• Journal of Korean Society for Quality Management
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• v.45 no.4
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• pp.943-956
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• 2017

Purpose: This paper proposes a VSS(Variable Sample Size) ${\bar{X}}$ control chart using surrogate variable and shows its effectiveness compared with FSS(Fixed Sample Size) ${\bar{X}}$ control chart using either performance variable or surrogate variable. Methods: The expected cost function of VSS ${\bar{X}}$ control chart is derived. The optimal designs are then found for numerical examples using a GA(genetic algorithm) and compared to those of the FSS ${\bar{X}}$ control charts. Results: Computational results show that VSS ${\bar{X}}$ control chart using surrogate variables is superior to FSS ${\bar{X}}$ control chart using either performance variable or surrogate variable from the economic view points. Conclusion: The proposed VSS ${\bar{X}}$ control chart will be useful in industry fields where a performance variable is not avaliable or too costly.

• Journal of Korean Society for Quality Management
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• v.32 no.4
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• pp.252-264
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• 2004

Variable sampling Interval (VSI) control charts vary the sampling interval according to value of the control statistic while the sample size is fixed. It is known that control charts with 2-state VSI scheme, which uses only two sampling intervals, give good statistical properties. Variable sample size (VSS) control charts vary the sample size according to value of the control statistic while the sampling interval is fixed. In the VSS scheme no optimal results are known for the number of sample sizes. It is also known that the variable sampling rate (VSR) $\bar{X}$ control chart with 2-state VSS and 2-state VSI scheme leads to large improvements In performance over the fixed sampling rate (FSR) $\bar{X}$ chart, but the optimal number of states for sample size Is not known. In this paper, the VSR Χ charts with multi-state VSS and 2-state VSI scheme are designed and compared to 2-state VSS and 2-state VSI scheme. The multi-state VSS scheme is considered to, achieve an additional improvement by switching from the 2-state VSS scheme. On the other hand, the multi-state VSI scheme is not considered because the 2-state scheme is known to be optimal. The 3-state VSS scheme improves substantially the sensitivity of the $\bar{X}$ chart especially for small and moderate mean shifts.

• 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.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 Korean Institute of Industrial Engineers
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• v.24 no.3
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• pp.333-343
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• 1998

This paper proposes variable stream and sample size(VSSS) group control charts in which both the number of streams selected for sampling and sample size from each of the selected streams are allowed to vary based on the values of the preceding sample statistics. The proposed charts select a small portion of streams and take samples of size n = 1 if both the largest and smallest of sample means fall between the lower and upper threshold limits, and select a large portion of streams and take samples of size n > 1 otherwise. A Markov chain approach is used to derive the formulas for evaluating the performances of the proposed charts. Numerical comparisons are made between the VSSS and fixed stream and sample size(FSSS) group control charts.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.107-116
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• 1999

We propose a sample design which minimize Bayes risk for cluster smpling in sampling inspection. We treat a pilot sample and an additional sample size as random variable. In addition we compute an appropriate cluster size for handling over-dispersion.

• Journal of the Korean Statistical Society
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• v.26 no.2
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• pp.181-198
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• 1997

The variable sampling rates scheme is proposed by taking random sample size and sampling interval during the process. The performance of the scheme is measured in terms of the average time to signal adjusted by teh sampling cost when the process is out of control. This measurement evaluates the effectiveness of the scheme in terms of the cost incurred due to nonconformation as well as sampling. The variable sampling rates scheme is shown to be effective especially for small and moderate shifts of the mean when compared to the standard scheme.

• Proceedings of the IEEK Conference
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• 2000.11d
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• pp.115-118
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• 2000

We present a new variable step size LMS algorithm using the correlation between reference input and error signal of adaptive filter. The proposed algorithm updates each weight of filter by different step size at same sample time. We applied this algorithm to adaptive multip]e-notch filter. Simulation results are presented to compare the performance of the proposed algorithm with the usual LMS algorithm and another variable step algorithm.

• Journal of Korean Society for Quality Management
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• v.33 no.4
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• pp.117-122
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• 2005

Variable sampling rate(VSR) scheme varies the sampling rate for the current sample depending on the previous value of the control statistic. In this paper, we propose EWMA control charts with variable parameter(VP) scheme, which allows both the sample rate(the sample size or the sampling interval) and the weight to vary. We investigate the effectiveness of the VP scheme relative to the fixed parameter(FP) scheme and the VSR scheme in EWMA control charts. It is shown that using the VP scheme gives some improvements to the ability in detecting small and moderate shifts in the process normal mean.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.289-305
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• 2014

In this paper we propose a new approach to the variable selection problem for a primary resolution and wavelet basis functions in wavelet regression. Most wavelet shrinkage methods focus on thresholding the wavelet coefficients, given a primary resolution which is usually determined by the sample size. However, both a primary resolution and the basis functions are affected by the shape of an unknown function rather than the sample size. Unlike existing methods, our method does not depend on the sample size and also takes into account the shape of the unknown function.