• Journal of the Korean Statistical Society
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• v.23 no.2
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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.

• Journal of the Korean Operations Research and Management Science Society
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• v.9 no.2
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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.

• Journal of Korean Society for Quality Management
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• v.28 no.3
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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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• v.31 no.4
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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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• v.9 no.2
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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.

• Journal of Korean Society for Quality Management
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• v.49 no.3
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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.

• Journal of the Korean Society of Clothing and Textiles
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• v.23 no.8
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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.

• The Korean Journal of Applied Statistics
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• v.20 no.3
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• pp.605-618
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• 2007

Adaptive sampling design is the selection procedure which depends on observed values of the variable of interest. It is the method which could be applied to the rare and unapproachable population. Adaptive cluster sampling strategies are more efficient than simple random sampling on equivalent sample size. Adaptive sampling with new estimators through the Rao-blackwell method have lower variance than Horvitz-Thompson (HT) and Hansen-Hurwitz (HH). Also, to determine suitable sample size, it was used expected sample and the method finding appropriate sample size by changing initial sample size were studied.

• The Korean Journal of Applied Statistics
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• v.11 no.2
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• pp.269-285
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• 1998

One of the most important issues in the area of clinical trial research is the determination of the sample size required to insure a specified power in detecting a real or clinically relevant difference of a stated magnitude. Increasingly, medical journals are requiring authors to provide information on the sample size needed to detect a given difference. We restrict our attention to the designs far comparirng two survival distributions. These are concerned with the survival time which is defined as the interval from a baseline(e.g. randomization) to failure (e.g. death, recurrence of disease). Survival times axe right censored when patients have not foiled by the time of analysis or have been loss to follow-up during the trial. For different types of clinical trials for comparing survival distributions, there have been marry research in sample size determination. We review the existing literature concerning commonly used sample size formulae in the design of randomized clinical trials, and compare the assumption, the power and the sample size calculation of these methods. We also compare by simulation the expected power and observed power of each method under various circumstances. As a result, guidelines in terms of practical usage are provided.

• Communications for Statistical Applications and Methods
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• v.15 no.3
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• pp.353-365
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• 2008

The sample size in a clinical trial is determined by the hypothesis, the variance of observations, the effect size, the power and the significance level. Dropouts in clinical trials are inevitable, so we need to consider dropouts on the determination of sample size. It is common that some proportion corresponding to the expected dropout rate would be added to the sample size calculated from a mathematical equation. This paper proposes new equations for calculating sample size dealing with dropouts. Since we observe data longitudinally in most clinical trials, we can use a last observation to impute for missing one in the intention to treat (ITT) trials, and this technique is called last observation carried forward(LOCF). But LOCF might make deviations on the assumed variance and effect size, so that we could not guarantee the power of test with the sample size obtained from the existing equation. This study suggests the formulas for sample size involving information about dropouts and shows the properties of the proposed method in testing equality of means.