• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.159-163
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• 1991

For a continuous-time absorvation Markov chain, we apply and simplify the general method of finding the transition rates given the transition probabilities obtained from discrete observation of the continuous system. An example is given.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.975-980
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• 1995

We suggest an improvement of the algorithm in [2] for calculating the transient solutions for continuous time Markov chain with countable state space.

• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.513-520
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• 2014

We study numerical methods to obtain the stationary probabilities of continuous-time Markov chains whose embedded chains are periodic. The power method is applied to the balance equations of the periodic embedded Markov chains. The power method can have the convergence speed of exponential rate that is ambiguous in its application to original continuous-time Markov chains since the embedded chains are discrete-time processes. An illustrative example is presented to investigate the numerical iteration of this paper. A numerical study shows that a rapid and stable solution for stationary probabilities can be achieved regardless of periodicity and initial conditions.

• Journal of Korean Institute of Industrial Engineers
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• v.39 no.4
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• pp.290-297
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• 2013

The increasing level of operation in high-tech industry is likely to require ever more complex structure in reliability problem. Furthermore, system failures are more significant on society as a whole than ever before. Reliability redundancy optimization problem (RROP) plays a important role in the designing and analyzing the complex system. RROP involves selection of components with multiple choices and redundancy levels for maximizing system reliability with constraints such as cost, weight, etc. Meanwhile, previous works on RROP dealt with system with perfect failure detection, which gave at most a good solution. However, we studied RROP with imperfect failure detection and switching. Using absorbing Markov Chain, we present not a good solution but the optimal one. In this study, the optimal system configuration is designed with warm and cold-standby redundancy for k-out-of-n system in terms of MTTF that is one of the performance measures of reliability.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37 no.1B
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• pp.50-58
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• 2012

The objective of this study is to develop the theoretical model of the telecommunication system service availability from the user perspective. We assume non-homogeneous Poisson process for the call arrival process and continuous time Markov chain for the system state. The proposed model effectively describes the user model of the user-perceived service reliability by including the time-varying call arrival rate. We also include the operational failure state where the user cannot receive any service even though the system is functioning.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.17-28
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• 2017

In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for solutions of one-dimensional mean-field BSDEs under Lipschitz condition.

• Journal of KIISE
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• v.42 no.6
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• pp.748-754
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• 2015

This paper proposes a sequential state estimation model consisting of continuous and discrete variables, as a way of generalizing all discrete-state factorial HMM, and gives a design of gait motion model based on the idea. The discrete state variable implements a Markov chain that models the gait dynamics, and for each state of the Markov chain, we created a Gaussian process over the space of the continuous variable. The Markov chain controls the switching among Gaussian processes, each of which models the rotation or various views of a gait state. Then a particle filter-based algorithm is presented to give an approximate filtering solution. Given an input vector sequence presented over time, this finds a trajectory that follows a Gaussian process and occasionally switches to another dynamically. Experimental results show that the proposed model can provide a very intuitive interpretation of video-based gait into a sequence of poses and a sequence of posture states.

• Journal of the Korean Society of Systems Engineering
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• v.14 no.1
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• pp.44-51
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• 2018

The purpose of RAM analysis in weapon systems is to reduce life cycle costs, along with improving combat readiness by meeting RAM target value. We analyzed the sensitivity of the RAM analysis parameters to the use of the operating system by using the Markov Process based model (MPS, Markov Process Simulation) developed for RAM analysis. A Markov process-based RAM analysis model was developed to analyze the sensitivity of parameters (MTBF, MTTR and ALDT) to the utility of the 81mm mortar. The time required for the application to reach the steady state is about 15,000H, which is about 2 years, and the sensitivity of the parameter is highest for ALDT. In order to improve combat readiness, there is a need for continuous improvement in ALDT.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.09a
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• pp.99-107
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• 1995

The Phase-type(PH) distribution, defined as a distribution of the time until the absorption in a finite continuous-time Markov chain state with one absorbing state, has been widely used for various stochastic modelling. But great computational burdens often make us hesitate to apply PH methods. In this paper, we propose a seemingly efficient approximation method for phase type distributions. We first describe methods to bound the first passage time distribution in continuous-time Markov chains. Next, we adapt these bounding methods to approximate phase-tupe distributions. Numerical computation results are given to verify their efficiency.

• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.1-12
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• 2017

Many stochastic processes satisfy the Markov property exactly or at least approximately. An interested property in the Markov process is the first passage time. Since the sequential analysis by Wald, the approximation of the first passage time has been studied extensively. The Statistical computing technique due to the development of high-speed computers made it possible to calculate the values of the properties close to the true ones. This article introduces an exponentially weighted moving average (EWMA) control chart as an example of the Markov process, and studied how to calculate the average run length with problematic issues that should be cautioned for correct calculation. The results derived for approximation of the first passage time in this research can be applied to any of the Markov processes. Especially the approximation of the continuous time Markov process to the discrete time Markov chain is useful for the studies of the properties of the stochastic process and makes computational approaches easy.