Search results for: Gibbs Sampling

Authors: Golnaz Shahtahmassebi, Jose Maria Sarabia

Abstract:

In this talk, we introduce a new class of conjugate prior distributions obtained from conditional specification methodology. We illustrate the application of such distribution in Bayesian change point detection in Poisson processes. We obtain the posterior distribution of model parameters using a general bivariate distribution with gamma conditionals. Simulation from the posterior is readily implemented using a Gibbs sampling algorithm. The Gibbs sampling is implemented even when using conditional densities that are incompatible or only compatible with an improper joint density. The application of such methods will be demonstrated using examples of simulated and real data.

Keywords: change point, bayesian inference, Gibbs sampler, conditional specification, gamma conditional distributions

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Authors: Jiaqi Huang, Lu Jin

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Pervious concrete features with high water permeability rate. However, due to the lack of fine aggregates, the compressive strength is usually lower than other conventional concrete products. Optimization of pervious concrete mix design has long been recognized as an effective mechanism to achieve high compressive strength while maintaining desired permeability rate. In this paper, a Gibbs Sampling based algorithm is proposed to approximate the optimal mix design to achieve a high compressive strength of pervious concrete. We prove that the proposed algorithm efficiently converges to the set of global optimal solutions. The convergence rate and accuracy depend on a control parameter employed in the proposed algorithm. The simulation results show that, by using the proposed approach, the system converges to the optimal solution quickly and the derived optimal mix design achieves the maximum compressive strength while maintaining the desired permeability rate.

Keywords: convergence, Gibbs Sampling, high compressive strength, optimal mix design, pervious concrete

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Authors: Vera Varazashvili, Murman Tsarakhov, Tamar Mirianashvili, Teimuraz Pavlenishvili, Tengiz Machaladze, Mzia Khundadze

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Standard Gibbs energy of formation ΔGfor(298.15) of lanthanide-iron double oxides of garnet-type crystal structure R3Fe5O12 - RIG (R – are rare earth ions) from initial oxides are evaluated. The calculation is based on the data of standard entropies S298.15 and standard enthalpies ΔH298.15 of formation of compounds which are involved in the process of garnets synthesis. Gibbs energy of formation is presented as temperature function ΔGfor(T) for the range 300-1600K. The necessary starting thermodynamic data were obtained from calorimetric study of heat capacity and by using the semi-empirical method for calculation of ΔH298.15 (formation). Thermodynamic functions for standard temperature – enthalpy, entropy and Gibbs energy - are recommended as reference data for technological evaluations. Through the isostructural series of rare earth-iron garnets the correlation between thermodynamic properties and characteristics of lanthanide ions are elucidated.

Keywords: calorimetry, entropy, heat capacity, Gibbs energy of formation, rare earth iron garnets

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Authors: David Ryan, Martin Breugst, Turlough Downes, Peter A. Byrne, Gerard P. McGlacken

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An ambident nucleophile is a nucleophile that possesses two or more distinct nucleophilic sites that are linked through resonance and are effectively “in competition” for reaction with an electrophile. Examples include enolates, pyridone anions, and nitrite anions, among many others. Reactions of ambident nucleophiles and electrophiles are extremely prevalent at all levels of organic synthesis. The principle of hard and soft acids and bases (the “HSAB principle”) is most commonly cited in the explanation of selectivities in such reactions. Although this rationale is pervasive in any discussion on ambident reactivity, the HSAB principle has received considerable criticism. As a result, the principle’s supplantation has become an area of active interest in recent years. This project focuses on developing a model for rationalizing ambident reactivity. Presented here is an approach that incorporates computational calculations and experimental kinetic data to construct Gibbs energy profile diagrams. The preferred site of alkylation of nitrite anion with a range of ‘hard’ and ‘soft’ alkylating agents was established by ¹H NMR spectroscopy. Pseudo-first-order rate constants were measured directly by ¹H NMR reaction monitoring, and the corresponding second-order constants and Gibbs energies of activation were derived. These, in combination with computationally derived standard Gibbs energies of reaction, were sufficient to construct Gibbs energy wells. By representing the ambident system as a series of overlapping Gibbs energy wells, a more intuitive picture of ambident reactivity emerges. Here, previously unexplained switches in reactivity in reactions involving closely related electrophiles are elucidated.

Keywords: ambident, Gibbs, nucleophile, rates

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Authors: Vera Varazashvili, Murman Tsarakhov, Tamar Mirianashvili, Teimuraz Pavlenishvili, Tengiz Machaladze, Mzia Khundadze

Abstract:

Standard Gibbs energy of formation ΔGfor(298.15) of lanthanide-iron double oxides of garnet-type crystal structure R3Fe5O12 - RIG (R – are rare earth ions) from initial oxides are evaluated. The calculation is based on the data of standard entropies S298.15 and standard enthalpies ΔH298.15 of formation of compounds which are involved in the process of garnets synthesis. Gibbs energy of formation is presented as temperature function ΔGfor(T) for the range 300-1600K. The necessary starting thermodynamic data were obtained from calorimetric study of heat capacity – temperature functions and by using the semi-empirical method for calculation of ΔH298.15 of formation. Thermodynamic functions for standard temperature – enthalpy, entropy and Gibbs energy - are recommended as reference data for technological evaluations. Through the isostructural series of rare earth-iron garnets the correlation between thermodynamic properties and characteristics of lanthanide ions are elucidated.

Keywords: calorimetry, entropy, enthalpy, heat capacity, gibbs energy of formation, rare earth iron garnets

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Authors: F. Amireche, I. Mokbel, J. Jose, B. F. Belaribi

Abstract:

The experimental vapour-liquid equilibria (VLE) at isothermal conditions and excess molar Gibbs energies GE are carried out for the three binary mixtures: 1, 2- dichloroethane + ethylene glycol dimethyl ether, + diethylene glycol dimethyl ether or + diethylene glycol diethyl ether, at ten temperatures ranging from 273 to 353.15 K. A good static device was employed for these measurements. The VLE data were reduced using the Redlich-Kister equation by taking into consideration the vapour pressure non-ideality in terms of the second molar virial coefficient. The experimental data were compared to the results predicted with the DISQUAC and Dortmund UNIFAC group contribution models for the total pressures P, the excess molar Gibbs energies GE and the excess molar enthalpies HE.

Keywords: Disquac model, Dortmund UNIFAC model, 1, 2- dichloroethane, excess molar Gibbs energies GE, polyethers, VLE

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Authors: Mahmoud I. Syam, Kamarulzaman Ibrahim, Amer I. Al-Omari

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Stratified double extreme ranked set sampling (SDERSS) method is introduced and considered for estimating the population mean. The SDERSS is compared with the simple random sampling (SRS), stratified ranked set sampling (SRSS) and stratified simple set sampling (SSRS). It is shown that the SDERSS estimator is an unbiased of the population mean and more efficient than the estimators using SRS, SRSS and SSRS when the underlying distribution of the variable of interest is symmetric or asymmetric.

Keywords: double extreme ranked set sampling, extreme ranked set sampling, ranked set sampling, stratified double extreme ranked set sampling

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Authors: Manjit Singh

Abstract:

Multiscale entropy (MSE) is an extensively used index to provide a general understanding of multiple complexity of physiologic mechanism of heart rate variability (HRV) that operates on a wide range of time scales. Accurate selection of electrocardiogram (ECG) sampling frequency is an essential concern for clinically significant HRV quantification; high ECG sampling rate increase memory requirements and processing time, whereas low sampling rate degrade signal quality and results in clinically misinterpreted HRV. In this work, the impact of ECG sampling frequency on MSE based HRV have been quantified. MSE measures are found to be sensitive to ECG sampling frequency and effect of sampling frequency will be a function of time scale.

Keywords: ECG (electrocardiogram), heart rate variability (HRV), multiscale entropy, sampling frequency

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Authors: Fouzia Amireche-Ziar, Ilham Mokbel, Jacques Jose

Abstract:

The vapour pressures of the three binary mixtures: 1, 2- dichloroethane + 1,3-dioxolane, + 1,4-dioxane or + tetrahydropyrane, are carried out at ten temperatures ranging from 273 to 353.15 K. An accurate static device was employed for these measurements. The VLE data were reduced using the Redlich-Kister equation by taking into consideration the vapour pressure non-ideality in terms of the second molar virial coefficient. The experimental data were compared to the results predicted with the DISQUAC and Dortmund UNIFAC group contribution models for the total pressures P and the excess molar Gibbs energies GE.

Keywords: disquac model, dortmund UNIFAC model, excess molar Gibbs energies GE, VLE

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Authors: Ana Staneva, Vessela Stoimenova

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A parametric estimation of the MBP with Power Series offspring distribution family is considered in this paper. The MLE for the parameters is obtained in the case when the observable data are incomplete and consist only with the generation sizes of the family tree of MBP. The parameter estimation is calculated by using the Monte Carlo EM algorithm. The estimation for the posterior distribution and for the offspring distribution parameters are calculated by using the Bayesian approach and the Gibbs sampler. The article proposes various examples with bivariate branching processes together with computational results, simulation and an implementation using R.

Keywords: Bayesian, branching processes, EM algorithm, Gibbs sampler, Monte Carlo methods, statistical estimation

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Authors: Sami Mestiri, Abdeljelil Farhat

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The aim of this current paper is to predict the credit risk of banks in Tunisia, over the period (2000-2005). For this purpose, two methods for the estimation of the logistic regression model with random effects: Penalized Quasi Likelihood (PQL) method and Gibbs Sampler algorithm are applied. By using the information on a sample of 528 Tunisian firms and 26 financial ratios, we show that Bayesian approach improves the quality of model predictions in terms of good classification as well as by the ROC curve result.

Keywords: forecasting, credit risk, Penalized Quasi Likelihood, Gibbs Sampler, logistic regression with random effects, curve ROC

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Authors: Fouzia Amireche-Ziar, Ilham Mokbel, Jacques Jose

Abstract:

The vapour pressures of the three binary mixtures: 1, 2- dichloroethane + 1,3-dioxolane, + 1,4-dioxane or + tetrahydropyrane, are carried out at ten temperatures ranging from 273 to 353.15 K. An accurate static device was employed for these measurements. The VLE data were reduced using the Redlich-Kister equation by taking into consideration the vapour pressure non-ideality in terms of the second molar virial coefficient. The experimental data were compared to the results predicted with the DISQUAC and Dortmund UNIFAC group contribution models for the total pressures P and the excess molar Gibbs energies GE.

Keywords: disquac model, dortmund UNIFAC model, excess molar Gibbs energies GE, VLE

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Authors: Said Ali Al-Hadhrami, Amer Ibrahim Al-Omari

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In this paper, Bayesian estimation for the mean of exponential distribution is considered using Moving Extremes Ranked Set Sampling (MERSS). Three priors are used; Jeffery, conjugate and constant using MERSS and Simple Random Sampling (SRS). Some properties of the proposed estimators are investigated. It is found that the suggested estimators using MERSS are more efficient than its counterparts based on SRS.

Keywords: Bayesian, efficiency, moving extreme ranked set sampling, ranked set sampling

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Authors: Maria Bercea, Bernhard A. Wolf

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The thermodynamic behavior for solutions of poly (methyl methacrylate-ran-t-butyl methacrylate) of variable composition as compared with the corresponding homopolymers was investigated by light scattering measurements carried out for dilute solutions and vapor pressure measurements of concentrated solutions. The complex dependencies of the Flory Huggins interaction parameter on concentration and copolymer composition in solvents of different polarity (toluene and chloroform) can be understood by taking into account the ability of the polymers to rearrange in a response to changes in their molecular surrounding. A recent unified thermodynamic approach was used for modeling the experimental data, being able to describe the behavior of the different solutions by means of two adjustable parameters, one representing the effective number of solvent segments and another one accounting for the interactions between the components. Thus, it was investigated how the solvent quality changes with the composition of the copolymers through the Gibbs energy of mixing as a function of polymer concentration. The largest reduction of the Gibbs energy at a given composition of the system was observed for the best solvent. The present investigation proves that the new unified thermodynamic approach is a general concept applicable to homo- and copolymers, independent of the chain conformation or shape, molecular and chemical architecture of the components and of other dissimilarities, such as electrical charges.

Keywords: random copolymers, Flory Huggins interaction parameter, Gibbs energy of mixing, chemical architecture

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Authors: Bina Kumari, Subir K. Sarkar, Pradipta Bandyopadhyay

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The autocorrelation function of the density fluctuation is studied in each of the two phases in a Gibbs Ensemble Monte Carlo (GEMC) simulation of the problem of phase separation for a square well potential with various values of its range. We find that the normalized autocorrelation function is described very well as a linear combination of an exponential function with a time scale τ₂ and a stretched exponential function with a time scale τ₁ and an exponent α. Dependence of (α, τ₁, τ₂) on the parameters of the GEMC algorithm and the range of the square well potential is investigated and interpreted. We also analyse the issue of how to choose the parameters of the GEMC simulation optimally.

Keywords: autocorrelation function, density fluctuation, GEMC, simulation

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Authors: Negar Riazifar, Nigel G. Stocks

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This paper proposes strategies in level crossing (LC) sampling and reconstruction that provide alias-free high-fidelity signal reconstruction for speech signals without exponentially increasing sample number with increasing bit-depth. We introduce methods in LC sampling that reduce the sampling rate close to the Nyquist frequency even for large bit-depth. The results indicate that larger variation in the sampling intervals leads to an alias-free sampling scheme; this is achieved by either reducing the bit-depth or adding jitter to the system for high bit-depths. In conjunction with windowing, the signal is reconstructed from the LC samples using an efficient Toeplitz reconstruction algorithm.

Keywords: alias-free, level crossing sampling, spectrum, trigonometric polynomial

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Authors: Davood Shishebori, Mohammad Saber Fallah Nezhad, Sina Seifi

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In this paper, a variable multiple dependent state (MDS) sampling plan is developed based on the process capability index using Bayesian approach. The optimal parameters of the developed sampling plan with respect to constraints related to the risk of consumer and producer are presented. Two comparison studies have been done. First, the methods of double sampling model, sampling plan for resubmitted lots and repetitive group sampling (RGS) plan are elaborated and average sample numbers of the developed MDS plan and other classical methods are compared. A comparison study between the developed MDS plan based on Bayesian approach and the exact probability distribution is carried out.

Keywords: MDS sampling plan, RGS plan, sampling plan for resubmitted lots, process capability index (PCI), average sample number (ASN), Bayesian approach

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Authors: Raghunath Arnab

Abstract:

The two-phase sampling which is also known as double sampling was introduced in 1938. In two-phase sampling, samples are selected in phases. In the first phase, a relatively large sample of size is selected by some suitable sampling design and only information on the auxiliary variable is collected. During the second phase, a sample of size is selected either from, the sample selected in the first phase or from the entire population by using a suitable sampling design and information regarding the study and auxiliary variable is collected. Evidently, two phase sampling is useful if the auxiliary information is relatively easy and cheaper to collect than the study variable as well as if the strength of the relationship between the variables and is high. If the sample is selected in more than two phases, the resulting sampling design is called a multi-phase sampling. In this article we will consider how one can use data collected at the first phase sampling at the stages of estimation of the parameter, stratification, selection of sample and their combinations in the second phase in a unified setup applicable to any sampling design and wider classes of estimators. The problem of the estimation of variance will also be considered. The variance of estimator is essential for estimating precision of the survey estimates, calculation of confidence intervals, determination of the optimal sample sizes and for testing of hypotheses amongst others. Although, the variance is a non-negative quantity but its estimators may not be non-negative. If the estimator of variance is negative, then it cannot be used for estimation of confidence intervals, testing of hypothesis or measure of sampling error. The non-negativity properties of the variance estimators will also be studied in details.

Keywords: auxiliary information, two-phase sampling, varying probability sampling, unbiased estimators

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Authors: Johnson Joseph Kwabina Arhinful, Owusu-Ansah Emmanuel Degraft Johnson, Okyere Gabrial Asare, Adebanji Atinuke Olusola

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This paper proposes a model to describe the blood types distribution of new Coronavirus (COVID-19) cases using the Bayesian Poisson - Hidden Markov Model (BP-HMM). With the help of the Gibbs sampler algorithm, using OpenBugs, the study first identifies the number of hidden states fitting European (EU) and African (AF) data sets of COVID-19 cases by blood type frequency. The study then compares the state-dependent mean of infection within and across the two geographical areas. The study findings show that the number of hidden states and infection rates within and across the two geographical areas differ according to blood type.

Keywords: BP-HMM, COVID-19, blood types, GIBBS sampler

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Authors: Mahmoud I. Syam

Abstract:

Stratified double median ranked set sampling (SDMRSS) method is suggested for estimating the population mean. The SDMRSS is compared with the simple random sampling (SRS), stratified simple random sampling (SSRS), and stratified ranked set sampling (SRSS). It is shown that SDMRSS estimator is an unbiased of the population mean and more efficient than SRS, SSRS, and SRSS. Also, by SDMRSS, we can increase the efficiency of mean estimator for specific value of the sample size. SDMRSS is applied on real life examples, and the results of the example agreed the theoretical results.

Keywords: efficiency, double ranked set sampling, median ranked set sampling, ranked set sampling, stratified

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Authors: B. K. Gill, Himani Sharma, V. K. Rattan

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Experimental data of refractive index, excess molar volume and viscosity of binary mixture of morpholine with cumene over the whole composition range at 298.15 K, 303.15 K, 308.15 K and normal atmospheric pressure have been measured. The experimental data were used to compute the density, deviation in molar refraction, deviation in viscosity and excess Gibbs free energy of activation as a function of composition. The experimental viscosity data have been correlated with empirical equations like Grunberg- Nissan, Herric correlation and three body McAllister’s equation. The excess thermodynamic properties were fitted to Redlich-Kister polynomial equation. The variation of these properties with composition and temperature of the binary mixtures are discussed in terms of intermolecular interactions.

Keywords: cumene, excess Gibbs free energy, excess molar volume, morpholine

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Authors: Khattab Al Qaisi, Nicholas Bowring

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This paper presents the simulation results of the effects of sampling frequency on the total harmonic distortion (THD) of three-phase inverters using the space vector pulse width modulation (SVPWM) and space vector control (SVC) algorithms. The relationship between the variables was studied using curve fitting techniques, and it has been shown that, for 50 Hz inverters, there is an exponential relation between the sampling frequency and THD up to around 8500 Hz, beyond which the performance of the model becomes irregular, and there is an negative exponential relation between the sampling frequency and the marginal improvement to the THD. It has also been found that the performance of SVPWM is better than that of SVC with the same sampling frequency in most frequency range, including the range where the performance of the former is irregular.

Keywords: DSI, SVPWM, THD, DC-AC converter, sampling frequency, performance

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Authors: Hilary Rutto, Linda Sibali

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In this study, the adsorption of lead and zinc ions from aqueous solutions by modified millet husk has been investigated. The effects of different parameters, such as pH, adsorbent dosage, concentration, temperature, and contact time, have been investigated. The results of the experiments showed that the adsorption of both metal ions increased by increasing pH values up to 11. Adsorption process was initially fast. The adsorption rate decreased then until it reached to equilibrium time of 120 min for both lead and zinc ions. The Langmuir, Freundlich, Dubinin-Radushkevich (D-R), and thermodynamic models (Gibbs free energy) were used to determine the isotherm parameters associated with the adsorption process. The positive values of Gibbs free energy change indicated that reaction is not spontaneous. Experimental data were also evaluated in terms of kinetic characteristics of adsorption, and it was found that adsorption process for both metal ions followed pseudo-first order for zinc and pseudo-second-order for lead.

Keywords: zinc, lead, adsorption, millet husks

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Authors: Nursel Koyuncu, Nihal Ata Tutkun

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Frailty model is a survival model that takes into account the unobserved heterogeneity for exploring the relationship between the survival of an individual and several covariates. In the recent years, proposed survival models become more complex and this feature causes convergence problems especially in large data sets. Therefore selection of sample from these big data sets is very important for estimation of parameters. In sampling literature, some authors have defined new sampling schemes to predict the parameters correctly. For this aim, we try to see the effect of sampling design in semi-parametric frailty model. We conducted a simulation study in R programme to estimate the parameters of semi-parametric frailty model for different sample sizes, censoring rates under classical simple random sampling and ranked set sampling schemes. In the simulation study, we used data set recording 17260 male Civil Servants aged 40–64 years with complete 10-year follow-up as population. Time to death from coronary heart disease is treated as a survival-time and age, systolic blood pressure are used as covariates. We select the 1000 samples from population using different sampling schemes and estimate the parameters. From the simulation study, we concluded that ranked set sampling design performs better than simple random sampling for each scenario.

Keywords: frailty model, ranked set sampling, efficiency, simple random sampling

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Authors: Muqaddas Javed, Muhammad Hanif

Abstract:

The generalized multivariate ratio and regression type estimators for population mean are suggested under multi-phase stratified systematic sampling (MPSSS) using multi auxiliary information. Estimators are developed under the two different situations of availability of auxiliary information. The expressions of bias and mean square error (MSE) are developed. Special cases of suggested estimators are also discussed and simulation study is conducted to observe the performance of estimators.

Keywords: generalized estimators, multi-phase sampling, stratified random sampling, systematic sampling

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Authors: Arijit Chakraborty, Anirban Roy

Abstract:

The Indian peninsula is strategically located in the Asian subcontinent with the Himalayas to the North and Oceans surrounding the other three directions with annual monsoons which takes care of water supply to the rivers. The total river water discharge into the Bay of Bengal and the Arabian Sea is 628 km³/year and 274 km³/year, respectively. Thus huge volumes of fresh water meet saline water, and this mixing of two streams of dissimilar salinity gives rise to tremendous mixing energies which can be harvested for various purposes like energy generation using pressure retarded osmosis or reverse electrodialysis. The present paper concentrates on analyzing the energy of mixing for the rivers in Goa. Goa has 10 rivers of various sizes all which meet the Arabian Sea. In the present work, the 8 rivers and their salinity (NaCl concentrations) have been analyzed along with their seasonal fluctuations. Next, a Gibbs free energy formulation has been implemented to analyze the energy of mixing of the selected rivers. The highest and lowest energies according to the seasonal fluctuations have been evaluated, and this provides two important insights into (i) amount of energy that can be harvested and (ii) decision on the location of such systems.

Keywords: Gibbs energy, mixing energy, salinity gradient energy, thermodynamics

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Authors: Encarnacion Alvarez, Noemı Hidalgo-Rebollo, Juan F. Munoz, Francisco J. Blanco-Encomienda

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Many companies use the technique named as acceptance sampling which consists on the inspection and decision making regarding products. According to the results derived from this method, the company takes the decision of acceptance or rejection of a product. The acceptance sampling can be applied to the technology management, since the acceptance sampling can be seen as a tool to improve the design planning, operation and control of technological products. The theoretical operating characteristic (OC) curves are widely used when dealing with acceptance sampling. In this paper, we carry out Monte Carlo simulation studies to compare numerically the empirical OC curves derived from the empirical results to the customary theoretical OC curves. We analyze various possible scenarios in such a way that the differences between the empirical and theoretical curves can be observed under different situations.

Keywords: single-sampling plan, lot, Monte Carlo simulation, quality control

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Authors: M. J. Park, S. H. Lee, C. H. Lee, O. M. Kwon

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This paper studies a secondary voltage control framework of the microgrids based on the consensus for a communication network of multiagent. The proposed control is designed by the communication network with one-way links. The communication network is modeled by a directed graph. At this time, the concept of sampling is considered as the communication constraint among each distributed generator in the microgrids. To analyze the sampling effects on the secondary voltage control of the microgrids, by using Lyapunov theory and some mathematical techniques, the sufficient condition for such problem will be established regarding linear matrix inequality (LMI). Finally, some simulation results are given to illustrate the necessity of the consideration of the sampling effects on the secondary voltage control of the microgrids.

Keywords: microgrids, secondary control, multiagent, sampling, LMI

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Authors: Michael B. C. Khoo, J. L. Khoo, W. C. Yeong, W. L. Teoh

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The Shewhart Xbar control chart is a useful process monitoring tool in manufacturing industries to detect the presence of assignable causes. However, it is insensitive in detecting small process shifts. To circumvent this problem, adaptive control charts are suggested. An adaptive chart enables at least one of the chart’s parameters to be adjusted to increase the chart’s sensitivity. Two common adaptive charts that exist in the literature are the double sampling (DS) Xbar and variable sampling interval (VSI) Xbar charts. This paper compares the performances of the DS and VSI Xbar charts, based on the average time to signal (ATS) criterion. The ATS profiles of the DS Xbar and VSI Xbar charts are obtained using the Mathematica and Statistical Analysis System (SAS) programs, respectively. The results show that the VSI Xbar chart is generally superior to the DS Xbar chart.

Keywords: adaptive charts, average time to signal, double sampling, charts, variable sampling interval

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Authors: Watcharin Sangma, Onsiri Chanmuang, Pitsanu Tongkhow

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A forecasting model for steel demand uncertainty in Thailand is proposed. It consists of trend, autocorrelation, and outliers in a hierarchical Bayesian frame work. The proposed model uses a cumulative Weibull distribution function, latent first-order autocorrelation, and binary selection, to account for trend, time-varying autocorrelation, and outliers, respectively. The Gibbs sampling Markov Chain Monte Carlo (MCMC) is used for parameter estimation. The proposed model is applied to steel demand index data in Thailand. The root mean square error (RMSE), mean absolute percentage error (MAPE), and mean absolute error (MAE) criteria are used for model comparison. The study reveals that the proposed model is more appropriate than the exponential smoothing method.

Keywords: forecasting model, steel demand uncertainty, hierarchical Bayesian framework, exponential smoothing method

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