• Title/Summary/Keyword: Pert distribution

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Theoretical Basis of PERT Formula and a New Estimation Method (PERT 공식의 이론적 근거와 새로운 추정방법)

  • Kim, Se-Hun;Won, Y.K.;Chae, Kyung-C.
    • Journal of Korean Institute of Industrial Engineers
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    • v.15 no.2
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    • pp.103-108
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    • 1989
  • PERT formulae for the mean and variance of activity time are near exact only over a short interval of the concentration parameter which is defined as the sum of the two shape parameters of the beta distribution. Aiming a better estimation of the mean and variance of activity time, we propose a method of subjectively estimating this concentration parameter via estimating the probability of completing the activity within a specified time interval.

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Probabilistic Evaluation of the Panel Life Time Using Steel Beam for Panel Mining in Soft Rock (연약암반내 패널채광시 강지보를 이용한 패널 유지기간의 확률론적 평가)

  • Jang, Myoung-Hwan
    • Tunnel and Underground Space
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    • v.28 no.4
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    • pp.325-342
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    • 2018
  • The ${\bigcirc}{\bigcirc}$ mines have been tried in various ways to perform secondary and tertiary mining in fragile rock properties. For such mining, the panels should be maintained while the mining compartments are divided and paneled. In this study, the mining gate between the panels was maintained by a steel beam and the panel life time was probabilistic evaluated. We used Taylor's formula for panel life time and modified the Pert distribution conceptually. The main input data were determined by the Pert distribution, and Monte Carlo simulation was performed to evaluate the panel life time for the probability distribution. As a result, it was analyzed that the panels could be stand-up time from a minimum of 6.5 days to a maximum of 20.6 days when the panel width was 18 to 25 m. At the confidence level of 90%, the panel life time was analyzed as 8.2-15.6 days. The short panel life time is not possible with the panel mining. Therefore, it was planned to construct a steel beam for panel maintenance. As result, it was analyzed that steel beam for panel maintenance with mining plan of less than 3 years according to mine could maintain panel within 90% confidence level.

Stochastic Project Scheduling Simulation System (SPSS III)

  • Lee Dong-Eun
    • Korean Journal of Construction Engineering and Management
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    • v.6 no.1 s.23
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    • pp.73-79
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    • 2005
  • This paper, introduces a Stochastic Project Scheduling Simulation system (SPSS III) developed by the author to predict a project completion probability in a certain time. The system integrates deterministic CPM, probabilistic PERT, and stochastic Discrete Event Simulation (DES) scheduling methods into one system. It implements automated statistical analysis methods for computing the minimum number of simulation runs, the significance of the difference between independent simulations, and the confidence interval for the mean project duration as well as sensitivity analysis method in What-if analyzer component. The SPSS 111 gives the several benefits to researchers in that it (1) complements PERT and Monte Carlo simulation by using stochastic activity durations via a web based JAVA simulation over the Internet, (2) provides a way to model a project network having different probability distribution functions, (3) implements statistical analyses method which enable to produce a reliable prediction of the probability of completing a project in a specified time, and (4) allows researchers to compare the outcome of CPM, PERT and DES under different variability or skewness in the activity duration data.

STOCHASTIC ACTIVITY NETWORKS WITH TRUNCATED EXPONENTIAL ACTIVITY TIMES

  • ABDELKADER YOUSRY H.
    • Journal of applied mathematics & informatics
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    • v.20 no.1_2
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    • pp.119-132
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    • 2006
  • This paper presents an approach for using right-truncated exponentially distributed random variables to model activity times in stochastic activity networks. The advantages of using the right-truncated exponential distribution are discussed. The moments of a project completion time using the proposed distribution are derived and compared with other estimated moments in literature.

A study on the behavioral-structure of production activity through the statistical analysis models - focus on the probability distribution of PERT, Queueing theory - (통계적(統計的) 계량분석(計量分析)모델을 통한 생산활동(活動)의 행태구조(行態構造)에 관한 연구 -RERT와 Queueing theory의 확률분포를 중심으로-)

  • Kim, Hong Jae
    • Journal of Korean Society for Quality Management
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    • v.19 no.2
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    • pp.145-157
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    • 1991
  • Thid study intends to pursue behavioral-structure of production behavior through statistical models which are using in PERT and Queueing theory. We can corprehand the orders of human production behavior's characteristics by several related attributes of probablity/statistics. These attributes are poisson, Beta, exponential distributions and P.S Laplace's natural probability. Human production behavior is related and regressed to these attributes in many divisions intermediately. Progressive numerical understanding in many essential human behavior acts on the application of practical behavior standard in production word and operation.

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Risk assessment for norovirus foodborne illness by raw oyster (Ostreidae) consumption and economic burden in Korea

  • Yoo, Yoonjeong;Oh, Hyemin;Lee, Yewon;Sung, Miseon;Hwang, Jeongeun;Zhao, Ziwei;Park, Sunho;Choi, Changsun;Yoon, Yohan
    • Fisheries and Aquatic Sciences
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    • v.25 no.5
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    • pp.287-297
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    • 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.

Investigations on Partial Discharge, Dielectric and Thermal Characteristics of Nano SiO2 Modified Sunflower Oil for Power Transformer Applications

  • Nagendran, S.;Chandrasekar, S.
    • Journal of Electrical Engineering and Technology
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    • v.13 no.3
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    • pp.1337-1345
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    • 2018
  • The reliability of power transmission and distribution depends up on the consistency of insulation in the high voltage power transformer. In recent times, considering the drawbacks of conventional mineral oils such as poor biodegradability and poor fire safety level, several research works are being carried out on natural ester based nanofluids. Earlier research works show that sunflower oil has similar dielectric characteristics compared with mineral oil. BIOTEMP oil which is now commercially available in the market for transformers is based on sunflower oil. Addition of nanofillers in the base oil improves the dielectric characteristics of liquid insulation. Only few results are available in the literature about the insulation characteristics of nano modified natural esters. Hence understanding the influence of addition of nanofillers in the dielectric properties of sunflower oil and collecting the database is important. Considering these facts, present work contributes to investigate the important characteristics such as partial discharge, lightning impulse, breakdown strength, tandelta, volume resistivity, viscosity and thermal characteristics of $SiO_2$ nano modified sunflower oil with different wt% concentration of nano filler material varied from 0.01wt% to 0.1wt%. From the obtained results, nano modified sunflower oil shows better performance than virgin sunflower oil and hence it may be a suitable candidate for power transformer applications.

Applying Monte Carlo Simulation for Supporting Decision Makings in Software Projects (소프트웨어 프로젝트 의사결정 지원을 위한 몬테카를로 시뮬레이션의 활용)

  • Han, Hyuk-Soo;Kim, Cho-Yi
    • Journal of Information Technology Services
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    • v.9 no.4
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    • pp.123-133
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    • 2010
  • There are many occasions on which the critical decisions should be made in software projects. Those decisions are basically related to estimating and predicting project parameters such as costs, efforts, and duration. The project managers are looking for methods to make better decisions. The decisions about project parameters are recommended to be performed based on historical data of Similar projects. The measures of the tasks in past projects may have different shapes of distributions. we need to add those measures to get a predicted project measures. To add measures with different shapes of distribution, we need to use Monte Carlo Simulation. In this paper, we suggest applying Monte Carlo Simulation for supporting decision makings in software project. We implemented best-fit case and scheduling estimations with Cristal Ball, a commercial product of Monte Carlo simulation and showed how the suggested approach supports those critical decision makings.

Probability Distribution of Project Completion Times in Simulation based Scheduling (시뮬레이션 일정기법;최종공사기간의 확률 통계적 특성 추정)

  • Lee, Dong-Eun;Kim, Ryul-Hee
    • Proceedings of the Korean Institute Of Construction Engineering and Management
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    • 2007.11a
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    • pp.327-330
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    • 2007
  • This paper verifies that the normality assumption that the simulation output data, Project Completion Times (PCTs), follow normal distribution is not always acceptable and the existing belief may lead to misleading results. A risk quantification method, which measures the effect caused by the assumption, relative to the probability distribution of PCTs is implemented as an algorithm in MATLAB. To validate the reliability of the quantification, several series of simulation experiments have been carried out to analyze a set of simulation output data which are obtained from different type of Probability Distribution Function (PDF) assigned to activities'duration in a network. The method facilitates to find the effect of PDF type and its parameters. The procedure necessary for performing the risk quantification method is described in detail along with the findings. This paper contributes to improving the reliability of simulation based scheduling method, as well as increasing the accuracy of analysis results.

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Quantitative microbial risk assessment indicates very low risk for Vibrio parahaemolyticus foodborne illness from Jeotgal in South Korea

  • Choi, Yukyung;Kang, Joohyun;Lee, Yewon;Seo, Yeongeun;Kim, Sejeong;Ha, Jimyeong;Oh, Hyemin;Kim, Yujin;Park, Eunyoung;Lee, Heeyoung;Lee, Soomin;Rhee, Min Suk;Yoon, Yohan
    • Fisheries and Aquatic Sciences
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    • v.25 no.9
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    • pp.463-472
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    • 2022
  • In this study, a microbial risk assessment was performed for the bacteria Vibrio parahaemolyticus, which causes a foodborne illness following the consumption of Jeotgal, a fermented seafood in South Korea. The assessment comprised of six stages: product, market, home, consumption, dose-response, and risk. The initial contamination level (IC) was calculated based on the prevalence of V. parahaemolyticus in 90 Jeotgal samples. The kinetic behavior of V. parahaemolyticus was described using predictive models. The data on transportation conditions from manufacturer to market and home were collected through personal communication and from previous studies. Data for the Jeotgal consumption status were obtained, and an appropriate probability distribution was established. The simulation models responding to the scenario were analyzed using the @RISK program. The IC of V. parahaemolyticus was estimated using beta distribution [Beta (1, 91)]. The cell counts during transportation were estimated using Weibull and polynomial models [δ = 1 / (0.0718 - 0.0097 × T + 0.0005 × T2)], while the probability distributions for time and temperature were estimated using Pert, Weibull, Uniform, and LogLogistic distributions. Daily average consumption amounts were assessed using the Pareto distribution [0.60284,1.32,Risk Truncate(0,155)]. The results indicated that the risk of V. parahaemolyticus infection through Jeotgal consumption is low in South Korea.