• Communications for Statistical Applications and Methods
• /
• 제11권2호
• /
• pp.297-311
• /
• 2004

In the sample survey for a highly skewed population, stratum jumpers often occur. Stratum jumpers are units having large discrepancies between a stratification variable and a study variable. We propose two models for stratum jumpers: a multiplicative model and a random replacement model. We also consider the modification of the L-H stratification algorithm such that we apply the previous models to L-H algorithm in determination of the sample sizes and the stratum boundaries. We evaluate the performances of the new stratification algorithms using real data. The result shows that L-H algorithm for the random replacement model outperforms other algorithms since the estimator has the least coefficient of variation.

• 응용통계연구
• /
• 제22권6호
• /
• pp.1277-1287
• /
• 2009

For stratifying skewed populations, the Lavall$\acute{e}$e-Hidiroglou(LH) algorithm is often considered to have a take-all stratum with the largest units and some take-some strata with the middle-size and small units. Related to its iterative nature have been reported some numerical difficulties such as the dependency of the ultimate stratum boundaries to a choice of initial boundaries and the slow convergence to locally-optimum boundaries. The geometric stratification has been recently proposed to provide initial boundaries that can avoid such numerical difficulties in implementing the LH algorithm. Since the geometric stratification does not pursuit the optimization but the equalization of the stratum CVs, the corresponding stratum boundaries may not be (near) optimal. This paper revisits these issues concerning convergence and near-optimality of optimal stratification algorithms using artificial numerical examples. We also discuss the formation of the strata and the sample allocation under the optimization process and some aspects related to discontinuity arisen from the finiteness of both population and sample as well.

• Communications for Statistical Applications and Methods
• /
• 제20권2호
• /
• pp.97-105
• /
• 2013

Stratification (among other applications) is a popular technique used in survey practice to improve the accuracy of estimators. Its full potential benefit can be gained by the effective use of auxiliary variables in stratification related to survey variables. This paper focuses on the problem of stratum formation when multiple stratification variables are available. We first review a variance reduction strategy in the case of univariate stratification. We then discuss its use for multivariate situations in convenient and efficient ways using three methods: compromised measures of size, principal components analysis and a K-means clustering algorithm. We also consider three types of compromising factors to data when using these three methods. Finally, we compare their efficiency using data from MU281 Swedish municipality population.

• Nuclear Engineering and Technology
• /
• 제32권2호
• /
• pp.169-179
• /
• 2000

A detailed numerical analysis of the evolution of thermal stratification in a curved piping system in a nuclear power plant is performed. A finite volume based thermal-hydraulic computer code has been developed employing a body-fitted, non-orthogonal curvilinear coordinate for this purpose. The cell-centered, non-staggered grid arrangement is adopted and the resulting checkerboard pressure oscillation is prevented by the application of momentum interpolation method. The SIMPLE algorithm is employed for the pressure and velocity coupling, and the convection terms are approximated by a higher-order bounded scheme. The thermal-hydraulic computer code developed in the present study has been applied to the analysis of thermal stratification in a curved duct and some of the predicted results are compared with the available experimental data. It is shown that the predicted results agree fairly well with the experimental measurements and the transient formation of thermal stratification in a curved duct is also well predicted.

• 대한기계학회논문집B
• /
• 제21권5호
• /
• pp.670-678
• /
• 1997

A method to mitigate the thermal stratification phenomenon of pressurizer surge line is proposed by heating bottom outside of horizontal pipe. Unsteady two dimensional model has been used to numerically investigate an effect of heating the bottom of pipe. The dimensionless governing equations are solved by using the control volume formulation and SIMPLE algorithm. Temperature and streamline profiles of fluids and pipe walls with time are compared with the previous study result. The numerical result of this study shows that the outside heating can relaxate the thermal stratification flow of the pressurizer surge line. Maximum dimensionless temperature difference between hot and cold sections of the pipe inner wall which causes thermal stratification was reduced from 0.514 to 0.424 at dimensionless time 1, 632 and 1, 500 respectively.

• 설비공학논문집
• /
• 제16권3호
• /
• pp.211-217
• /
• 2004

Effect of a solid insert on thermal stratification in the natural convection enclosure is numerically investigated. The enclosure consists of two differently heated vertical walls and two adiabatic horizontal walls. A solid insert is located in the middle of the enclosure. The non-dimensional governing equations are solved by using the SIMPLER algorithm. The computations are carried out with the variations of thermal conductivity, width and height of the solid insert. The Prandtl number of the fluid in an enclosure is fixed at Pr=0.71, Two cases of Rayleigh number are considered in the present study, i.e., Ra:10$^3$ and 10$^{6}$ . The thermal stratification attenuates as thermal conductivity, width, and height of the solid insert are increased. As the thermal conductivity ratio of a solid insert to fluid increases beyond (equation omitted)10$^3$, the thermal stratification ratio shows an asymptotic value.

• 한국조사연구학회지:조사연구
• /
• 제9권1호
• /
• pp.69-85
• /
• 2008

층화는 표본설계 단계에서 예비정보를 활용하는 대표적인 방법으로 대부분의 전국 단위의 표본설계에서 널리 활용된다. 층화의 효율을 극대화시키기 위해서는 조사목적에 부합되는 적절한 층화변수를 선택하는 것이 매우 중요하다. 하나의 표본을 통해 여러 개의 관심변수를 동시에 조사하는 다목적조사에서 다변량 층화변수가 있을 때 층화 전략을 세우는 것은 매우 복잡한 양상을 띤다. 본 연구에서는 관심변수의 수가 매우 많은 다목적조사를 위한 층화전략을 다룬다. 층화를 위해 구체적으로 사용하는 통계적 도구는 요인분석과 군집분석 등의 다변량 통계기법인데, 먼저 요인분석을 통해 적절한 층화변수들을 선정한 후 그 변수들을 이용하여 군집분석을 통해 층화를 하는 전략을 소개한다. 본 연구에서는 구체적으로 해양수산부의 어업비계통생산량조사를 위한 표본설계에서의 층화과정을 다룬다.

• 대한기계학회논문집B
• /
• 제20권4호
• /
• pp.1449-1457
• /
• 1996

In this paper, the unsteady two dimensional model for the thermal stratification in the pressurizer surge line of PWR plant has been proposed to numerically investigate the heat transfer and flow characteristics. The dimensionless governing equations are solved by using the Control Volume Formulation and SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. The temperature profile of fluids and pipe wall with time are shown when the thermal stratification occurs in the horizontal pipe. The numerical result shows that the maximum dimensionless temperature difference is about O.514 between hot and cold section of pipe wall at dimensionless time 1,632.

• Nuclear Engineering and Technology
• /
• 제30권6호
• /
• pp.581-591
• /
• 1998

Numerical analysis was peformed for the two-dimensional turbulent natural convection for a long horizontal line with different end temperatures. The turbulent model has been applied a standard k-$\varepsilon$ two equation model of turbulence similar to that the proposed by the Launder and Spalding. The dimensionless governing equations are solved by using SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm which is developed using control volumes and staggered grids. The numerical results are verified by comparison with the operating PWR test data. The analysis focuses on the effects of variation of the heat transfer rates at the pipe surface, the thermal conductivities of the pipe material and the thickness of the pipe wall on the thermal stratification. The results show that the heat transfer rate at the pipe surface is the controlling parameter for mitigating of thermal stratification in the long horizontal pipe. A significant reduction and disappearance of the thermal stratification phenomenon is observed at the Biot number of 4.82$\times$10$^{-1}$ . The results also show that the increment of the thermal conductivity and thickness of the wall weakens a little the thermal stratification and somewhat reduces temperature gradient of y-direction in the pipe wall. These effects are however minor, when compared with those due to the variation of the heat transfer rates at the surface of the pipe wall.

• 한국원자력학회:학술대회논문집
• /
• 한국원자력학회 1997년도 춘계학술발표회논문집(1)
• /
• pp.304-309
• /
• 1997

A method to mitigate the thermal stratification flow of a horizontal pipe line is proposed by heating external bottom of the pipe with electrical heat tracing. Unsteady two dimensional model has been used to numerically investigate an effect of the external Denting to the thermally stratified flow. The dimensionless governing equations are solved by using the control volume formulation and SIMPLE algorithm. Temperature distribution, streamline profile and Nusselt numbers of fluids and pipe walls with time are analyzed in case of externally heating condition. no numerical result of this study shows that the maximum dimensionless temperature difference between the hot and the cold sections of pipe inner wall is 0.424 at dimensionless time 1,500 ann the thermal stratification phenomena is disappeared at about dimensionless time 9,000. This result means that external heat tracing can mitigate the thermal stratification phenomena by lessening $\Delta$ $T_{ma}$ about 0.1 and shortening the dimensionless time about 132 in comparison with no external heat tracing.rnal heat tracing.