• Structural Engineering and Mechanics
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• v.38 no.5
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• pp.651-674
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• 2011

This paper presents a novel method for predicting the failure probability of structural or mechanical systems subjected to random loads and material properties involving multiple design points. The method involves Multicut High Dimensional Model Representation (Multicut-HDMR) technique in conjunction with moving least squares to approximate the original implicit limit state/performance function with an explicit function. Depending on the order chosen sometimes truncated Cut-HDMR expansion is unable to approximate the original implicit limit state/performance function when multiple design points exist on the limit state/performance function or when the problem domain is large. Multicut-HDMR addresses this problem by using multiple reference points to improve accuracy of the approximate limit state/performance function. Numerical examples show the accuracy and efficiency of the proposed approach in estimating the failure probability.

• Korean Management Science Review
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• v.14 no.2
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• pp.63-68
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• 1997

Limiting probability in the steady state of regenerative process is one of the most useful characteristics. The formula for this limiting probability in the steady state of the regenerative process is presented in this paper. Because this formula is for the general model, it can be applied to many special systems including 2-unit redundant system. An example for this formula is also presented.

• Computers and Concrete
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• v.15 no.1
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• pp.37-54
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• 2015

In general, cracks significantly deteriorate the in-situ performance of concrete members and structures, especially in urban metro tunnels that have been embedded in saturated soft soils. The microcapsule self-healing method is a newly developed healing method for repairing cracked concrete. To investigate the optimal microcapsule parameters that will have the best healing effect in concrete, a 3D analytical probability healing model is proposed; it is based on the microcapsule self-healing method's healing mechanism, and its purpose is to predict the healing efficiency and healing probability of given cracks. The proposed model comprehensively considers the radius and the volume fraction of microcapsules, the expected healing efficiency, the parameters of cracks, the broken ratio and the healing probability. Furthermore, a simplified probability healing model is proposed to facilitate the calculation. Then, a Monte Carlo test is conducted to verify the proposed 3D analytical probability healing model. Finally, the influences of microcapsules' parameters on the healing efficiency and the healing probability of the microcapsule self-healing method are examined in light of the proposed probability model.

• Structural Engineering and Mechanics
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• v.57 no.4
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• pp.587-602
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• 2016

In structural reliability analysis, the response surface method is widely adopted because of its numerical efficiency. It should be understood that the response function must approximate the actual limit state function accurately in the main region influencing failure probability where it is evaluated. However, the size of main region influencing failure probability was not defined clearly in current response surface methods. In this study, the concept of sub-region of interest is constructed, and an improved response surface method is proposed based on the sub-region of interest. The sub-region of interest can clearly define the size of main region influencing failure probability, so that the accuracy of the evaluation of failure probability is increased. Some examples are introduced to demonstrate the efficiency and the accuracy of the proposed method for both numerical and implicit limit state functions.

• Journal of the Korean Data and Information Science Society
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• v.20 no.1
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• pp.191-202
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• 2009

In this study, we drive the one dimensional marginal transform function, probability density function and probability distribution function for the random variables $T_{{\xi}N}$ (Time taken by the servers during the vacations), ${\xi}_N$(Number of vacations taken by the servers) and ${\eta}_N$(Number of customers or units arrive in the system) by controlling the variability of two random variables simultaneously.

• Industrial Engineering and Management Systems
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• v.7 no.2
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• pp.143-149
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• 2008

There have been some approximation analysis methods for a GI/G/1 queueing system. As one of them, an approximation technique for the steady-state probability in the GI/G/1 queueing system based on the iteration numerical calculation has been proposed. As another one, an approximation formula of the average queue length in the GI/G/1 queueing system by using the diffusion approximation or the heuristics extended diffusion approximation has been developed. In this article, an approximation technique in order to analyze the GI/G/1 queueing system is considered and then the formulae of both the steady-state probability and the average queue length in the GI/G/1 queueing system are proposed. Through some numerical examples by the proposed technique, the existing approximation methods, and the Monte Carlo simulation, the effectiveness of the proposed approximation technique is verified.

• Journal of the Korean Institute of Telematics and Electronics
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• v.20 no.2
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• pp.16-22
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• 1983

In this paper, we obtained PFME(probability for maximum entropy) and entropy when a conditional probability was given in a binary list order Markov Information Source. And, when steady state probability was constant, the influence of change of a conditional probability on entropy was examined, too.

• Asian Pacific Journal of Cancer Prevention
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• v.15 no.9
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• pp.4109-4115
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• 2014

Background: Accurate assessment of disease progression requires proper understanding of natural disease process which is often hidden and unobservable. For this purpose, disease status should be clearly detected. But in most diseases it is not possible to detect such status. This study, therefore, aims to present a model which both investigates the unobservable disease process and considers the error probability in diagnosis of disease states. Materials and Methods: Data from 330 patients with gastric cancer undergoing surgery at the Iran Cancer Institute from 1995 to 1999 were analyzed. Moreover, to estimate and assess the effect of demographic, diagnostic and clinical factors as well as medical and post-surgical variables on transition rates and the probability of misdiagnosis of relapse, a hidden Markov multi-state model was employed. Results: Classification errors of patients in alive state without a relapse ($e_{21}$) and with a relapse ($e_{12}$) were 0.22 (95% CI: 0.04-0.63) and 0.02 (95% CI: 0.00-0.09), respectively. Only variables of age and number of renewed treatments affected misdiagnosis of relapse. In addition, patient age and distant metastasis were among factors affecting the occurrence of relapse (state1${\rightarrow}$state2) while the number of renewed treatments and the type and extent of surgery had a significant effect on death hazard without relapse (state2${\rightarrow}$state3)and death hazard with relapse (state2${\rightarrow}$state3). Conclusions: A hidden Markov multi-state model provides the possibility of estimating classification error between different states of disease. Moreover, based on this model, factors affecting the probability of this error can be identified and researchers can be helped with understanding the mechanisms of classification error.

• MALSORI
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• no.45
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• pp.117-126
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• 2003

Decision tree-based state tying has been proposed in recent years as the most popular approach for clustering the states of context-dependent hidden Markov model-based speech recognition. The aims of state tying is to reduce the number of free parameters and predict state probability distributions of unseen models. But, when doing state tying, the size of a decision tree is very important for word independent recognition. In this paper, we try to construct optimized decision tree based on the average of feature vectors in state pool and the number of seen modes. We observed that the proposed optimal decision tree is effective in predicting the state probability distribution of unseen models.

• 전기의세계
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• v.22 no.3
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• pp.49-62
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• 1973

An algorithm for the state estimation and identification of multivariable nonlinear systems with noisy nonlinear observation has been investigated on the basis of the multidimensional Hermitian expansion for the a posteriori probability densities of the predicted observation, the predicted state and the observation conditioned by the state. A new approach for construction of this sequential nonlinear estimator, retaining up to the second order term of the observation error, has been developed, along with the approximation of nonlinear system functions, truncating at the second term. The estimation of the unknown parameters has been established by extending the state estimation technique, regarding the parameters as another state variables. The results of investigation indicate the feasibility of the schemes presented in this paper.