Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 17542

Search results for: Markov chain model

17542 Markov-Chain-Based Optimal Filtering and Smoothing

Authors: Garry A. Einicke, Langford B. White

Abstract:

This paper describes an optimum filter and smoother for recovering a Markov process message from noisy measurements. The developments follow from an equivalence between a state space model and a hidden Markov chain. The ensuing filter and smoother employ transition probability matrices and approximate probability distribution vectors. The properties of the optimum solutions are retained, namely, the estimates are unbiased and minimize the variance of the output estimation error, provided that the assumed parameter set are correct. Methods for estimating unknown parameters from noisy measurements are discussed. Signal recovery examples are described in which performance benefits are demonstrated at an increased calculation cost.

Keywords: optimal filtering, smoothing, Markov chains

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17541 Maintenance Alternatives Related to Costs of Wind Turbines Using Finite State Markov Model

Authors: Boukelkoul Lahcen

Abstract:

The cumulative costs for O&M may represent as much as 65%-90% of the turbine's investment cost. Nowadays the cost effectiveness concept becomes a decision-making and technology evaluation metric. The cost of energy metric accounts for the effect replacement cost and unscheduled maintenance cost parameters. One key of the proposed approach is the idea of maintaining the WTs which can be captured via use of a finite state Markov chain. Such a model can be embedded within a probabilistic operation and maintenance simulation reflecting the action to be done. In this paper, an approach of estimating the cost of O&M is presented. The finite state Markov model is used for decision problems with number of determined periods (life cycle) to predict the cost according to various options of maintenance.

Keywords: cost, finite state, Markov model, operation and maintenance

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17540 Finite State Markov Chain Model of Pollutants from Service Stations

Authors: Amina Boukelkoul, Rahil Boukelkoul, Leila Maachia

Abstract:

The cumulative vapors emitted from the service stations may represent a hazard to the environment and the population. Besides fuel spill and their penetration into deep soil layers are the main contributors to soil and ground-water contamination in the vicinity of the petrol stations. The amount of the effluents from the service stations depends on strategy of maintenance and the policy adopted by the management to reduce the pollution. One key of the proposed approach is the idea of managing the effluents from the service stations which can be captured via use of a finite state Markov chain. Such a model can be embedded within a probabilistic operation and maintenance simulation reflecting the action to be done. In this paper, an approach of estimating a probabilistic percentage of the amount of emitted pollutants is presented. The finite state Markov model is used for decision problems with number of determined periods (life cycle) to predict the amount according to various options of operation.

Keywords: environment, markov modeling, pollution, service station

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17539 A New Verification Based Congestion Control Scheme in Mobile Networks

Authors: P. K. Guha Thakurta, Shouvik Roy, Bhawana Raj

Abstract:

A congestion control scheme in mobile networks is proposed in this paper through a verification based model. The model proposed in this work is represented through performance metric like buffer Occupancy, latency and packet loss rate. Based on pre-defined values, each of the metric is introduced in terms of three different states. A Markov chain based model for the proposed work is introduced to monitor the occurrence of the corresponding state transitions. Thus, the estimation of the network status is obtained in terms of performance metric. In addition, the improved performance of our proposed model over existing works is shown with experimental results.

Keywords: congestion, mobile networks, buffer, delay, call drop, markov chain

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17538 A Semi-Markov Chain-Based Model for the Prediction of Deterioration of Concrete Bridges in Quebec

Authors: Eslam Mohammed Abdelkader, Mohamed Marzouk, Tarek Zayed

Abstract:

Infrastructure systems are crucial to every aspect of life on Earth. Existing Infrastructure is subjected to degradation while the demands are growing for a better infrastructure system in response to the high standards of safety, health, population growth, and environmental protection. Bridges play a crucial role in urban transportation networks. Moreover, they are subjected to high level of deterioration because of the variable traffic loading, extreme weather conditions, cycles of freeze and thaw, etc. The development of Bridge Management Systems (BMSs) has become a fundamental imperative nowadays especially in the large transportation networks due to the huge variance between the need for maintenance actions, and the available funds to perform such actions. Deterioration models represent a very important aspect for the effective use of BMSs. This paper presents a probabilistic time-based model that is capable of predicting the condition ratings of the concrete bridge decks along its service life. The deterioration process of the concrete bridge decks is modeled using semi-Markov process. One of the main challenges of the Markov Chain Decision Process (MCDP) is the construction of the transition probability matrix. Yet, the proposed model overcomes this issue by modeling the sojourn times based on some probability density functions. The sojourn times of each condition state are fitted to probability density functions based on some goodness of fit tests such as Kolmogorov-Smirnov test, Anderson Darling, and chi-squared test. The parameters of the probability density functions are obtained using maximum likelihood estimation (MLE). The condition ratings obtained from the Ministry of Transportation in Quebec (MTQ) are utilized as a database to construct the deterioration model. Finally, a comparison is conducted between the Markov Chain and semi-Markov chain to select the most feasible prediction model.

Keywords: bridge management system, bridge decks, deterioration model, Semi-Markov chain, sojourn times, maximum likelihood estimation

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17537 Markov Characteristics of the Power Line Communication Channels in China

Authors: Ming-Yue Zhai

Abstract:

Due to the multipath and pulse noise nature, power line communications(PLC) channel can be modelled as a memory one with the finite states Markov model(FSMC). As the most important parameter modelling a Markov channel,the memory order in an FSMC is not solved in PLC systems yet. In the paper, the mutual information is used as a measure of the dependence between the different symbols, treated as the received SNA or amplitude of the current channel symbol or that of previous symbols. The joint distribution probabilities of the envelopes in PLC systems are computed based on the multi-path channel model, which is commonly used in PLC. we confirm that given the information of the symbol immediately preceding the current one, any other previous symbol is independent of the current one in PLC systems, which means the PLC channels is a Markov chain with the first-order. The field test is also performed to model the received OFDM signals with the help of AR model. The results show that the first-order AR model is enough to model the fading channel in PLC systems, which means the amount of uncertainty remaining in the current symbol should be negligible, given the information corresponding to the immediately preceding one.

Keywords: power line communication, channel model, markovian, information theory, first-order

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17536 A Comparative Analysis of Geometric and Exponential Laws in Modelling the Distribution of the Duration of Daily Precipitation

Authors: Mounia El Hafyani, Khalid El Himdi

Abstract:

Precipitation is one of the key variables in water resource planning. The importance of modeling wet and dry durations is a crucial pointer in engineering hydrology. The objective of this study is to model and analyze the distribution of wet and dry durations. For this purpose, the daily rainfall data from 1967 to 2017 of the Moroccan city of Kenitra’s station are used. Three models are implemented for the distribution of wet and dry durations, namely the first-order Markov chain, the second-order Markov chain, and the truncated negative binomial law. The adherence of the data to the proposed models is evaluated using Chi-square and Kolmogorov-Smirnov tests. The Akaike information criterion is applied to assess the most effective model distribution. We go further and study the law of the number of wet and dry days among k consecutive days. The calculation of this law is done through an algorithm that we have implemented based on conditional laws. We complete our work by comparing the observed moments of the numbers of wet/dry days among k consecutive days to the calculated moment of the three estimated models. The study shows the effectiveness of our approach in modeling wet and dry durations of daily precipitation.

Keywords: Markov chain, rainfall, truncated negative binomial law, wet and dry durations

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17535 Segmentation of Piecewise Polynomial Regression Model by Using Reversible Jump MCMC Algorithm

Authors: Suparman

Abstract:

Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model.

Keywords: piecewise regression, bayesian, reversible jump MCMC, segmentation

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17534 Modeling of Production Lines Systems with Layout Constraints

Authors: Sadegh Abebi

Abstract:

There are problems with estimating time of product process of products, especially when there is variable serving time, like control stage. These problems will cause overestimation of process time. Layout constraints, reworking constraints and inflexible product schedule in multi product lines, needs a precise planning to reduce volume in particular situation of line stock. In this article, by analyzing real queue systems with layout constraints and by using concepts and principles of Markov chain in queue theory, a hybrid model has been presented. This model can be a base to assess queue systems with probable parameters of service. Here by presenting a case study, the proposed model will be described. so, production lines of a home application manufacturer will be analyzed.

Keywords: Queuing theory, Markov Chain, layout, line balance

Procedia PDF Downloads 581
17533 New Estimation in Autoregressive Models with Exponential White Noise by Using Reversible Jump MCMC Algorithm

Authors: Suparman Suparman

Abstract:

A white noise in autoregressive (AR) model is often assumed to be normally distributed. In application, the white noise usually do not follows a normal distribution. This paper aims to estimate a parameter of AR model that has a exponential white noise. A Bayesian method is adopted. A prior distribution of the parameter of AR model is selected and then this prior distribution is combined with a likelihood function of data to get a posterior distribution. Based on this posterior distribution, a Bayesian estimator for the parameter of AR model is estimated. Because the order of AR model is considered a parameter, this Bayesian estimator cannot be explicitly calculated. To resolve this problem, a method of reversible jump Markov Chain Monte Carlo (MCMC) is adopted. A result is a estimation of the parameter AR model can be simultaneously calculated.

Keywords: autoregressive (AR) model, exponential white Noise, bayesian, reversible jump Markov Chain Monte Carlo (MCMC)

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17532 Valuation of Caps and Floors in a LIBOR Market Model with Markov Jump Risks

Authors: Shih-Kuei Lin

Abstract:

The characterization of the arbitrage-free dynamics of interest rates is developed in this study under the presence of Markov jump risks, when the term structure of the interest rates is modeled through simple forward rates. We consider Markov jump risks by allowing randomness in jump sizes, independence between jump sizes and jump times. The Markov jump diffusion model is used to capture empirical phenomena and to accurately describe interest jump risks in a financial market. We derive the arbitrage-free model of simple forward rates under the spot measure. Moreover, the analytical pricing formulas for a cap and a floor are derived under the forward measure when the jump size follows a lognormal distribution. In our empirical analysis, we find that the LIBOR market model with Markov jump risk better accounts for changes from/to different states and different rates.

Keywords: arbitrage-free, cap and floor, Markov jump diffusion model, simple forward rate model, volatility smile, EM algorithm

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17531 Mean Field Model Interaction for Computer and Communication Systems: Modeling and Analysis of Wireless Sensor Networks

Authors: Irina A. Gudkova, Yousra Demigha

Abstract:

Scientific research is moving more and more towards the study of complex systems in several areas of economics, biology physics, and computer science. In this paper, we will work on complex systems in communication networks, Wireless Sensor Networks (WSN) that are considered as stochastic systems composed of interacting entities. The current advancements of the sensing in computing and communication systems is an investment ground for research in several tracks. A detailed presentation was made for the WSN, their use, modeling, different problems that can occur in their application and some solutions. The main goal of this work reintroduces the idea of mean field method since it is a powerful technique to solve this type of models especially systems that evolve according to a Continuous Time Markov Chain (CTMC). Modeling of a CTMC has been focused; we obtained a large system of interacting Continuous Time Markov Chain with population entities. The main idea was to work on one entity and replace the others with an average or effective interaction. In this context to make the solution easier, we consider a wireless sensor network as a multi-body problem and we reduce it to one body problem. The method was applied to a system of WSN modeled as a Markovian queue showing the results of the used technique.

Keywords: Continuous-Time Markov Chain, Hidden Markov Chain, mean field method, Wireless sensor networks

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17530 Bayesian Using Markov Chain Monte Carlo and Lindley's Approximation Based on Type-I Censored Data

Authors: Al Omari Moahmmed Ahmed

Abstract:

These papers describe the Bayesian Estimator using Markov Chain Monte Carlo and Lindley’s approximation and the maximum likelihood estimation of the Weibull distribution with Type-I censored data. The maximum likelihood method can’t estimate the shape parameter in closed forms, although it can be solved by numerical methods. Moreover, the Bayesian estimates of the parameters, the survival and hazard functions cannot be solved analytically. Hence Markov Chain Monte Carlo method and Lindley’s approximation are used, where the full conditional distribution for the parameters of Weibull distribution are obtained via Gibbs sampling and Metropolis-Hastings algorithm (HM) followed by estimate the survival and hazard functions. The methods are compared to Maximum Likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) and absolute bias to determine the better method in scale and shape parameters, the survival and hazard functions.

Keywords: weibull distribution, bayesian method, markov chain mote carlo, survival and hazard functions

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17529 Bayesian Parameter Inference for Continuous Time Markov Chains with Intractable Likelihood

Authors: Randa Alharbi, Vladislav Vyshemirsky

Abstract:

Systems biology is an important field in science which focuses on studying behaviour of biological systems. Modelling is required to produce detailed description of the elements of a biological system, their function, and their interactions. A well-designed model requires selecting a suitable mechanism which can capture the main features of the system, define the essential components of the system and represent an appropriate law that can define the interactions between its components. Complex biological systems exhibit stochastic behaviour. Thus, using probabilistic models are suitable to describe and analyse biological systems. Continuous-Time Markov Chain (CTMC) is one of the probabilistic models that describe the system as a set of discrete states with continuous time transitions between them. The system is then characterised by a set of probability distributions that describe the transition from one state to another at a given time. The evolution of these probabilities through time can be obtained by chemical master equation which is analytically intractable but it can be simulated. Uncertain parameters of such a model can be inferred using methods of Bayesian inference. Yet, inference in such a complex system is challenging as it requires the evaluation of the likelihood which is intractable in most cases. There are different statistical methods that allow simulating from the model despite intractability of the likelihood. Approximate Bayesian computation is a common approach for tackling inference which relies on simulation of the model to approximate the intractable likelihood. Particle Markov chain Monte Carlo (PMCMC) is another approach which is based on using sequential Monte Carlo to estimate intractable likelihood. However, both methods are computationally expensive. In this paper we discuss the efficiency and possible practical issues for each method, taking into account the computational time for these methods. We demonstrate likelihood-free inference by performing analysing a model of the Repressilator using both methods. Detailed investigation is performed to quantify the difference between these methods in terms of efficiency and computational cost.

Keywords: Approximate Bayesian computation(ABC), Continuous-Time Markov Chains, Sequential Monte Carlo, Particle Markov chain Monte Carlo (PMCMC)

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17528 Stability Bound of Ruin Probability in a Reduced Two-Dimensional Risk Model

Authors: Zina Benouaret, Djamil Aissani

Abstract:

In this work, we introduce the qualitative and quantitative concept of the strong stability method in the risk process modeling two lines of business of the same insurance company or an insurance and re-insurance companies that divide between them both claims and premiums with a certain proportion. The approach proposed is based on the identification of the ruin probability associate to the model considered, with a stationary distribution of a Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation domain of parameters, is to obtain the stability inequality of the ruin probability which is applied to estimate the approximation error of a model with disturbance parameters by the considered model. In the stability bound obtained, all constants are explicitly written.

Keywords: Markov chain, risk models, ruin probabilities, strong stability analysis

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17527 Extended Kalman Filter and Markov Chain Monte Carlo Method for Uncertainty Estimation: Application to X-Ray Fluorescence Machine Calibration and Metal Testing

Authors: S. Bouhouche, R. Drai, J. Bast

Abstract:

This paper is concerned with a method for uncertainty evaluation of steel sample content using X-Ray Fluorescence method. The considered method of analysis is a comparative technique based on the X-Ray Fluorescence; the calibration step assumes the adequate chemical composition of metallic analyzed sample. It is proposed in this work a new combined approach using the Kalman Filter and Markov Chain Monte Carlo (MCMC) for uncertainty estimation of steel content analysis. The Kalman filter algorithm is extended to the model identification of the chemical analysis process using the main factors affecting the analysis results; in this case, the estimated states are reduced to the model parameters. The MCMC is a stochastic method that computes the statistical properties of the considered states such as the probability distribution function (PDF) according to the initial state and the target distribution using Monte Carlo simulation algorithm. Conventional approach is based on the linear correlation, the uncertainty budget is established for steel Mn(wt%), Cr(wt%), Ni(wt%) and Mo(wt%) content respectively. A comparative study between the conventional procedure and the proposed method is given. This kind of approaches is applied for constructing an accurate computing procedure of uncertainty measurement.

Keywords: Kalman filter, Markov chain Monte Carlo, x-ray fluorescence calibration and testing, steel content measurement, uncertainty measurement

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17526 Finite Dynamic Programming to Decision Making in the Use of Industrial Residual Water Treatment Plants

Authors: Oscar Vega Camacho, Andrea Vargas, Ellery Ariza

Abstract:

This paper presents the application of finite dynamic programming, specifically the "Markov Chain" model, as part of the decision making process of a company in the cosmetics sector located in the vicinity of Bogota DC. The objective of this process was to decide whether the company should completely reconstruct its waste water treatment plant or instead optimize the plant through the addition of equipment. The goal of both of these options was to make the required improvements in order to comply with parameters established by national legislation regarding the treatment of waste before it is released into the environment. This technique will allow the company to select the best option and implement a solution for the processing of waste to minimize environmental damage and the acquisition and implementation costs.

Keywords: decision making, markov chain, optimization, waste water

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17525 Application of Finite Dynamic Programming to Decision Making in the Use of Industrial Residual Water Treatment Plants

Authors: Oscar Vega Camacho, Andrea Vargas Guevara, Ellery Rowina Ariza

Abstract:

This paper presents the application of finite dynamic programming, specifically the "Markov Chain" model, as part of the decision making process of a company in the cosmetics sector located in the vicinity of Bogota DC. The objective of this process was to decide whether the company should completely reconstruct its wastewater treatment plant or instead optimize the plant through the addition of equipment. The goal of both of these options was to make the required improvements in order to comply with parameters established by national legislation regarding the treatment of waste before it is released into the environment. This technique will allow the company to select the best option and implement a solution for the processing of waste to minimize environmental damage and the acquisition and implementation costs.

Keywords: decision making, Markov chain, optimization, wastewater

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17524 A Mathematical Model for Reliability Redundancy Optimization Problem of K-Out-Of-N: G System

Authors: Gak-Gyu Kim, Won Il Jung

Abstract:

According to a remarkable development of science and technology, function and role of the system of engineering fields has recently been diversified. The system has become increasingly more complex and precise, and thus, system designers intended to maximize reliability concentrate more effort at the design stage. This study deals with the reliability redundancy optimization problem (RROP) for k-out-of-n: G system configuration with cold standby and warm standby components. This paper further intends to present the optimal mathematical model through which the following three elements of (i) multiple components choices, (ii) redundant components quantity and (iii) the choice of redundancy strategies may be combined in order to maximize the reliability of the system. Therefore, we focus on the following three issues. First, we consider RROP that there exists warm standby state as well as cold standby state of the component. Second, as eliminating an approximation approach of the previous RROP studies, we construct a precise model for system reliability. Third, given transition time when the state of components changes, we present not simply a workable solution but the advanced method. For the wide applicability of RROPs, moreover, we use absorbing continuous time Markov chain and matrix analytic methods in the suggested mathematical model.

Keywords: RROP, matrix analytic methods, k-out-of-n: G system, MTTF, absorbing continuous time Markov Chain

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17523 Vulnerability Assessment of Healthcare Interdependent Critical Infrastructure Coloured Petri Net Model

Authors: N. Nivedita, S. Durbha

Abstract:

Critical Infrastructure (CI) consists of services and technological networks such as healthcare, transport, water supply, electricity supply, information technology etc. These systems are necessary for the well-being and to maintain effective functioning of society. Critical Infrastructures can be represented as nodes in a network where they are connected through a set of links depicting the logical relationship among them; these nodes are interdependent on each other and interact with each at other at various levels, such that the state of each infrastructure influences or is correlated to the state of another. Disruption in the service of one infrastructure nodes of the network during a disaster would lead to cascading and escalating disruptions across other infrastructures nodes in the network. The operation of Healthcare Infrastructure is one such Critical Infrastructure that depends upon a complex interdependent network of other Critical Infrastructure, and during disasters it is very vital for the Healthcare Infrastructure to be protected, accessible and prepared for a mass casualty. To reduce the consequences of a disaster on the Critical Infrastructure and to ensure a resilient Critical Health Infrastructure network, knowledge, understanding, modeling, and analyzing the inter-dependencies between the infrastructures is required. The paper would present inter-dependencies related to Healthcare Critical Infrastructure based on Hierarchical Coloured Petri Nets modeling approach, given a flood scenario as the disaster which would disrupt the infrastructure nodes. The model properties are being analyzed for the various state changes which occur when there is a disruption or damage to any of the Critical Infrastructure. The failure probabilities for the failure risk of interconnected systems are calculated by deriving a reachability graph, which is later mapped to a Markov chain. By analytically solving and analyzing the Markov chain, the overall vulnerability of the Healthcare CI HCPN model is demonstrated. The entire model would be integrated with Geographic information-based decision support system to visualize the dynamic behavior of the interdependency of the Healthcare and related CI network in a geographically based environment.

Keywords: critical infrastructure interdependency, hierarchical coloured petrinet, healthcare critical infrastructure, Petri Nets, Markov chain

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17522 Hidden Markov Model for the Simulation Study of Neural States and Intentionality

Authors: R. B. Mishra

Abstract:

Hidden Markov Model (HMM) has been used in prediction and determination of states that generate different neural activations as well as mental working conditions. This paper addresses two applications of HMM; one to determine the optimal sequence of states for two neural states: Active (AC) and Inactive (IA) for the three emission (observations) which are for No Working (NW), Waiting (WT) and Working (W) conditions of human beings. Another is for the determination of optimal sequence of intentionality i.e. Believe (B), Desire (D), and Intention (I) as the states and three observational sequences: NW, WT and W. The computational results are encouraging and useful.

Keywords: hiden markov model, believe desire intention, neural activation, simulation

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17521 Modeling of System Availability and Bayesian Analysis of Bivariate Distribution

Authors: Muhammad Farooq, Ahtasham Gul

Abstract:

To meet the desired standard, it is important to monitor and analyze different engineering processes to get desired output. The bivariate distributions got a lot of attention in recent years to describe the randomness of natural as well as artificial mechanisms. In this article, a bivariate model is constructed using two independent models developed by the nesting approach to study the effect of each component on reliability for better understanding. Further, the Bayes analysis of system availability is studied by considering prior parametric variations in the failure time and repair time distributions. Basic statistical characteristics of marginal distribution, like mean median and quantile function, are discussed. We use inverse Gamma prior to study its frequentist properties by conducting Monte Carlo Markov Chain (MCMC) sampling scheme.

Keywords: reliability, system availability Weibull, inverse Lomax, Monte Carlo Markov Chain, Bayesian

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17520 Research on Coordination Strategies for Coordinating Supply Chain Based on Auction Mechanisms

Authors: Changtong Wang, Lingyun Wei

Abstract:

The combination of auctions and supply chains is of great significance in improving the supply chain management system and enhancing the efficiency of economic and social operations. To address the gap in research on supply chain strategies under the auction mechanism, a model is developed for the 1-N auction model in a complete information environment, and it is concluded that the two-part contract auction model for retailers in this model can achieve supply chain coordination. The model is validated by substituting the model into the scenario of a fresh-cut flower industry flower auction in exchange for arithmetic examples to further prove the validity of the conclusions.

Keywords: auction mechanism, supply chain coordination strategy, fresh cut flowers industry, supply chain management

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17519 Supply Chain Competitiveness with the Perspective of Service Performance Between Supply Chain Actors and Functions: A Theoretical Model

Authors: Umer Mukhtar

Abstract:

Supply Chain Competitiveness is the capability of a supply chain to deliver value to the customer for the sake of competitive advantage. Service Performance and Quality intervene between supply chain actors including functions inside the firm in a significant way for the supply chain to achieve a competitive position in the market to gain competitive advantage. Supply Chain competitiveness is the current issue of interest because of supply chains’ competition for competitive advantage rather than firms’. A proposed theoretical model is developed by extracting and integrating different theories to pursue further inquiry based on case studies and survey design. It is also intended to develop a scale of service performance for functions of the focal firm that is a revolving center for a whole supply chain.

Keywords: supply chain competitiveness, service performance in supply chain, service quality in supply chain, competitive advantage by supply chain, networks and supply chain, customer value, value supply chain, value chain

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17518 An Estimating Parameter of the Mean in Normal Distribution by Maximum Likelihood, Bayes, and Markov Chain Monte Carlo Methods

Authors: Autcha Araveeporn

Abstract:

This paper is to compare the parameter estimation of the mean in normal distribution by Maximum Likelihood (ML), Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML estimator is estimated by the average of data, the Bayes method is considered from the prior distribution to estimate Bayes estimator, and MCMC estimator is approximated by Gibbs sampling from posterior distribution. These methods are also to estimate a parameter then the hypothesis testing is used to check a robustness of the estimators. Data are simulated from normal distribution with the true parameter of mean 2, and variance 4, 9, and 16 when the sample sizes is set as 10, 20, 30, and 50. From the results, it can be seen that the estimation of MLE, and MCMC are perceivably different from the true parameter when the sample size is 10 and 20 with variance 16. Furthermore, the Bayes estimator is estimated from the prior distribution when mean is 1, and variance is 12 which showed the significant difference in mean with variance 9 at the sample size 10 and 20.

Keywords: Bayes method, Markov chain Monte Carlo method, maximum likelihood method, normal distribution

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17517 The Realization of a System’s State Space Based on Markov Parameters by Using Flexible Neural Networks

Authors: Ali Isapour, Ramin Nateghi

Abstract:

— Markov parameters are unique parameters of the system and remain unchanged under similarity transformations. Markov parameters from a power series that is convergent only if the system matrix’s eigenvalues are inside the unity circle. Therefore, Markov parameters of a stable discrete-time system are convergent. In this study, we aim to realize the system based on Markov parameters by using Artificial Neural Networks (ANN), and this end, we use Flexible Neural Networks. Realization means determining the elements of matrices A, B, C, and D.

Keywords: Markov parameters, realization, activation function, flexible neural network

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17516 Metamorphic Computer Virus Classification Using Hidden Markov Model

Authors: Babak Bashari Rad

Abstract:

A metamorphic computer virus uses different code transformation techniques to mutate its body in duplicated instances. Characteristics and function of new instances are mostly similar to their parents, but they cannot be easily detected by the majority of antivirus in market, as they depend on string signature-based detection techniques. The purpose of this research is to propose a Hidden Markov Model for classification of metamorphic viruses in executable files. In the proposed solution, portable executable files are inspected to extract the instructions opcodes needed for the examination of code. A Hidden Markov Model trained on portable executable files is employed to classify the metamorphic viruses of the same family. The proposed model is able to generate and recognize common statistical features of mutated code. The model has been evaluated by examining the model on a test data set. The performance of the model has been practically tested and evaluated based on False Positive Rate, Detection Rate and Overall Accuracy. The result showed an acceptable performance with high average of 99.7% Detection Rate.

Keywords: malware classification, computer virus classification, metamorphic virus, metamorphic malware, Hidden Markov Model

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17515 Volatility Model with Markov Regime Switching to Forecast Baht/USD

Authors: Nop Sopipan

Abstract:

In this paper, we forecast the volatility of Baht/USDs using Markov Regime Switching GARCH (MRS-GARCH) models. These models allow volatility to have different dynamics according to unobserved regime variables. The main purpose of this paper is to find out whether MRS-GARCH models are an improvement on the GARCH type models in terms of modeling and forecasting Baht/USD volatility. The MRS-GARCH is the best performance model for Baht/USD volatility in short term but the GARCH model is best perform for long term.

Keywords: volatility, Markov Regime Switching, forecasting, Baht/USD

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17514 Degradation Model for UK Railway Drainage System

Authors: Yiqi Wu, Simon Tait, Andrew Nichols

Abstract:

Management of UK railway drainage assets is challenging due to the large amounts of historical assets with long asset life cycles. A major concern for asset managers is to maintain the required performance economically and efficiently while complying with the relevant regulation and legislation. As the majority of the drainage assets are buried underground and are often difficult or costly to examine, it is important for asset managers to understand and model the degradation process in order to foresee the upcoming reduction in asset performance and conduct proactive maintenance accordingly. In this research, a Markov chain approach is used to model the deterioration process of rail drainage assets. The study is based on historical condition scores and characteristics of drainage assets across the whole railway network in England, Scotland, and Wales. The model is used to examine the effect of various characteristics on the probabilities of degradation, for example, the regional difference in probabilities of degradation, and how material and shape can influence the deterioration process for chambers, channels, and pipes.

Keywords: deterioration, degradation, markov models, probability, railway drainage

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17513 Estimating Bridge Deterioration for Small Data Sets Using Regression and Markov Models

Authors: Yina F. Muñoz, Alexander Paz, Hanns De La Fuente-Mella, Joaquin V. Fariña, Guilherme M. Sales

Abstract:

The primary approach for estimating bridge deterioration uses Markov-chain models and regression analysis. Traditional Markov models have problems in estimating the required transition probabilities when a small sample size is used. Often, reliable bridge data have not been taken over large periods, thus large data sets may not be available. This study presents an important change to the traditional approach by using the Small Data Method to estimate transition probabilities. The results illustrate that the Small Data Method and traditional approach both provide similar estimates; however, the former method provides results that are more conservative. That is, Small Data Method provided slightly lower than expected bridge condition ratings compared with the traditional approach. Considering that bridges are critical infrastructures, the Small Data Method, which uses more information and provides more conservative estimates, may be more appropriate when the available sample size is small. In addition, regression analysis was used to calculate bridge deterioration. Condition ratings were determined for bridge groups, and the best regression model was selected for each group. The results obtained were very similar to those obtained when using Markov chains; however, it is desirable to use more data for better results.

Keywords: concrete bridges, deterioration, Markov chains, probability matrix

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