• The Korean Journal of Applied Statistics
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• v.23 no.1
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• pp.189-196
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• 2010

It is never an easy task to physically randomize the sequence of cards. For instance, US 1970 draft lottery resulted in a social turmoil since the outcome sequence of 366 birthday numbers showed a significant relationship with the input order (Wikipedia, "Draft Lottery 1969", Retrieved 2009/05/01). We are motivated by Laplace's 1825 book titled Philosophical Essay on Probabilities that says "Suppose that the numbers 1, 2, ..., 100 are placed, according to their natural ordering, in an urn, and suppose further that, after having shaken the urn, to shuffle the numbers, one draws one number. It is clear that if the shuffling has been properly done, each number will have the same chance of being drawn. But if we fear that there are small differences between them depending on the order in which the numbers were put into the urn, we can decrease these differences considerably by placing these numbers in a second urn in the order in which they are drawn from the first urn, and then shaking the second urn to shuffle the numbers. These differences, already imperceptible in the second urn, would be diminished more and more by using a third urn, a fourth urn, &c." (translated by Andrew 1. Dale, 1995, Springer. pp. 35-36). Laplace foresaw what would happen to us in 150 years later, and, even more, suggested the possible tool to handle the problem. But he did omit the detailed arguments for the solution. Thus we would like to write the supplement in modern terms for Laplace in this research note. We formulate the problem with a lottery box model, to which Markov chain theory can be applied. By applying Markov chains repeatedly, one expects the uniform distribution on k states as stationary distribution. Additionally, we show that the probability of even-number of successes in binomial distribution with trials and the success probability $\theta$ approaches to 0.5, as n increases to infinity. Our theory is illustrated to the cases of truncated geometric distribution and the US 1970 draft lottery.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.6
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• pp.558-565
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• 2021

The Republic of Korea Navy has deployed naval fleets in the East, West, and South seas to effectively respond to threats from North Korea and its neighbors. However, it is difficult to allocate proper missions due to high uncertainties, such as the year of introduction for the ship, the number of mission days completed, arms capabilities, crew shift times, and the failure rate of the ship. For this reason, there is an increasing proportion of expenses, or mission alerts with high fatigue in the number of workers and traps. In this paper, we present a simulation model that can optimize the assignment of naval vessels' missions by using a continuous time absorbing Markov chain that is easy to model and that can analyze complex phenomena with varying event rates over time. A numerical analysis model allows us to determine the optimal mission durations and warship quantities to maintain the target operating rates, and we find that allocating optimal warships for each mission reduces unnecessary alerts and reduces crew fatigue and failures. This model is significant in that it can be expanded to various fields, not only for assignment of duties but also for calculation of appropriate requirements and for inventory analysis.

• Journal of the Korean Operations Research and Management Science Society
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• v.35 no.1
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• pp.83-95
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• 2010

This paper considers a firm that operates make-to-stock and make-to-order facilities in successive stages. The make-to-stock facility produces components which are consumed by the external market demand as well as the internal make-to-order operation. The make-to-order facility processes customer orders with the option of acceptance or rejection. In this paper, we address the problem of coordinating how to allocate the capacity of the make-to-stock facility to internal and external demands and how to control incoming customer orders at the make-to-order facility so as to maximize the firm's profit subject to the system costs. To deal with this issue, we formulate the problem as a Markov decision process and characterize the structure of the optimal inventory allocation and customer order control. In a numerical experiment, we compare the performance of the optimal policy to the heuristic with static inventory allocation and admission control under different operating conditions of the system.

• Asian Pacific Journal of Cancer Prevention
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• v.16 no.11
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• pp.4677-4683
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• 2015

When there is no sampling frame within a certain group or the group is concerned that making its population public would bring social stigma, we say the population is hidden. It is difficult to approach this kind of population survey-methodologically because the response rate is low and its members are not quite honest with their responses when probability sampling is used. The only alternative known to address the problems caused by previous methods such as snowball sampling is respondent-driven sampling (RDS), which was developed by Heckathorn and his colleagues. RDS is based on a Markov chain, and uses the social network information of the respondent. This characteristic allows for probability sampling when we survey a hidden population. We verified through computer simulation whether RDS can be used on a hidden population of cancer survivors. According to the simulation results of this thesis, the chain-referral sampling of RDS tends to minimize as the sample gets bigger, and it becomes stabilized as the wave progresses. Therefore, it shows that the final sample information can be completely independent from the initial seeds if a certain level of sample size is secured even if the initial seeds were selected through convenient sampling. Thus, RDS can be considered as an alternative which can improve upon both key informant sampling and ethnographic surveys, and it needs to be utilized for various cases domestically as well.

• Journal of Korea Water Resources Association
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• v.39 no.5 s.166
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• pp.453-466
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• 2006

The objective of this study was to analyze the changes in the hydrological environment in Soyanggang-dam watershed due to climate change results (in yews 2050 and 2100) which were simulated using CCCma CGCM2 based on SRES A2 and B2. The SRES A2 and B2 were used to estimate NDVI values for selected land use using the relation of NDVI-Temperature using linear regression of observed data (in years 1998$\sim$2002). Land use change based on SRES A2 and B2 was estimated every 5- and 10-year period using the CA-Markov technique based on the 1985, 1990, 1995 and 2000 land cover map classified by Landsat TM satellite images. As a result, the trend in land use change in each land class was reflected. When land use changes in years 2050 and 2100 were simulated using the CA-Markov method, the forest class area declined while the urban, bareground and grassland classes increased. When simulation was done further for future scenarios, the transition change converged and no increasing trend was reflected. The impact assessment of evapotranspiration was conducted by comparing the observed data with the computed results based on three cases supposition scenarios of meteorological data (temperature, global radiation and wind speed) using the FAO Penman-Monteith method. The results showed that the runoff was reduced by about 50% compared with the present hydrologic condition when each SRES and periods were compared. If there was no land use change, the runoff would decline further to about 3$\sim$5%.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.12
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• pp.1855-1869
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• 1993

For the traditional ALOHA system without capture, the Markov chain obtained using the number of backlogged users at each slot if shown to be non-ergodic. So the infinite population ALOHA with fixed retransmission probabilities is unstable for any choice of the arrival rates and retransmission probabilities. The capture ALOHA system of also shown to be unstable for any arrival rate unless it has perfect. In this paper, we study a stabilization policy for capture ALOHA system that controls the retransmission probabilities and prove the stability of its multidimensional Markovian model by empolying a continuous Lyapunov function, and thus identify the stability region. We also study a delay performance through computer simulation th show the stability for any input rate below the maximum achievable channel throughput.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.1
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• pp.17-32
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• 1996

In this paper, a model for two-layered video traffic is proposed. The performance analysis of the proposed model and the effects of two-layer coding scehemes in ATM networks are also studied. ATM-based networks give the possibility to support image codingat variable bit rate(VBR). Two layer coding is one of the very promising methods among many proposed methods to compensate the cell loss, the major drawback in ATM networks. From the experimental data of the 2-layer coded video traffics, it is observed that traffic patterns of base layer and enhanced layer are highly correlate to each other, when constant image quality is kept. With this observation, coded two layered video traffic can be modeled as 2-dimensional Markov chain. The model well fit the real experimental data. The model was used for the analysis of the performance of statistical multiplexer with priorites in ATM networks.

• The Korean Journal of Applied Statistics
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• v.22 no.2
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• pp.425-433
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• 2009

Spatial models suitable for describing the evolving random fields in climate and environmental systems have been developed by many researchers. In general, rainfall in South Korea is highly variable in intensity and amount across space. This study characterizes the monthly and regional variation of rainfall fields using the spatial modeling. The main objective of this research is spatial prediction with the Bayesian hierarchical modeling (kriging) in order to further our understanding of water resources over space. We use the Bayesian approach in order to estimate the parameters and produce more reliable prediction. The Bayesian kriging also provides a promising solution for analyzing and predicting rainfall data.

• Journal of Integrative Natural Science
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• v.5 no.4
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• pp.246-252
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• 2012

Multivariate cumulative sum (CUSUM) control charts for simultaneously monitoring both means and variances under multivariate normal process are investigated. Performances of multivariate CUSUM schemes are evaluated for matched fixed sampling interval (FSI) and variable sampling interval (VSI) features in terms of average time to signal (ATS), average number of samples to signal (ANSS). Multivariate Shewhart charts are also considered to compare the properties of multivariate CUSUM charts. Numerical results show that presented CUSUM charts are more efficient than the corresponding Shewhart chart for small or moderate shifts and VSI feature with two sampling intervals is more efficient than FSI feature. When small changes in the production process have occurred, CUSUM chart with small reference values will be recommended in terms of the time to signal.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.29-36
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• 2014

The limiting diffusion of special diploid model can be defined as a discrete generator for the rescaled Markov chain. Choi([2]) defined the operator of projection $S_t$ on limiting diffusion and new measure $dQ=S_tdP$. and showed the martingale property on this operator and measure. Let $P_{\rho}$ be the unique solution of the martingale problem for $\mathcal{L}_0$ starting at ${\rho}$ and ${\pi}_1,{\pi}_2,{\cdots},{\pi}_n$ the projection of $E^n$ on $x_1,x_2,{\cdots},x_n$. In this note we define $$dQ_{\rho}=S_tdP_{\rho}$$ and show that $Q_{\rho}$ solves the martingale problem for $\mathcal{L}_{\pi}$ starting at ${\rho}$.