• Journal of the Korean Statistical Society
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• 제23권2호
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• pp.403-420
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• 1994

An economic design of the $\bar{X}-R$ chart using variable sample size (VSS) scheme is proposed in this paper. In this design the sample size at each sampling time changes according to the values of the previous two sample statistics, sample mean and range. The VSS scheme uses large sample if the sample statistics appear near inside the control limits and smaller sample otherwise. The set of process parameters, such as the sampling interval, control limits and the sample sizes, are chosen to minimize the expected cost per hour. The efficiency of the VSS scheme is compared to the fixed sample size one for cases where there is multiple of assignable causes. Percent reductions of the expected cost in the VSS design are calculated for some given sets of cost parameters. It is shown that the VSS scheme improves the confidence of the procedure and performs statistically better in terms of the number of false alarms and the average time to signal, respectively.

• 한국경영과학회지
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• 제9권2호
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• pp.23-27
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• 1984

We Observe a sequence of i. i. d random variables with density f or g. Only if g is true we should stop the process. Hence. the testing problem is completely described by a stopping time. Among all stopping times with error probability of first kind not exceeding a given bound, the one-sided sequential probability ratio test has smallest expected sample size if g is true. Moreover, the generalized one-sided SPRT has smallest expected sample size for g in the class of stopping times with expected sample size under f not falling below a given bound.

• 품질경영학회지
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• 제28권3호
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• pp.18-30
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• 2000

Recent studies have shown that the $\bar{X}$ chart with variable sampling intervals(VSI) and the $\bar{X}$ chart with variable sample size(VSS) are much quicker than Shewhart $\bar{X}$ chart in detecting shiks in the process. Shewhart $\bar{X}$ chart has been beneficial to detect large shifts but it is hard to apply Shewhart $\bar{X}$ chart in detecting moderate shifts in the process mean. In this article the $\bar{X}$ chart using variable sample size(VSS) and variable sampling Intervals(VSI) has been proposed to supplement the weak point mentioned above. So the purpose of this paper is to consider finding the design parameters which minimize expected loss costs for unit process time and measure the performance of VSSI(variable sample size and sampling interval) $\bar{X}$ chart. It is important that assignable causes be detected to maintain the process controlled. This paper has been studied under the assumption that one cycle is from starting of the process to eliminating the assignable causes in the process. The other purpose of this article is to represent the expected loss costs in one cycle with three process parameters(sample size, sampling interval and control limits) function and find the three parameters.

• Journal of the Korean Statistical Society
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• 제31권4호
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• pp.433-445
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• 2002

Using some available information about the unknown variance $\sigma$$^2$ of a normal distribution with mean $\mu$, a sequential approach is used to estimate $\sigma$$^2$. Two cases have been considered regarding the mean $\mu$ being known or unknown. The mean square error (MSE) of the new estimators are compared to that of the usual estimator of $\sigma$$^2$, namely, the sample variance based on a sample of size equal to the expected sample size. Simulation results indicates that, the new estimator is more efficient than the usual estimator of $\sigma$$^2$whenever the actual value of $\sigma$$^2$ is not too far from the prior information.

• Journal of the Korean Statistical Society
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• 제9권2호
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• pp.213-217
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• 1980

This paper aimed at studying an efficient sampling design of the survey for non-consignment fishery products including both marine fisheries and seaculture. An analysis was done on the relationship between precision and sample size. On the basis of the analysis, the sample size was determined to be 1,080 fishery house holds with the expected precision of 4%-5%. The molluscs and seaculture were recognized to be correlated with the non-consignment products. An attempt was made to investigate the coverage of the fish kinds by the sample about 100 fish kinds were found in the 80 selected sample villages, whereas the population includes about 120 in total. This shows that the sample represents the population with satisfaction.

• 품질경영학회지
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• 제49권3호
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• pp.341-358
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• 2021

Purpose: After product development, a Reliability Demonstration Test(RDT) is performed to confirm that the target life has been achieved. In the RDT, there are cases where the test equipment cannot accommodate all samples. Therefore, this study considers a test method to most economically demonstrate the target life of the product at a certain confidence level when the sample size is larger than the capacity of the test equipment. Methods: If the sample size is larger than the capacity of the test equipment, test equipments may be added or the test time of individual samples may be increased. So the test method is designed to cover this situation with limited capacity. A zero-failure test method is applied as a test method to RDT. To minimize the cost, the test cost is defined and the cost function is obtained. Finally, we obtain the optimal test plan. Results: A zero-failure test method is designed when the sample size is larger than the capacity of the test equipment, and the expected total cost is derived. In addition, the process of calculating the appropriate sample size, test time, and number of test equipment is illustrated through an example, and the effects of model parameters to the optimal solutions are investigated numerically. Conclusion: In this paper, we study a zero-failure RDT with test equipment that has limited capacity. The expected total cost is derived and the optimal sample size, test time, and number of test equipment are determined to minimize the expected total cost. We also studied numerical examples and for further studies, we can relax some restrictions in the test model and optimize the test method.

• 한국의류학회지
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• 제23권8호
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• pp.1240-1247
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• 1999

The purpose of this study was to classify size specifications of Korean adult male for the men's ready-made garments especially jacket and dress shirts By the stratified sampling method data were collected by the real anthropometric measurement. Sample size was 263 subjects as the sample and their age range was from 36 to 43 years old 66 variables from the direct anthropometric data were applied to analyze. ANOVA is SPSSWIN 8.0 package was applied to the data and the expected frequency distribution of 10.000 men was calculated by the extraction of density function. This study was performed to classify size specificatios by the control dimensions. The drop values of 9,12 and 6 have the high coverage rate of 28.52% 23.44% respectively Obese body type ; H type HD type and HE type are composed of the majority of 55.47% of the subjects. According to the drop values size specifications and distribution of control dimensions are predicted About 69.82% of the expected frequency distribution were covered by 19 size specifications.

• 응용통계연구
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• 제20권3호
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• pp.605-618
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• 2007

모집단 단위들이 희박하게 존재하고 접근하기 어려운 경우에 적용하는 적응추출설계에서의 추출과정은 관심변수의 관측값에 의존한다. 동일한 표본크기에서 적응집락추출의 추정량은 단순임의추출의 추정량에 비해 효율이 더 좋다 적응추출에서 Rao-blackwell의 정리를 적용하여 Murthy의 추정량의 형태로 수정한 한센-휴비_(HH) 추정량과 호르비_-톰슨 (HT) 추정량은 기존의 추정량에 비해 작은 분산을 가진다. 본 연구는 초기표본을 바꿔가면서 기대표본크기와 적응추출의 표본크기 하의 단순임의추출의 추정량과 적응추출의 추정량의 효율을 비교하였다.

• 응용통계연구
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• 제11권2호
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• pp.269-285
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• 1998

임상시험연구의 설계에서 적절한 표본수의 결정은 매우 중요한 문제 중의 하나이다. 본 논문에서는 생존분포를 비교하기 위한 여러 가지 방법들을 소개하고, 각 방법에서의 가정들을 고찰하였다. 또한 다양한 상황에서의 표본수와 검정력 등을 비교제시하고 모의실험을 통해 각 방법들의 이론상의 검정력과 실제 검정력을 알아보았다 그 결과로서 의학연구자들이 처한 여러 상황에 적합한 표본수의 결정방법을 제시하였다.

• Communications for Statistical Applications and Methods
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• 제15권3호
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• pp.353-365
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• 2008

임상시험에서 피험자수는 검정가설, 변수값의 분산과 유효차이, 검정력과 유의수준 등에 의해 결정되어진다. 일반적으로 수학적으로 계산된 피험자수에 중도탈락 예상치를 고려한 피험자수를 추가하여 최종적인 실험참가자수를 결정하는데 본 논문에서는 이론적인 계산식에서부터 중도탈락을 고려하여 피험자수를 결정하는 방법을 제안한다. 임상시험에서 많은 자료는 경시적(longitudinal) 형태를 갖고, ITT(intention to treat) 실험의 경우 중도탈락이 생기면 결측값으로 처리하지 않고 탈락직전에 관측된 값을 최종값으로 대체하는 LOCF(last observation carried forward) 방법을 주로 사용한다. 이러한 LOCF 방법은 피험자수 계산에 사용했던 분산과 유효차이 값의 가정에 왜곡을 가져오기 때문에 우리가 원하는 검정력을 보장 받지 못할 수 있다. 본 연구에서는 중도탈락률에 관한 정보를 포함하는 피험자수의 결정식을 제안하고 평균의 동일성 검정 경우에 검정력을 비교하여 이러한 산출방식이 합리적임을 실증하였다.