• Journal of the Korean Statistical Society
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• v.27 no.4
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• pp.459-469
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• 1998

Balanced half sample method is a simple variance estimation method for complex sampling designs. Since it is simple and flexible, it has been widely used in large scale sample surveys. However, the usual BHS method overestimate the true variance in without replacement sampling and two-stage cluster sampling. Focusing on this point , we proposed an unbiased BHS variance estimator in a stratified two-stage cluster sampling and then described an implementation method of the proposed estimator. Finally, partially BHS design is explained as a tool of reducing the number of replications of the proposed estimator.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.305-313
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• 2002

Regarding to inference about a scalar measure of internal scatter of Ρ-variate normal population, this paper considers an interval estimation of the generalized variance, │$\Sigma$│. Due to complicate sampling distribution, fully parametric frequentist approach for the interval estimation is not available and thus Bayesian method is pursued to calculate the highest probability density (HPD) interval for the generalized variance. It is seen that the marginal posterior distribution of the generalized variance is intractable, and hence a weighted Monte Carlo method, a variant of Chen and Shao (1999) method, is developed to calculate the HPD interval of the generalized variance. Necessary theories involved in the method and computation are provided. Finally, a simulation study is given to illustrate and examine the proposed method.

• Journal of the Korean Data and Information Science Society
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• v.22 no.3
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• pp.381-387
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• 2011

This paper suggests a method for estimating components of variance in one-factor random model. Estimates of variance components are given by the method of moments. Sums of squares due to variance sources are obtained by projections. This paper also shows how to use eigenvalues for getting the coefficients of variance components in the expression of the expectations of the mean squares. The suggested method shows easier and faster than the method of Harley's synthesis.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.6 no.8
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• pp.81-91
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• 1983

In this study the methods of the overhead standard setting and the overhead variance analysis, which raise problems especially in business practice in case that small businesses introduce the standard cost accounting system, were examined by hypothetical examples. As the result of this study small businesses are advised to take the following in setting the overhead cost. (1) To divide the mixed cost into variable overhead and fixed overhead, it is desirable to take Beast square method. (2) In setting the overhead standard, it is desirable to fake the flexible budget system and to make a budget by the inspection method, after dividing the overhead into variable overhead and fixed overhead. (3) After dividing the overhead variance into variable overhead variance and fixed overhead variance, it is desirable to analyze them as follows. (A) Variable overhead variance is analyzed into spending variance and efficiency variance. (B) Fixed overhead valiance is analyzed into budget variance and denominator variance.

• Nuclear Engineering and Technology
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• v.51 no.4
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• pp.954-962
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• 2019

It is well known that the variance of tally is biased in a Monte Carlo calculation based on the power iteration method. Several studies have been conducted to estimate the real variance. Among them, the batch method, which was proposed by Gelbard and Prael, has been utilized actively in many Monte Carlo codes because the method is straightforward, and it is easy to implement the method in the codes. However, there is a problem when utilizing the batch method because the estimated variance varies depending on batch size. Often, the appropriate batch size is not realized before the completion of several Monte Carlo calculations. This study recognizes this shortcoming and addresses it by permitting selection of an appropriate batch size.

• Journal of Magnetics
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• v.19 no.4
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• pp.385-392
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• 2014

Uncertainties in loads, materials and manufacturing quality must be considered during electromagnetic devices design. This paper presents an effective methodology for robust optimization design based on the variance decomposition in order to keep higher accuracy of the robustness prediction. Sobol' theory is employed to estimate the response variance under some specific tolerance in design variables. Then, an optimal design is obtained by adding a criterion of response variance upon typical optimization problems as a constraint of the optimization. The main contribution of this paper is that the proposed method applies the variance decomposition to obtain a more accurate variance of the response, as well save the computational cost. The performance and robustness of the proposed algorithms are investigated through a numerical experiment with both an analytic function and the TEAM 22 problem.

• Journal of the Korean Statistical Society
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• v.18 no.2
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• pp.118-124
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• 1989

In the one-way random effect model, we often estimate the variance components by the ANOVA method and then estimate the population mean. Whe there are only two distint group sizes, the conventional mean estimator is represented as a weighted average of two normal means with weights being the function of variance component estimators. In this paper, we will study a method which can compute the exact variance of the mean estimator when we set the negative variance component estimate to zero.

• Journal of Korean Society for Quality Management
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• v.33 no.3
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• pp.149-155
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• 2005

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

• Proceedings of the Korean Society for Quality Management Conference
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• 2006.04a
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• pp.135-141
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• 2006

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

• Earthquakes and Structures
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• v.23 no.2
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• pp.115-128
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• 2022

One common method to select input ground motions to predict dynamic behavior of structures subjected to seismic excitation requires spectral acceleration (S_a) match target mean response spectrum. However, dispersion of ground motions, which explicitly affects the structural response, is rarely discussed in this method. Generally, selecting ground motions matching target mean and variance has been utilized as an appropriate method to predict reliable seismic response. The goal of this paper is to investigate the impact of target spectra variance of ground motions on structural seismic response. Two sets of ground motions with different target variances (zero variance and minimum variance larger than inherent variance of the target spectrum) are selected as input to two different structures. Structural responses at different heights are compared, in terms of peak, mean and dispersion. Results show that increase of target spectra variance tends to increase peak floor acceleration, peak deformation and dispersions of response of interest remarkably. To short-period structures, dispersion increase ratios of seismic response are close to that of S_a of input ground motions at the first period. To long-period structures, dispersions of floor acceleration and floor response spectra increase more significantly at the bottom, while dispersion increase ratios of IDR and deformation are close to that of S_a of input ground motions at the first period. This study could further provide useful information on selecting appropriate ground motion to predict seismic behavior of different types of structures.