• 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.

• 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.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.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.429-440
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• 2003

Variable sampling rate (VSR) control charts vary the sampling interval and/or the sample size according to value of the control statistic. It is known that $\bar{X}$ charts with VSR scheme lead to large improvements in performance over those with fixed sampling rate (FSR) scheme. In this paper, we studied $\bar{X}$ charts with several VSR schemes, and compared their statistical performance each other.

• Journal of the Korean Statistical Society
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• v.35 no.4
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• pp.441-452
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• 2006

Here an efficient regression type estimator for a stratified population mean is proposed under the two-phase sampling scheme. While constructing the proposed estimator, it is assumed that the first auxiliary variable x is directly and highly correlated with the study variable y, and the second auxiliary variable z is directly and highly correlated with the first auxiliary variable x. However the variable z is not directly correlated with the variable y, but they are just correlated with each other only due to their direct and high correlation with the variable x. The proposed regression type estimator is found to be always more efficient than the existing estimators defined under the same situation.

• Communications for Statistical Applications and Methods
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• v.31 no.1
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• pp.65-85
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• 2024

The tail probability of a function of a multivariate random variable is not easy to estimate by the crude Monte Carlo simulation. When the occurrence of the function value over a threshold is rare, the accurate estimation of the corresponding probability requires a huge number of samples. When the explicit form of the cumulative distribution function of each component of the variable is known, the inverse transform likelihood ratio method is directly applicable scheme to estimate the tail probability efficiently. The method is a type of the importance sampling and its efficiency depends on the selection of the importance sampling distribution. When the cumulative distribution of the multivariate random variable is represented by a copula and its marginal distributions, we develop an iterative algorithm to find the optimal importance sampling distribution, and show the convergence of the algorithm. The performance of the proposed scheme is compared with the crude Monte Carlo simulation numerically.

• Industrial Engineering and Management Systems
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• v.8 no.3
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• pp.131-138
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• 2009

The variable sampling inspection scheme with screening for the purpose of assuring the upper limit of maximum expected surplus loss after inspection has been proposed. In this inspection scheme, it has been assumed that a product lot consists of products manufactured through a single production line and lot quality characteristics follow a normal distribution. In the previous literature with respect to inspection schemes, it has been commonly assumed that lot quality characteristics obey a single normal distribution under the condition that all products are manufactured in the same condition. On the other hand, the production line is designed in order that the workload of respective processes becomes uniform from the viewpoint of line balancing. One of the solutions for the bottleneck process is to arrange the workshops in parallel. The lot quality characteristics from such a production line with the process consisting of some parallel workshops might not follow strictly the single normal distribution. Therefore, we expand an applicable scope of the above mentioned variable sampling inspection scheme with screening in this article. Concretely, we consider the variable sampling inspection with screening for the purpose of assuring the upper limit of average outgoing surplus quality loss in the production lots when the lot quality follows the mixed normal distribution.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.18 no.33
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• pp.143-151
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• 1995

In this design the sampling interval that each sampling time changes according to the valuse of the previous to sample statistics, sample mean and ranges. The VSI scheme uses large sample if the sample statistics appear near in side the control limits and smaller sample otherwise. The efficiency of the VSI scheme is compare to the FSI. It is shown that VSI control chart improves the confidence of the procedure and performens better than FSI control chart.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.191-196
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• 2005

Knowing the time of the process change could lead to quicker identification of the responsible special cause and less process down time, and it could help to reduce the probability of incorrectly identifying the special cause. In this paper, we propose a MLE of the process change point when control charts with the fixed sampling rate (FSR) scheme or the variable sampling rate (VSR) scheme monitor a process to detect changes in the process mean and/or variance of a normal quality variable.

• 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.