Search results for: Distribution System Operator
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 9973

Search results for: Distribution System Operator

9853 Profit Optimization for Solar Plant Electricity Production

Authors: Fl. Loury, P. Sablonière

Abstract:

In this paper a stochastic scenario-based model predictive control applied to molten salt storage systems in concentrated solar tower power plant is presented. The main goal of this study is to build up a tool to analyze current and expected future resources for evaluating the weekly power to be advertised on electricity secondary market. This tool will allow plant operator to maximize profits while hedging the impact on the system of stochastic variables such as resources or sunlight shortage.

Solving the problem first requires a mixed logic dynamic modeling of the plant. The two stochastic variables, respectively the sunlight incoming energy and electricity demands from secondary market, are modeled by least square regression. Robustness is achieved by drawing a certain number of random variables realizations and applying the most restrictive one to the system. This scenario approach control technique provides the plant operator a confidence interval containing a given percentage of possible stochastic variable realizations in such a way that robust control is always achieved within its bounds. The results obtained from many trajectory simulations show the existence of a ‘’reliable’’ interval, which experimentally confirms the algorithm robustness.

Keywords: Molten Salt Storage System, Concentrated Solar Tower Power Plant, Robust Stochastic Model Predictive Control.

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9852 Fluid Flow Analysis and Design of a Flow Distributor in a Domestic Gas Boiler Using a Commercial CFD Software

Authors: Lukasz Peronski, Roy Bratley, Derek B. Ingham, Lin Ma, Mohamed Pourkashanian, StephenTaylor

Abstract:

The aim of the study was to investigate the possible use of commercial Computational Fluid Dynamics (CFD) software in the design process of a domestic gas boiler. Because of the limited computational resources some simplifications had to be made in order to contribute to the design in a reasonable timescale. The porous media model was used in order to simulate the influence of the pressure drop characteristic of particular elements of a heat transfer system on the water-flow distribution in the system. Further, a combination of CFD analyses and spread sheet calculations was used in order to solve the flow distribution problem.

Keywords: CFD, domestic gas boilers, flow distribution, heatexchanger, porous media

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9851 Exponentiated Transmuted Weibull Distribution A Generalization of the Weibull Distribution

Authors: Abd El Hady N. Ebraheim

Abstract:

This paper introduces a new generalization of the two parameter Weibull distribution. To this end, the quadratic rank transmutation map has been used. This new distribution is named exponentiated transmuted Weibull (ETW) distribution. The ETW distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, eleven lifetime distributions such as the Weibull, exponentiated Weibull, Rayleigh and exponential distributions, among others follow as special cases. The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters. Explicit expressions are derived for the quantiles. The moments of the distribution are derived, and the order statistics are examined.

Keywords: Exponentiated, Inversion Method, Maximum Likelihood Estimation, Transmutation Map.

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9850 Using Jumping Particle Swarm Optimization for Optimal Operation of Pump in Water Distribution Networks

Authors: R. Rajabpour, N. Talebbeydokhti, M. H. Ahmadi

Abstract:

Carefully scheduling the operations of pumps can be resulted to significant energy savings. Schedules can be defined either implicit, in terms of other elements of the network such as tank levels, or explicit by specifying the time during which each pump is on/off. In this study, two new explicit representations based on timecontrolled triggers were analyzed, where the maximum number of pump switches was established beforehand, and the schedule may contain fewer switches than the maximum. The optimal operation of pumping stations was determined using a Jumping Particle Swarm Optimization (JPSO) algorithm to achieve the minimum energy cost. The model integrates JPSO optimizer and EPANET hydraulic network solver. The optimal pump operation schedule of VanZyl water distribution system was determined using the proposed model and compared with those from Genetic and Ant Colony algorithms. The results indicate that the proposed model utilizing the JPSO algorithm is a versatile management model for the operation of realworld water distribution system.

Keywords: JPSO, operation, optimization, water distribution system.

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9849 Nodal Load Profiles Estimation for Time Series Load Flow Using Independent Component Analysis

Authors: Mashitah Mohd Hussain, Salleh Serwan, Zuhaina Hj Zakaria

Abstract:

This paper presents a method to estimate load profile in a multiple power flow solutions for every minutes in 24 hours per day. A method to calculate multiple solutions of non linear profile is introduced. The Power System Simulation/Engineering (PSS®E) and python has been used to solve the load power flow. The result of this power flow solutions has been used to estimate the load profiles for each load at buses using Independent Component Analysis (ICA) without any knowledge of parameter and network topology of the systems. The proposed algorithm is tested with IEEE 69 test bus system represents for distribution part and the method of ICA has been programmed in MATLAB R2012b version. Simulation results and errors of estimations are discussed in this paper.

Keywords: Electrical Distribution System, Power Flow Solution, Distribution Network, Independent Component Analysis, Newton Raphson, Power System Simulation for Engineering.

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9848 Optimal Embedded Generation Allocation in Distribution System Employing Real Coded Genetic Algorithm Method

Authors: Mohd Herwan Sulaiman, Omar Aliman, Siti Rafidah Abdul Rahim

Abstract:

This paper proposes a new methodology for the optimal allocation and sizing of Embedded Generation (EG) employing Real Coded Genetic Algorithm (RCGA) to minimize the total power losses and to improve voltage profiles in the radial distribution networks. RCGA is a method that uses continuous floating numbers as representation which is different from conventional binary numbers. The RCGA is used as solution tool, which can determine the optimal location and size of EG in radial system simultaneously. This method is developed in MATLAB. The effect of EG units- installation and their sizing to the distribution networks are demonstrated using 24 bus system.

Keywords: Embedded generation (EG), load flow study, optimal allocation, real coded genetic algorithm (RCGA).

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9847 Stability of Property (gm) under Perturbation and Spectral Properties Type Weyl Theorems

Authors: M. H. M. Rashid

Abstract:

A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl’s theorem, Weyl spectrum, polaroid operators, property (gm), property (m).

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9846 Simplified Models to Determine Nodal Voltagesin Problems of Optimal Allocation of Capacitor Banks in Power Distribution Networks

Authors: A. Pereira, S. Haffner, L. V. Gasperin

Abstract:

This paper presents two simplified models to determine nodal voltages in power distribution networks. These models allow estimating the impact of the installation of reactive power compensations equipments like fixed or switched capacitor banks. The procedure used to develop the models is similar to the procedure used to develop linear power flow models of transmission lines, which have been widely used in optimization problems of operation planning and system expansion. The steady state non-linear load flow equations are approximated by linear equations relating the voltage amplitude and currents. The approximations of the linear equations are based on the high relationship between line resistance and line reactance (ratio R/X), which is valid for power distribution networks. The performance and accuracy of the models are evaluated through comparisons with the exact results obtained from the solution of the load flow using two test networks: a hypothetical network with 23 nodes and a real network with 217 nodes.

Keywords: Distribution network models, distribution systems, optimization, power system planning.

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9845 FEM Investigation of Induction Heating System for Pipe Brazing

Authors: Ilona I. Iatcheva, Rumena D. Stancheva, Mario Metodiev

Abstract:

The paper deals with determination of electromagnetic and temperature field distribution of induction heating system used for pipe brazing. The problem is considered as coupled – time harmonic electromagnetic and transient thermal field. It has been solved using finite element method. The detailed maps of electromagnetic and thermal field distribution have been obtained. The good understanding of the processes in the considered system ensures possibilities for control, management and increasing the efficiency of the welding process.

Keywords: Electromagnetic field, temperature field, finiteelement method, induction heating, pipe brazing.

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9844 Spherical Spectrum Properties of Quaternionic Operators

Authors: Yiwan Guo, Fahui Zhai

Abstract:

In this paper, the similarity invariant and the upper semi-continuity of spherical spectrum, and the spherical spectrum properties for infinite direct sums of quaternionic operators are characterized, respectively. As an application of some results established, a concrete example about the computation of the spherical spectrum of a compact quaternionic operator with form of infinite direct sums of quaternionic matrices is also given.

Keywords: Spherical spectrum, Quaternionic operator, Upper semi-continuity, Direct sum of operators.

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9843 Super-ellipsoidal Potential Function for Autonomous Collision Avoidance of a Teleoperated UAV

Authors: Mohammed Qasim, Kyoung-Dae Kim

Abstract:

In this paper, we present the design of the super-ellipsoidal potential function (SEPF), that can be used for autonomous collision avoidance of an unmanned aerial vehicle (UAV) in a 3-dimensional space. In the design of SEPF, we have the full control over the shape and size of the potential function. In particular, we can adjust the length, width, height, and the amount of flattening at the tips of the potential function so that the collision avoidance motion vector generated from the potential function can be adjusted accordingly. Based on the idea of the SEPF, we also propose an approach for the local autonomy of a UAV for its collision avoidance when the UAV is teleoperated by a human operator. In our proposed approach, a teleoperated UAV can not only avoid collision autonomously with other surrounding objects but also track the operator’s control input as closely as possible. As a result, an operator can always be in control of the UAV for his/her high-level guidance and navigation task without worrying too much about the UAVs collision avoidance while it is being teleoperated. The effectiveness of the proposed approach is demonstrated through a human-in-the-loop simulation of quadrotor UAV teleoperation using virtual robot experimentation platform (v-rep) and Matlab programs.

Keywords: Artificial potential function, autonomy, collision avoidance, teleoperation, quadrotor, UAV.

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9842 Design of Distribution Network for Gas Cylinders in Jordan

Authors: Hazem J. Smadi

Abstract:

Performance of a supply chain is directly related to a distribution network that entails the location of storing materials or products and how products are delivered to the end customer through different stages in the supply chain. This study analyses the current distribution network used for delivering gas cylinders to end customer in Jordan. Evaluation of current distribution has been conducted across customer service components. A modification on the current distribution network in terms of central warehousing in each city in the country improves the response time and customer experience. 

Keywords: Distribution network, gas cylinder, Jordan, supply chain.

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9841 Thermal Analysis of a Sliding Electric Contact System Using Finite Element Method

Authors: Adrian T. Pleșca

Abstract:

In this paper a three dimensional thermal model of a sliding contact system is proposed for both steady-state or transient conditions. The influence of contact force, electric current and ambient temperature on the temperature distribution, has been investigated. A thermal analysis of the different type of the graphite material of fixed electric contact and its influence on contact system temperature rise, has been performed. To validate the three dimensional thermal model, some experimental tests have been done. There is a good correlation between experimental and simulation results.

Keywords: Sliding electric contact, temperature distribution, thermal analysis.

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9840 Some Separations in Covering Approximation Spaces

Authors: Xun Ge, Jinjin Li, Ying Ge

Abstract:

Adopting Zakowski-s upper approximation operator C and lower approximation operator C, this paper investigates granularity-wise separations in covering approximation spaces. Some characterizations of granularity-wise separations are obtained by means of Pawlak rough sets and some relations among granularitywise separations are established, which makes it possible to research covering approximation spaces by logical methods and mathematical methods in computer science. Results of this paper give further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.

Keywords: Rough set, covering approximation space, granularitywise separation.

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9839 A New Distribution and Application on the Lifetime Data

Authors: Gamze Ozel, Selen Cakmakyapan

Abstract:

We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of a simulation study. 

Keywords: Marshall-Olkin distribution, Rayleigh distribution, estimation, maximum likelihood.

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9838 Comparison of Evolutionary Algorithms and their Hybrids Applied to MarioAI

Authors: Hidehiko Okada, Yuki Fujii

Abstract:

Researchers have been applying artificial/ computational intelligence (AI/CI) methods to computer games. In this research field, further researchesare required to compare AI/CI methods with respect to each game application. In thispaper, we report our experimental result on the comparison of evolution strategy, genetic algorithm and their hybrids, applied to evolving controller agents for MarioAI. GA revealed its advantage in our experiment, whereas the expected ability of ES in exploiting (fine-tuning) solutions was not clearly observed. The blend crossover operator and the mutation operator of GA might contribute well to explore the vast search space.

Keywords: Evolutionary algorithm, autonomous game controller agent, neuroevolutions, MarioAI

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9837 Application of Pearson Parametric Distribution Model in Fatigue Life Reliability Evaluation

Authors: E. A. Azrulhisham, Y. M. Asri, A. W. Dzuraidah, A. H. Hairul Fahmi

Abstract:

The aim of this paper is to introduce a parametric distribution model in fatigue life reliability analysis dealing with variation in material properties. Service loads in terms of responsetime history signal of Belgian pave were replicated on a multi-axial spindle coupled road simulator and stress-life method was used to estimate the fatigue life of automotive stub axle. A PSN curve was obtained by monotonic tension test and two-parameter Weibull distribution function was used to acquire the mean life of the component. A Pearson system was developed to evaluate the fatigue life reliability by considering stress range intercept and slope of the PSN curve as random variables. Considering normal distribution of fatigue strength, it is found that the fatigue life of the stub axle to have the highest reliability between 10000 – 15000 cycles. Taking into account the variation of material properties associated with the size effect, machining and manufacturing conditions, the method described in this study can be effectively applied in determination of probability of failure of mass-produced parts.

Keywords: Stub axle, Fatigue life reliability, Stress-life, PSN curve, Weibull distribution, Pearson system

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9836 Network Reconfiguration of Distribution System Using Artificial Bee Colony Algorithm

Authors: S. Ganesh

Abstract:

Power distribution systems typically have tie and sectionalizing switches whose states determine the topological configuration of the network. The aim of network reconfiguration of the distribution network is to minimize the losses for a load arrangement at a particular time. Thus the objective function is to minimize the losses of the network by satisfying the distribution network constraints. The various constraints are radiality, voltage limits and the power balance condition. In this paper the status of the switches is obtained by using Artificial Bee Colony (ABC) algorithm. ABC is based on a particular intelligent behavior of honeybee swarms. ABC is developed based on inspecting the behaviors of real bees to find nectar and sharing the information of food sources to the bees in the hive. The proposed methodology has three stages. In stage one ABC is used to find the tie switches, in stage two the identified tie switches are checked for radiality constraint and if the radilaity constraint is satisfied then the procedure is proceeded to stage three otherwise the process is repeated. In stage three load flow analysis is performed. The process is repeated till the losses are minimized. The ABC is implemented to find the power flow path and the Forward Sweeper algorithm is used to calculate the power flow parameters. The proposed methodology is applied for a 33–bus single feeder distribution network using MATLAB.

Keywords: Artificial Bee Colony (ABC) algorithm, Distribution system, Loss reduction, Network reconfiguration.

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9835 Adaptive Rfid Positioning System Using Signal Level Matrix

Authors: Ching-Sheng Wang, Xin-Mao Huang, Ming-Yu Hung

Abstract:

In this paper, we present a method named Signal Level Matrix (SLM) which can improve the accuracy and stability of active RFID indoor positioning system. Considering the accuracy and cost, we use uniform distribution mode to set up and separate the overlapped signal covering areas, in order to achieve preliminary location setting. Then, based on the proposed SLM concept and the characteristic of the signal strength value that attenuates as the distance increases, this system cross-examines the distribution of adjacent signals to locate the users more accurately. The experimental results indicate that the adaptive positioning method proposed in this paper could improve the accuracy and stability of the positioning system effectively and satisfyingly.

Keywords: RFID positioning, localization, indoor, location-aware.

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9834 Concept of Automation in Management of Electric Power Systems

Authors: Richard Joseph, Nerey Mvungi

Abstract:

An electric power system includes a generating, a transmission, a distribution, and consumers subsystems. An electrical power network in Tanzania keeps growing larger by the day and become more complex so that, most utilities have long wished for real-time monitoring and remote control of electrical power system elements such as substations, intelligent devices, power lines, capacitor banks, feeder switches, fault analyzers and other physical facilities. In this paper, the concept of automation of management of power systems from generation level to end user levels was determined by using Power System Simulator for Engineering (PSS/E) version 30.3.2.

Keywords: Automation, Distribution subsystem, Generating subsystem, PSS/E, TANESCO, Transmission subsystem.

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9833 Coordination on Agrifood Supply Chain

Authors: Martha Liliana Reina Usuga, Wilson Adarme Jaimes, Oscar Eduardo Suarez

Abstract:

Coordinated supply chain represents major challenges for the different actors involved in it, because each agent responds to individual interests. The paper presents a framework with the reviewed literature regarding the system's decision structure and nature of demand. Later, it characterizes an agri food supply chain in the Central Region of Colombia, it responds to a decentralized distribution system and a stochastic demand. Finally, the paper recommends coordinating the chain based on shared information, and mechanisms for each agent, as VMI (vendor-managed inventory) strategy for farmer-buyer relationship, information system for farmers and contracts for transportation service providers.

Keywords: Agri-food supply chain, Coordination mechanisms, Decentralized distribution system, Supply chain coordination.

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9832 Space Charge Distribution in 22 kV XLPE Insulated Cable by Using Pulse Electroacoustic Measurement Technique

Authors: N. Ruangkajonmathee, R. Thiamsri, B. Marungsri

Abstract:

This paper presents the experimental results on space charge distribution in cross-linked polyethylene (XLPE) insulating material for 22 kV power distribution system cable by using pulse electroacoustic measurement technique (PEA). Numbers of XLPE insulating material ribbon having thickness 60 μm taken from unused 22 kV high voltage cable were used as specimen in this study. DC electric field stress was applied to test specimen at room temperature (25°C). Four levels of electric field stress, 25 kV/mm, 50 kV/mm, 75 kV/mm and 100 kV/mm, were used. In order to investigate space charge distribution characteristic, space charge distribution characteristics were measured after applying electric field stress 15 min, 30 min and 60 min, respectively. The results show that applied time and magnitude of dc electric field stress play an important role to the formation of space charge.

Keywords: Space charge distribution, pulsed electroacoustic(PEA) technique, cross-linked polyethylene (XLPE), DC electrical fields stress.

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9831 A New Technique for Multi Resolution Characterization of Epileptic Spikes in EEG

Authors: H. N. Suresh, Dr. V. Udaya Shankara

Abstract:

A technique proposed for the automatic detection of spikes in electroencephalograms (EEG). A multi-resolution approach and a non-linear energy operator are exploited. The signal on each EEG channel is decomposed into three sub bands using a non-decimated wavelet transform (WT). The WT is a powerful tool for multi-resolution analysis of non-stationary signal as well as for signal compression, recognition and restoration. Each sub band is analyzed by using a non-linear energy operator, in order to detect spikes. A decision rule detects the presence of spikes in the EEG, relying upon the energy of the three sub-bands. The effectiveness of the proposed technique was confirmed by analyzing both test signals and EEG layouts.

Keywords: EEG, Spike, SNEO, Wavelet Transform

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9830 Capacitor Placement in Radial Distribution System for Loss Reduction Using Artificial Bee Colony Algorithm

Authors: R. Srinivasa Rao

Abstract:

This paper presents a new method which applies an artificial bee colony algorithm (ABC) for capacitor placement in distribution systems with an objective of improving the voltage profile and reduction of power loss. The ABC algorithm is a new population based meta heuristic approach inspired by intelligent foraging behavior of honeybee swarm. The advantage of ABC algorithm is that it does not require external parameters such as cross over rate and mutation rate as in case of genetic algorithm and differential evolution and it is hard to determine these parameters in prior. The other advantage is that the global search ability in the algorithm is implemented by introducing neighborhood source production mechanism which is a similar to mutation process. To demonstrate the validity of the proposed algorithm, computer simulations are carried out on 69-bus system and compared the results with the other approach available in the literature. The proposed method has outperformed the other methods in terms of the quality of solution and computational efficiency.

Keywords: Distribution system, Capacitor Placement, Loss reduction, Artificial Bee Colony Algorithm.

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9829 ATC in Competitive Electricity Market Using TCSC

Authors: S. K. Gupta, Richa Bansal

Abstract:

In a deregulated power system structure, power producers and customers share a common transmission network for wheeling power from the point of generation to the point of consumption. All parties in this open access environment may try to purchase the energy from the cheaper source for greater profit margins, which may lead to overloading and congestion of certain corridors of the transmission network. This may result in violation of line flow, voltage and stability limits and thereby undermine the system security. Utilities therefore need to determine adequately their available transfer capability (ATC) to ensure that system reliability is maintained while serving a wide range of bilateral and multilateral transactions. This paper presents power transfer distribution factor based on AC load flow for the determination and enhancement of ATC. The study has been carried out for IEEE 24 bus Reliability Test System.

Keywords: Available Transfer Capability, FACTS devices, Power Transfer Distribution Factors.

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9828 Workplace Monitoring During Interventional Cardiology Procedures

Authors: N. Todorovic, I. Bikit, J. Nikolov, S. Forkapic, D. Mrdja, S. Todorovic

Abstract:

Interventional cardiologists are at greater risk from radiation exposure as a result of the procedures they undertake than most other medical specialists. A study was performed to evaluate operator dose during interventional cardiology procedures and to establish methods of operator dose reduction with a radiation protective device. Different procedure technique and use of protective tools can explain big difference in the annual equivalent dose received by the professionals. Strategies to prevent and monitor radiation exposure, advanced protective shielding and effective radiation monitoring methods should be applied.

Keywords: absorbed dose rate measurements, annualequivalent dose, protective device.

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9827 A Note on Negative Hypergeometric Distribution and Its Approximation

Authors: S. B. Mansuri

Abstract:

In this paper, at first we explain about negative hypergeometric distribution and its properties. Then we use the w-function and the Stein identity to give a result on the poisson approximation to the negative hypergeometric distribution in terms of the total variation distance between the negative hypergeometric and poisson distributions and its upper bound.

Keywords: Negative hypergeometric distribution, Poisson distribution, Poisson approximation, Stein-Chen identity, w-function.

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9826 Applications of Stable Distributions in Time Series Analysis, Computer Sciences and Financial Markets

Authors: Mohammad Ali Baradaran Ghahfarokhi, Parvin Baradaran Ghahfarokhi

Abstract:

In this paper, first we introduce the stable distribution, stable process and theirs characteristics. The a -stable distribution family has received great interest in the last decade due to its success in modeling data, which are too impulsive to be accommodated by the Gaussian distribution. In the second part, we propose major applications of alpha stable distribution in telecommunication, computer science such as network delays and signal processing and financial markets. At the end, we focus on using stable distribution to estimate measure of risk in stock markets and show simulated data with statistical softwares.

Keywords: stable distribution, SaS, infinite variance, heavy tail networks, VaR.

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9825 The Current Situation of Ang Thong Province’s Court Doll Distribution

Authors: P. Waiyawuththanapoom

Abstract:

This research is objected to study the pattern and channel of distribution of Ang Thong’s court doll OTOP product and try to develop the quality of distribution of the court doll product. The population of this research is 50 court doll manufacturers of Ang Thong’s court doll. The data and information was collected by using the questionnaire and use percentage, mean and standard deviation as an analysis tools. The distribution channel of Ang Thong’s court doll can be separated into 3 channels which are direct distribution from the manufacturer, via the middleman and via the co-operated manufacturing group. In the direct distribution from the manufacturer channel, it was found that the manufacturer is given the highest rate of importance to how they keep the inventory. In the distribution via the middleman channel, it was found that the manufacturer is given the highest rate of importance to the distribution efficiency. But in the distribution via the co-operated manufacturing group, it was found that the manufacturer is given the highest rate of importance to the public relationship.

Keywords: Distribution, Court Doll, Ang Thong Province.

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9824 Application of Reliability Prediction Model Adapted for the Analysis of the ERP System

Authors: F. Urem, K. Fertalj, Ž. Mikulić

Abstract:

This paper presents the possibilities of using Weibull statistical distribution in modeling the distribution of defects in ERP systems. There follows a case study, which examines helpdesk records of defects that were reported as the result of one ERP subsystem upgrade. The result of the applied modeling is in modeling the reliability of the ERP system from a user perspective with estimated parameters like expected maximum number of defects in one day or predicted minimum of defects between two upgrades. Applied measurement-based analysis framework is proved to be suitable in predicting future states of the reliability of the observed ERP subsystems.

Keywords: ERP, reliability, Weibull

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