• 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.

• 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.

• 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.

• 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.