• The Korean Journal of Applied Statistics
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• v.24 no.4
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• pp.657-676
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• 2011

Properties of statistical process control procedures may not be derived analytically in many cases; however, the application of a Markov chain can solve such problems. This article shows how to derive the properties of the process control procedures using the generated Markov chains when the control statistic satisfies the Markov property. Markov chain approaches that appear in the literature (such as the statistical design and economic design of the control chart as well as the variable sampling rate design) are reviewed along with the introduction of research results for application to a new control procedure and reset chart. The joint application of a Markov chain approach and analytical solutions (when available) can guarantee the correct derivation of the properties. A Markov chain approach is recommended over simulation studies due to its precise derivation of properties and short calculation times.

• The Korean Journal of Applied Statistics
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• v.34 no.4
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• pp.537-556
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• 2021

Properties of statistical process control procedures may not be derived analytically in many cases; however, the application of a Markov chain can solve such problems. This article shows how to derive the properties of the process control procedures using the generated Markov chains when the control statistic satisfies the Markov property. Markov chain approaches that appear in the literature (such as the statistical design and economic design of the control chart as well as the variable sampling rate design) are reviewed along with the introduction of research results for application to a new control procedure and reset chart. The joint application of a Markov chain approach and analytical solutions (when available) can guarantee the correct derivation of the properties. A Markov chain approach is recommended over simulation studies due to its precise derivation of properties and short calculation times.

• Journal of Communications and Networks
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• v.10 no.3
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• pp.287-296
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• 2008

The IEEE 802.11 wireless standard uses the carrier sense multiple access with collision avoidance (CSMA/CA) as its MAC protocol (during the distributed coordination function period). This protocol is an adaptation of the CSMA/CD of the wired networks. CSMA/CA mechanism cannot guarantee quality of service (QoS) required by the application because orits random access method. In this study, we propose a new MAC protocol that considers different types of traffic (e.g., voice and data) and for each traffic type different priority levels are assigned. To improve the QoS of IEEE 802.11 MAC protocols over a multi-channel CSMA/CA, we have developed a new admission policy for both voice and data traffics. This protocol can be performed in direct sequence spread spectrum (DSSS) or frequency hopping spread spectrum (FHSS). For voice traffic we reserve a channel, while for data traffic the access is random using a CSMA/CA mechanism, and in this case a selective reject and push-out mechanism is added to meet the quality of service required by data traffic. To study the performance of the proposed protocol and to show the benefits of our design, a mathematical model is built based on Markov chains. The system could be represented by a Markov chain which is difficult to solve as the state-space is too large. This is due to the resource management and user mobility. Thus, we propose to build an aggregated Markov chain with a smaller state-space that allows performance measures to be computed easily. We have used stochastic comparisons of Markov chains to prove that the proposed access protocol (with selective reject and push-out mechanisms) gives less loss rates of high priority connections (data and voices) than the traditional one (without admission policy and selective reject and push-out mechanisms). We give numerical results to confirm mathematical proofs.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.909-928
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• 1996

In this paper, an empirical law of the iterated logarithm is investigated in the context of a stationary and ergodic martingale differences whose values taking in a measurable space.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.79-90
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• 2006

We consider the subdiagonal bilinear model and ARMA model with subdiagonal bilinear errors. Sufficient conditions for geometric ergodicity of associated Markov chains are derived by using results on generalized random coefficient autoregressive models and then strict stationarity and ,a-mixing property with exponential decay rates for given processes are obtained.

• Journal of the Korean Statistical Society
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• v.28 no.2
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• pp.235-251
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• 1999

In this paper we examine extremal behavior of a $textsc{k}$th-order stationary Markov chain {X\ulcorner} by considering excesses over a high level which typically appear in clusters. Excesses over a high level within a cluster define a cluster damage, i.e., a normalized sum of all excesses within a cluster, and all excesses define a damage point process. Under some distributional assumptions for {X\ulcorner}, we prove convergence in distribution of the cluster damage and obtain a representation for the limiting cluster damage distribution which is well suited for simulation. We also derive formulas for the mean and the variance of the limiting cluster damage distribution. These results guarantee a compound Poisson limit for the damage point process, provided that it is strongly mixing.

• Smart Structures and Systems
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• v.15 no.3
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• pp.735-749
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• 2015

The major difficulty of using Bayesian probabilistic inference for system identification is to obtain the posterior probability density of parameters conditioned by the measured response. The posterior density of structural parameters indicates how plausible each model is when considering the uncertainty of prediction errors. The Markov chain Monte Carlo (MCMC) method is a widespread medium for posterior inference but its convergence is often slow. The differential evolution adaptive Metropolis-Hasting (DREAM) algorithm boasts a population-based mechanism, which nms multiple different Markov chains simultaneously, and a global optimum exploration ability. This paper proposes an improved differential evolution adaptive Metropolis-Hasting algorithm (IDREAM) strategy to estimate the posterior density of structural parameters. The main benefit of IDREAM is its efficient MCMC simulation through its use of the adaptive Metropolis (AM) method with a mutation strategy for ensuring quick convergence and robust solutions. Its effectiveness was demonstrated in simulations on identifying the structural parameters with limited output data and noise polluted measurements.

• Journal of the Korean Data and Information Science Society
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• v.27 no.5
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• pp.1241-1251
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• 2016

We consider a correlated discrete-time random walk in which the current jump size depends on the previous jump size and a noncorrelated discrete-time random walk where the jump size is determined independently. By using the strong law of large numbers of Markov chains we derive the formula for the asymptotic means of the random mixture and the periodic pattern of these two random walks and then we show that there exists Parrondo's paradox where each random walk has mean 0 but their random mixture and periodic pattern have negative or positive means. We describe the parameter sets at which Parrondo's paradox holds in each case.

• Nuclear Engineering and Technology
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• v.51 no.2
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• pp.444-452
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• 2019

To assess the availability of a nuclear power plant's dynamic systems, it is necessary to consider the impact of dynamic interactions, such as components, software, and operating processes. However, there is currently no simple, easy-to-use tool for assessing the availability of these dynamic systems. The existing method, such as Markov chains, derives an accurate solution but has difficulty in modeling the system. When using conventional fault trees, the reliability of a system with dynamic characteristics cannot be evaluated accurately because the fault trees consider reliability of a specific operating configuration of the system. The dynamic reliability graph with general gates (DRGGG) allows an intuitive modeling similar to the actual system configuration, which can reduce the human errors that can occur during modeling of the target system. However, because the current DRGGG is able to evaluate the dynamic system in terms of only reliability without repair, a new evaluation method that can calculate the availability of the dynamic system with repair is proposed through this study. The proposed method extends the DRGGG by adding the repair condition to the dynamic gates. As a result of comparing the proposed method with Markov chains regarding a simple verification model, it is confirmed that the quantified value converges to the solution.

• Journal of the Korea Society of Computer and Information
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• v.17 no.11
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• pp.107-116
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• 2012

In this paper we propose a method that can generate the risk probability map in the form of raster shape by using Markov Chain methodology applied to the object interpretation keys and quantified risk indexes. These object interpretation keys, which are primarily characteristics that can be identified by the naked eye, are set based on the objects that comprise the spatial information of a certain urban area. Each key is divided into a cell, and then is weighted by its own risk index. These keys in turn are used to generate the unified risk probability map using various levels of crime prediction probability maps. The risk probability map may vary over time and means of applying different sets of object interpretation keys. Therefore, this method can be used to prevent crimes by providing the ways of setting up the best possible police patrol beat as well as the optimal arrangement of surveillance equipments.