urban Commercial Areas

  • Yang, Jaeho;Kim, Eungcheol;Na, Young-Woo;Choi, Byoung-Gil
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.36 no.3
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    • pp.153-164
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    • 2018
  • Calculating the relevant length of left turn storages in urban intersections is very crucial in road designs. A left turn lane consists of deceleration lanes and left turn storages. In this study, we developed methods for calculating relevant lengths of left turn storages that vary at each intersection using UAV (Unmanned Aerial Vehicle) spatial images. Problems of conventional design techniques are applying the same number of left turn vehicles (N) using Poisson distribution without considering land use types, using a vehicle length that may not be measurable when applying the length of waiting vehicles (S), and using same storage length coefficient (${\alpha}$), 1.5, for every intersections. In order to solve these problems, we estimated the number of left turn vehicles (N) using an empirical distribution, suggested to use headways of vehicles for (S) to calculate the length of waiting vehicles (S) with a help of using UAV spatial images, and defined ranges of storage length coefficient (${\alpha}$) from 1.0 to 1.5 for flexible design. For more convenient design, it is suitable to classify two cases when possible to know and impossible to know about ratio of large trucks among vehicles when planning an intersection. We developed formula for each case to calculate left turn storage lengths of a minimum and a maximum. By applying developed methods and values, more efficient signalized intersection operation can be accomplished.

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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