• Journal of Korea Water Resources Association
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• v.45 no.8
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• pp.827-837
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• 2012

The estimation of the rainfall quantile is of great importance in designing hydrologic structures. Conventionally, the rainfall quantile is estimated by univariate frequency analysis with an appropriate probability distribution. There is a limitation in which duration of rainfall is restrictive. To overcome this limitation, bivariate frequency analysis by using 3 copula models is performed in this study. Annual maximum rainfall events in 5 stations are used for frequency analysis and rainfall depth and duration are used as random variables. Gumbel (GUM), generalized logistic (GLO) distributions are applied for rainfall depth and generalized extreme value (GEV), GUM, GLO distributions are applied for rainfall duration. Copula models used in this study are Frank, Joe, and Gumbel-Hougaard models. Maximum pseudo-likelihood estimation method is used to estimate the parameter of copula, and the method of probability weighted moments is used to estimate the parameters of marginal distributions. Rainfall quantile from this procedure is compared with various marginal distributions and copula models. As a result, in change of marginal distribution, distribution of duration does not significantly affect on rainfall quantile. There are slight differences depending on the distribution of rainfall depth. In the case which the marginal distribution of rainfall depth is GUM, there is more significantly increasing along the return period than GLO. Comparing with rainfall quantiles from each copula model, Joe and Gumbel-Hougaard models show similar trend while Frank model shows rapidly increasing trend with increment of return period.

• International Journal of Reliability and Applications
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• v.11 no.1
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• pp.41-53
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• 2010

In the present paper we develop a mathematical model that facilitates the calculation of reliability of a complex repairable system having three units namely super priority, priority and ordinary. The system is analyzed with the application of Gumbel Hougaard copula when different types of repair possible at a particular state due to deliberate failure. Various reliability measures such as reliability, MTTF and profit function have been evaluated by using supplementary variable and Laplace transform techniques.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.183-183
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• 2015

수공구조물 설계 시 중요한 요소 중 하나인 확률강우량은 일반적으로 고정지속기간별 강우량에 대하여 일변량 빈도해석을 수행하고 가장 적절한 분포형을 선택하는 지점빈도해석의 과정을 거친다. 그러나 일변량 빈도해석을 수행하기 위해서는 지속시간을 고정하고 강우량의 변화로만 해석해야 단점이 있으며 이를 보완하기 위해 본 연구에서는 다변량 확률모형인 copula 모형을 이용하여 이변량 빈도해석을 수행하였다. 확률변수로는 강우량과 지속기간(hr)을 사용하였고, 주변분포형으로 강수량 - Gumbel (GUM), generalized logistic (GLO) 분포형, 지속기간(hr) - generalized extreme value (GEV), GUM, GLO 분포형을 사용하였으며, copula 모형은 Gumbel-Hougaard 모형을 이용하였다. 주변분포형의 매개변수는 일반적으로 가장 많이 사용하는 확률가중모멘트법을 이용하여 추정하였으며, copula 모형의 매개변수는 maximum pseudolikelihood(MPL) 방법을 사용하였다. 이를 통해 얻어진 이변량 빈도해석의 확률강우량 결과와 기존 지점빈도해석의 결과를 비교하였다.

• International Journal of Reliability and Applications
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• v.11 no.2
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• pp.107-122
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• 2010

This paper deals with the reliability analysis of a complex system, which consists of two subsystems A and B connected in series. Subsystem A has only one unit and B has two units $B_1$ and $B_2$. Marked process has been applied to model the complex system. Present reliability model incorporated two repairmen: supervisor and novice to repair the failed units. Supervisor is always there and the novice remains in vacation and is called for repair as per demand. The repair rates for supervisor and novice follow general and exponential distributions respectively and the failure time for both the subsystems follows exponential distribution. The model is analyzed under "Head of line repair discipline". By employing supplementary variable technique, Laplace transformation and Gumbel-Hougaard family of copula various transition state probabilities, reliability, availability and cost analysis have been obtained along with the steady state behaviour of the system. At the end some special cases of the system have been taken.

• International Journal of Reliability and Applications
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• v.12 no.1
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• pp.15-39
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• 2011

This paper deals with the reliability analysis of a complex system with three possibilities at the time of repair. The considered system consists of two subsystems A and Bin series configuration (1-out-of-2: F). Subsystem A has n units which are connected in series whereas subsystem B consists of n units in parallel configuration. The configuration of subsystem A is of 1-out-of-n: F whereas subsystem B is of k-out-of-n: D and k+1-out-of-n: F nature. System has three states: Good, degraded and failed. Supplementary variable technique has been used for mathematical formulation of the model. Laplace transform is being utilized to solve the mathematical equation. Reliability, Availability, M.T.T.F., Busy Period and Cost effectiveness of the system have been computed. The repairs from state $S_7$ to $S_0$, $S_8$ to $S_0$, $S_9$ to $S_0$ and $S_{11}$ to $S_0$ have two types namely exponential and general. Joint probability distribution of repair rate from $S_7$ to $S_0$, $S_8$ to $S_0$, $S_9$ to $S_0$ and $S_{11}$ to $S_0$ is computed by Gumbel-Hougaard family of copula. Some particular cases of the system have also been derived to see the practical importance of the model.

• Proceedings of the Korea Water Resources Association Conference
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• 2011.05a
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• pp.376-380
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• 2011

강우사상은 강우량, 지속기간, 강우강도 등의 특성으로 표현될 수 있으며 이런 인자들을 같이 고려할수록 그 현상을 보다 종합적으로 표현할 수 있다. 하지만 현재 일반적으로 이루어지는 일변량 빈도해석절차에서는 지속기간을 고정시켜놓고 각 지속시간에 따른 결과만을 도출해 낼 수 있기 때문에 지속기간에 대해 제약적이고 입력자료에 존재하지 않는 지속기간에 대한 결과를 얻기가 어렵다. Copula모델은 두 일변량 분포형을 다변량 분포형으로 연결하여 주는 모델이다. 따라서 강우량과 지속기간을 변수로 사용하면 Copula모델을 통한 이변량 강우빈도해석은 보편적으로 이루어지고 있는 일변량 지점빈도해석보다 지속기간에 대해 유연한 결과를 나타낼 수 있다. 즉, 강우와 지속기간이 동시에 변수로 사용되기 때문에 임의의 지속기간이나 강우에 대해서 확률강우량 및 확률지속기간을 얻을 수 있다. 본 연구에서는 서울지점을 대상으로 1961∼2009년 동안 발생한 강우사상 중 각 년도에서 최대강우량이 발생한 사상을 추출하여 입력자료로 사용하였다. Copula 모형은 Gumbel-Hougaard, Frank, Joe, Clayton, Galambos등 총 5개의 모델을 적용하였고 각 Copula의 매개변수는 준모수방법인 maximum pseudolikelihood estimator를 이용하여 추정하였다.

• International Journal of Internet, Broadcasting and Communication
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• v.15 no.4
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• pp.279-293
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• 2023

This study investigates network effects to measure how strongly the early adopters affect the brand choice of the potential consumer. By using the Gumbel-Hougaard (GH) copula, this study checks the magnitude of network effects varied from country to country. To consider consumer heterogeneity and network effects in the growth market, this study proposes the multi-brand Gamma/Shifted-Gompertz (m-G/SG) model based on the GH copula. Out of eighteen Western European cellular phone market data and South Korea smartphone data sets, the m-G/SG model provides an improvement in the estimation accuracy over the Libai, Muller, and Peres model. The results show that network effects enhance (i) the polarization of brand choice probabilities as time elapses; (ii) the dominance of the more preferred and the earlier entered brand; and (iii) the deceleration of category-level diffusion. Potential followers can analyze their relationship with earlier entrants through the m-G/SG model and also establish an optimal market entry strategy.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.420-420
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• 2015

일반적으로 호우사상의 특성은 강우강도, 지속기간, 총 강우량으로 정량화된다. 주어진 호우 사상에 대한 재현기간은 보통 위 세 개 변량 중 두 개의 변량에 대한 이변량 빈도해석을 통해 결정된다. 따라서 3 가지의 다른 빈도해석이 가능하며, 원칙적으로 이 세 가지 빈도해석 결과는 같아야 한다. 그러나, 문제는 어떤 변량을 선택하느냐에 따라 빈도해석 결과가 달라진다는 점이다. 본 연구에서는 이 문제를 해결하고자 다음과 같은 연구를 수행하였다. 첫 번째로 1961-2010년에 관측된 서울지점 연최대치 호우사상에 대한 이변량 빈도해석을 수행하였다. 이변량 빈도해석은 Frank, Gumbel-Hougaard, Clayton, ali-Mikhail-Haq copula 모형을 이용하여 수행하였으며, 모형의 매개변수는 두 변량의 상관관계를 나타내는 Kendall's tau를 이용하여 추정하였다. 호우사상에 대한 이변량 빈도해석을 수행한 결과, 결과가 일관되지 않고 고려한 두 가지 강우변량에 따라 다르게 나타난 것을 확인하였다. 두 번째로 보편적인 강우강도식을 이용하여 호우사상을 이루는 세변량의 특성을 분석하였다. 본 연구에서 고려한 강우강도식은 Talbot 형, Sherman 형, Japanese 형, Grunsky 형이다. 일반적인 강우강도식에서 지속기간과 강우강도의 관계는 I~t^a와 같이 나타나며, 이 때 a의 범위는 -0.5부터 -1까지 값으로 정해진다. 마지막으로, 호우사상을 이루는 세 변량의 상관관계를 이용하여 가장 적절한 이변량 빈도해석결과를 도출하는 강우 변량의 조합을 결정하였다. 결론적으로, 본 연구에서는 지속기간과 강우강도를 copula 모형을 이용한 이변량 빈도 해석의 가장 적절한 것으로 판단되었다.

• The Pure and Applied Mathematics
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• v.27 no.3
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• pp.137-155
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• 2020

Redundancy is commonly employed to improve system reliability. In most situations, components in the standby configurations are assumed statistically similar but independent. In many realistic models, all parts in standby are not treated as identical as they have different failure possibilities. The operational structure of the system has subsystem-1 with five identical components working under 2-out-of-5: G; policy, and the subsystem-2 has two units and functioning under 1-out-of-2: G; policy. Failure rates of units of subsystems are constant and assumed to follow an exponential distribution. Computed results give a new aspect to the scientific community to adopt multi-dimension repair in the form of the copula.

• International Journal of Reliability and Applications
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• v.13 no.1
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• pp.1-17
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• 2012

This Paper deals with the stochastic behavior and failure analysis of a Viscose Staple Fibre Plant which produces fibre for making clothes. The fibre making plant is a complex system with various subsystems as: Vendor (supplies Charcoal and Sulphur, raw materials for the process), Carbon di sulphide Plant, Acid Plant, Pulp Plant and Processing Plant. The considered system can completely fail due to failure of any of the subsystems. The Carbon di Sulphide Plant can fail in two different ways, due to lack of Sulphur or Charcoal. Processing Plant has the configuration 5-out-of-10: d and 6-out-of-10: f. It is also assumed that the system can fail due to workers strike and catastrophic failure. All failures follow exponential time distribution whereas all repairs follow general time distribution. Preventive Maintenance policy has been applied to reduce the failure in the system. Various reliability characteristics such as transition state probabilities, steady state behavior, reliability, availability, M.T.T.F and the cost analysis have been obtained using supplementary variable technique and Gumbel-Hougaard copula methodology.