• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권3호
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• pp.153-160
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• 2008

A size-biased Poisson distribution is defined. Its characterization by using a recurrence relation for first order negative moment of the distribution is obtained. Different estimation methods for the parameter of the model are also discussed. R-Software has been used for making a comparison among the three different estimation methods.

• 산업공학
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• 제17권1호
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• pp.1-12
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• 2004

In a modern semiconductor device manufacturing industry, statistical bin limits on wafer level test bin data are used for minimizing value added to defective product as well as protecting end customers from potential quality and reliability excursion. Most wafer level test bin data show skewed distributions. By Monte Carlo simulation, this paper evaluates methods and sample size effect regarding determination of statistical bin limits. In the simulation, it is assumed that wafer level test bin data follow the Poisson distribution. Hence, typical shapes of the data distribution can be specified in terms of the distribution's parameter. This study examines three different methods; 1) percentile based methodology; 2) data transformation; and 3) Poisson model fitting. The mean square error is adopted as a performance measure for each simulation scenario. Then, a case study is presented. Results show that the percentile and transformation based methods give more stable statistical bin limits associated with the real dataset. However, with highly skewed distributions, the transformation based method should be used with caution in determining statistical bin limits. When the data are well fitted to a certain probability distribution, the model fitting approach can be used in the determination. As for the sample size effect, the mean square error seems to reduce exponentially according to the sample size.

• 응용통계연구
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• 제19권3호
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• pp.505-519
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• 2006

셀 수 있는 이산 자료(discrete count data)에 대한 분석은 여러 분야에서 활용되고 있지만 영(zero)을 과도하게 포함하고 있는 영과잉 자료는 자료의 성격상 포아송 분포를 따르지 못할 때가 있어 분석에 어려움이 따른다. Zero-Inflated Poisson(ZIP)모형은 이런 어려움을 극복하기 위하여 영에 대한 점확률을 가지는 분포와 포아송 분포를 합성하여 과도한 영과 영이 아닌 자료를 설명하는 모형이다. 설명 변수가 존재할 때는 포아송 분포 부분에서 반응변수의 평균과 공변량사이에 로그선형 연결함수를 사용한 Zero-Inflated Poisson Regression(ZIPR)모형이 사용될 수 있다. 본 논문에서는 Markov Chain Monte Carlo 기법을 이용한 ZIPR모형의 베이지안 추론방법을 제안하고, 이를 실제 구강위생 자료에 적용하며 다른 모형들과 비교한다. 그 결과 베이지안 추론 방법을 적용한 영과잉 모형의 추정오차가 다른 모형들의 추정오차보다 작았고, 예측치가 더 정확했다는 점에서 우수함을 알 수 있었다.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2003년도 추계학술대회 논문집 Vol.16
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• pp.128-131
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• 2003

The number of grain is determined based on Poisson distribution in respectively different active channel and it is converted to grain size which affects to the mobility and threshold voltage. the acquired data is applied to the SPICE for observing the variation of I-V characteristic with several channel lengths. we can confirm the effect on device.

• Communications for Statistical Applications and Methods
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• 제31권1호
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• pp.55-64
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• 2024

In this study, we consider the sample size determination problem for clustered count data with many zeros. In general, zero-inflated Poisson and binomial models are commonly used for zero-inflated data; however, in real data the assumptions that should be satisfied when using each model might be violated. We calculate the required sample size based on a discrete Weibull regression model that can handle both underdispersed and overdispersed data types. We use the Monte Carlo simulation to compute the required sample size. With our proposed method, a unified model with a low failure risk can be used to cope with the dispersed data type and handle data with many zeros, which appear in groups or clusters sharing a common variation source. A simulation study shows that our proposed method provides accurate results, revealing that the sample size is affected by the distribution skewness, covariance structure of covariates, and amount of zeros. We apply our method to the pancreas disorder length of the stay data collected from Western Australia.

• 한국경영과학회지
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• 제31권1호
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• pp.15-24
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• 2006

In simulation input modeling, it is important to identify a probability distribution to represent the input process of interest. In this paper, an appropriate sample size is determined for parameter estimation associated with some typical probability distributions frequently encountered in simulation input modeling. For this purpose, a statistical measure is proposed to evaluate the effect of sample size on the precision as well as the accuracy related to the parameter estimation, square rooted mean square error to parameter ratio. Based on this evaluation measure, this sample size effect can be not only analyzed dimensionlessly against parameter's unit but also scaled regardless of parameter's magnitude. In the Monte Carlo simulation experiments, three continuous and one discrete probability distributions are investigated such as ; 1) exponential ; 2) gamma ; 3) normal ; and 4) poisson. The parameter's magnitudes tested are designed in order to represent distinct skewness respectively. Results show that ; 1) the evaluation measure drastically improves until the sample size approaches around 200 ; 2) up to the sample size about 400, the improvement continues but becomes ineffective ; and 3) plots of the evaluation measure have a similar plateau pattern beyond the sample size of 400. A case study with real datasets presents for verifying the experimental results.

• 전자공학회논문지A
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• 제32A권8호
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• pp.31-38
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• 1995

In this paper, we consider the leaky bucket parameter dimensioning problem in the presence of the cell delay variation(CDV) which arises at the customer premises network dud to the multiplexing with other traffic streams. We consider an ATM multiplexer in which a single CBR stream and several heterogeneous VBR traffic streams are multiplexed. Choosing an MMPP model for the bursty traffic streams, we derive an (MMPP+DD)/D/1/K queueing model for the evaluation of the CDV experienced by the CBR stream. We first evaluate the equilibrium queue length distribution embedded at tagged-cell arrival-time instants, based on whcih we calcuate the inter-cell time distribution and the distribution kof the number of tagged-cell departures in an arbitrary interval. Then we apply the analysis to the dimensionging problem of the leaky bucket parameters, examining how the employed traffic model affects the determination of the bucket size. Through numerical examples, we confirm that the Poisson traffic model can underestimate the bucket size, thus causing a considerable blocking probability for compliant use cells while the MMPP model can optimally design the bucket size which keeps the blocking probability under the target value.

• Genomics & Informatics
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• 제19권3호
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• pp.34.1-34.6
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• 2021

Digital PCR (dPCR) is the third-generation PCR that enables real-time absolute quantification without reference materials. Recently, global diagnosis companies have developed new dPCR equipment. In line with the development, the Lab On An Array (LOAA) dPCR analyzer (Optolane) was launched last year. The LOAA dPCR is a semiconductor chip-based separation PCR type equipment. The LOAA dPCR includes Micro Electro Mechanical System that can be injected by partitioning the target gene into 56 to 20,000 wells. The amount of target gene per wells is digitized to 0 or 1 as the number of well gradually increases to 20,000 wells because its principle follows Poisson distribution, which allows the LOAA dPCR to perform precise absolute quantification. LOAA determined region of interest first prior to dPCR operation. To exclude invalid wells for the quantification, the LOAA dPCR has applied various filtering methods using brightness, slope, baseline, and noise filters. As the coronavirus disease 2019 has now spread around the world, needs for diagnostic equipment of point of care testing (POCT) are increasing. The LOAA dPCR is expected to be suitable for POCT diagnosis due to its compact size and high accuracy. Here, we describe the quantitative principle of the LOAA dPCR and suggest that it can be applied to various fields.

• 한국정보통신학회논문지
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• 제14권2호
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• pp.321-328
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• 2010

본 논문은 수동형 RFID 시스템에서 리더 충돌을 회피시킬 수 있는 코디네이터 기반 TDMA 프로토콜을 제시한다. 제시한 프로토콜에서는 코디네이터가 포아송 분포로 네트워크에 참여하는 리더에게 슬롯을 효율적으로 할당하고 관리하여 빈 슬롯 발생을 최소화하며 프레임 크기 제한을 통해서 네트워크에 참여하는 리더의 대기 시간을 줄 일 수 있다. 제안된 프로토콜은 이동식 및 고정형 RFID 네트워크 형태로 구현이 가능하며 이를 위한 프레임 및 슬롯구조를 제시한다. 모의실험을 통해서 제시한 프로토콜이 성공적으로 동작하며 특히 프레임 크기의 한계 값과 네트워크에 참여하는 리더의 통계적 분포가 총 슬롯 및 리더의 평균대기 시간에 결정적인 역할을 함을 보인다.

• Steel and Composite Structures
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• 제33권3호
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• pp.463-472
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• 2019

Initial thermo-elastic and steady state creep deformation of a rotating functionally graded simple blade is studied using first-order shear deformation theory. A variable thickness model for cantilever beam has been considered. The blade geometry and loading are defined as functions of length so that one can define his own blade profile and loading using any arbitrary function. The blade is subjected to a transverse distributed load, an inertia body force due to rotation and a distributed temperature field due to a thermal gradient between the tip and the root. All mechanical and thermal properties except Poisson's ratio are assumed to be longitudinally variable based on the volume fraction of reinforcement. The creep behaviour is modelled by Norton's law. Considering creep strains in stress strain relation, Prandtl-Reuss relations, Norton' law and effective stress relation differential equation in term of effective creep strain is established. This differential equation is solved numerically. By effective creep strain, steady state stresses and deflections are obtained. It is concluded that reinforcement particle size and form of distribution of reinforcement has significant effect on the steady state creep behavior of the blade.