• 대한산업공학회지
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• 제38권1호
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• pp.25-30
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• 2012

Desirability approaches have been proposed to find an optimum of multiple response problem. The existing desirability approaches use either of mean or min of individual desirability in aggregation of multiple responses. However, in order to find an optimum having high mean and low dispersion among individual desirability, the dispersion needs to be simultaneously considered with its mean. This study proposes bias and variance (BV) method which aggregates bias (ideal target-mean) and variance of individual desirability in multiple response optimization. The proposed BV method was applied to an example to evaluate its usefulness by comparing with existing methods. Evaluation results showed that the solution of BV method was a fairly good compared with DS (Derringer and Suich, 1980) and KL (Kim and Lin, 2000) methods. The BV method can be utilized to multiple response surface problems when decision makers want to find an optimum having high mean and low variance among responses.

• 품질경영학회지
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• 제22권4호
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• pp.1-12
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• 1994

각각의 설계인자들의 실험조건에서 얻어지는 특성치들의 분산은 평균에 영향을 받는다. 많은 경우에 평균이 커짐에 따라서 분산이 커지는 경향이 있다. 다구찌가 산포제어인자를 찾기 위해서 제시한 SN 비인 $(SN)_i$ = 10 log ($\bar{y}_{i}^{2}/s_{i}^{2}$) 은 분산이 평균의 제곱에 비례하여 커지는 경우이다. 그런데 분산이 평균의 제곱보다 더 느리게 또는 더 빠르게 커질 수도 있기 때문에 이 논문에서는 간단한 자료분석적 기법에 의해서 그 관계를 추측하여, 합당한 SN 비를 사용할 것을 제시하였고, 평균조정인자를 찾기위한 통계량인 감도 $(S)_i$ 의 통계적 성질들을 논의하였다.

• Journal of the Korean Statistical Society
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• 제26권2호
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• pp.199-210
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• 1997

Using regression methods based on quasi-likelihood equation, one only needs to specify the conditional mean and variance functions for the response variable in the analysis. In this paper, an omnibus lack-of-fit test is proposed to test the validity of these two functions. Our test is consistent against the alternative under which either the mean or the variance is not the one specified in the null hypothesis. The large-sample null distribution of our test statistics can be approximated through simulations. Extensive numerical studies are performed to demonstrate that the new test preserves the prescribed type I error probability. Power comparisons are conducted to show the advantage of the new proposal.

• Journal of the Korean Data and Information Science Society
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• 제28권2호
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• pp.443-449
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• 2017

Estimation of population proportion like the distribution rate of LED TV and the prevalence of a disease are often estimated based on survey sample data. Population proportion is generally considered as a special form of population mean. In complex sampling like stratified multistage sampling with unequal probability sampling, the denominator of mean may be random variable and it is estimated like ratio estimator. In this research, we examined the estimation of distribution rate based on stratified multistage sampling, and determined some numerical outcomes using stratified random sample data with about 25% of missing observations. In the data used for this research, the survey weight was determined by deterministic way. So, the weights are not random variable, and the population distribution rate and its variance estimator can be estimated like population mean estimation. When the weights are not random variable, if one estimates the variance of proportion estimator using ratio method, then the variances may be inflated. Therefore, in estimating variance for population proportion, we need to examine the structure of data and survey design before making any decision for estimation methods.

• Korean Journal of Hydrosciences
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• 제6권
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• pp.13-22
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• 1995

The augmenting hydrologic data using a correlation procedure has been used to improve the estimates of the mean and variance at the site of interest with short record when one or more near by sites with longer records are available. The variance of the unbiased maximum likelihood estimator of $ derived by Moran based on the multivariate normal distribytion is modified into the form of Matalas and Jacobs for the biveriate normal distribution to get the critical minimum values of the multiple correlation coefficient which give the improvement for estimating the variance at the site of interest. Those values are tabulated for various lengths of short records and the number of sites.

• 인터넷정보학회논문지
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• 제13권3호
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• pp.61-73
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• 2012

본 논문에서는 영상의 밝기 평균과 분산을 이용하여 영상의 엔트로피를 최대화하는 히스토그램 명세화 기반의 영상 향상 기법을 제안한다. 제안 방법은 히스토그램 명세화 과정에서 입력 히스토그램과 목적 히스토그램 모두를 가우시안 분포로 모델링한다. 이 과정에서 입력 가우시안 분포의 평균과 분산은 입력영상의 밝기 평균값과 분산을 각각 그대로 사용한다. 목적 가우시안 분포의 평균도 입력영상의 밝기 평균값을 사용하지만, 분산은 출력 영상의 엔트로피가 최대화되는 분산을 결정하여 사용한다. 다양한 영상에 대한 실험 결과에 의하면, 기존 방법들에 비해 제안 방법은 영상의 평균 밝기를 잘 유지하면서 자연스러운 개선 결과를 보여준다.

• Communications for Statistical Applications and Methods
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• 제19권1호
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• pp.23-32
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• 2012

본 논문은 유한모집단에서 회귀계수추정량의 근사편향과 근사분산을 다루고 있다. 유한모집단에서 고정크기 포함확률비례표본을 추출하고 이 표본에서 조사된 데이터에 기초하여 회귀계수를 일반최소제곱추정량과 가중최소제곱추정량으로 추정할 때 두 추정량의 편향, 분산 그리고 평균제곱오차의 근사식을 유도하였다. 그리고 두 추정량의 효율을 비교하기 위하여 두 추정량의 분산을 비교하는 필요충분조건을 제시하였다. 또한 수치적인 비교를 위하여 간단한 예제를 소개하였다.

• 품질경영학회지
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• 제33권3호
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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.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 2006년도 춘계학술대회
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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.

• Communications for Statistical Applications and Methods
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• 제15권6호
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• pp.993-1002
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• 2008

Correlated responses have been widely analyzed since Liang and Zeger (1986) introduced the famous Generalized Estimating Equations(GEE). However, their variance functions were restricted to known quantifies multiplied by scale parameter. In so many industries and academic/research fields, power-of-the-mean variance function is one of the common variance function. We suggest GEE-type pseudolikelihood estimation based on the power-of-the-mean variance using existing software and investigate it's efficiency for different working correlation matrices.