• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.469-480
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• 2019

A generalized tiling is defined as a generalization of the properties of tiling a region of ${\mathbb{Z}}^2$ with dominoes, and comprises tiling with rhombus and any other tilings that admits height functions which can be ordered into a distributive lattice. By using properties of the distributive lattice, we prove that the Markov chain consisting of moving from one height function to the next by a flip is fast mixing and the mixing time ${\tau}({\epsilon})$ is given by ${\tau}({\epsilon}){\leq}(kmn)^3(mn\;{\ln}\;k+{\ln}\;{\epsilon}^{-1})$, where mn is the area of the grid ${\Gamma}$ that is a k-regular polycell. This result generalizes the result of the authors (T-tetromino tiling Markov chain is fast mixing, Theor. Comp. Sci. (2018)) and improves on the mixing time obtained by using coupling arguments by N. Destainville and by M. Luby, D. Randall, A. Sinclair.

• Management Science and Financial Engineering
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• v.19 no.2
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• pp.49-53
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• 2013

A Markov-chain Monte Carlo sampling algorithm samples a new point around the latest sample due to the Markov property, which prevents it from sampling from multi-modal distributions since the corresponding chain often fails to search entire support of the target distribution. In this paper, to overcome this problem, mode switching scheme is applied to the conventional MCMC algorithms. The algorithm separates the reducible Markov chain into several mutually exclusive classes and use mode switching scheme to increase mixing rate. Simulation results are given to illustrate the algorithm with promising results.

• Journal of Applied Reliability
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• v.17 no.4
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• pp.332-342
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• 2017

Purpose: In this study, the lifetime distribution of a k-out-of-n system with heterogeneous components is suggested as Markov model, and the time-to-failure (TTF) distribution of each component is considered as phase-type distribution (PHD). Furthermore, based on the model, a redundancy allocation problem with a mix of components (RAPMC) is proposed. Methods: The lifetime distribution model for the system is formulated by the structured Markov chain. From the model, the various information on the system lifetime can be ascertained by the matrix-analytic (or-geometric) method. Conclusion: By the generalization of TTF distribution (PHD) and the consideration of heterogeneous components, the lifetime distribution model can delineate many real systems and be exploited for developing system operation policies such as preventive maintenance, warranty. Moreover, the effectiveness of the proposed RAPMC is verified by numerical experiments. That is, under the equivalent design conditions, it presented a system with higher reliability than RAP without component mixing (RAPCM).