• Journal of the Korean Data and Information Science Society
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• 제4권
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• pp.31-44
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• 1993

Multivariate exponentially weighted moving average (EWMA) control charts for monitoring the variance-covariance matrix are investigated. A variable sampling interval (VSI) feature is considered in these charts. Multivariate EWMA control charts for monitoring the variance-covariance matrix are compared on the basis of their average time to signal (ATS) performances. The numerical results show that multivariate VSI EWMA control charts are more efficient than corrsponding multivariate fixed sampling interval (FSI) EWMA control charts.

• 품질경영학회지
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• 제32권4호
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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 the Korean Data and Information Science Society
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• 제20권4호
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• pp.741-747
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• 2009

Properties of multivariate Shewhart and EWMA (Exponentially Weighted Moving Average) control charts for monitoring variance-covariance matrix of quality variables are investigated. Performances of the proposed charts are evaluated for matched fixed sampling interval (FSI) and variable sampling interval (VSI) charts in terms of average time to signal (ATS) and average number of samples to signal (ANSS). Average number of swiches (ANSW) of the proposed VSI charts are also investigated.

• Journal of the Korean Data and Information Science Society
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• 제21권4호
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• pp.819-829
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• 2010

Properties of multivariate variable sampling interval (VSI) Shewhart and CUSUM charts for monitoring mean vector of related quality variables are investigated. To evaluate average time to signal (ATS) and average number of switches (ANSW) of the proposed charts, Markov chain approaches and simulations are applied. Performances of the proposed charts are also investigated both when the process is in-control and when it is out-of-control.

• 품질경영학회지
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• 제32권1호
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• pp.92-101
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• 2004

Tris paper present an economic statistical design which have statistically constraints for the optimal design of an EWMA control charts with variable sampling interval. Cost function use that proposed by Lorenzen and Vance, and the optimal design parameters include the sample size, control limit width, sampling interval, EWMA weight value. Comparisons between VSI EWMA control charts optimal economic design and optimal economic statistical designs show the following fact. Although have demerits which are more costly than economic design, have merits which to detect shifts more efficiently and to improve statistical performance.

• 품질경영학회지
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• 제30권4호
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• pp.1-14
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• 2002

Traditional SPC techniques are looking out variation of process by fixed sampling interval and fixed sample size about every hour, the process of in-control or out-of-control couldn't be detected actually when the sample points are plotted near control limits, and it takes no notice of expense concerned with such sample points. In this paper, to overcome that, consider VSI(variable sampling interval) EWMA control charts which VSI method is applied. The VSI control charts use a short sampling internal if previous sample points are plotted near control limits, then the process has high probability of out-of-control. But it uses a long sampling interval if they are plotted near centerline of the control chart, since process has high possibility of in-control. And then a comparison and analysis between FSI(fixed sampling interval) and VSI EWMA in the statistical aspect and economic aspect is studied. Finally, we show that VSI EWMA control chart is more efficient than FSI EWMA control chart in the both aspects.

• Journal of the Korean Data and Information Science Society
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• 제14권3호
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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.

• 대한산업공학회지
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• 제39권5호
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• pp.422-428
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• 2013

In many cases, an $\bar{X}$ control chart which is based on the performance variable is used in industrial fields. However, if the performance variable is too costly or impossible to measure and a less expensive surrogate variable is available, the process may be more efficiently controlled using surrogate variables. In this paper, we propose a model for the economic design of a VSI (Variable Sampling Interval) $\bar{X}$ control chart using a surrogate variable that is linearly correlated with the performance variable. The total average profit model is constructed, which involves the profit per cycle time, the cost of sampling and testing, the cost of detecting and eliminating an assignable cause, and the cost associated with production during out-of-control state. The VSI $\bar{X}$ control charts using surrogate variables are expected to be superior to the Shewhart FSI (Fixed Sampling Interval) $\bar{X}$ control charts using surrogate variables with respect to the expected profit per unit cycle time from economic viewpoint.

• Journal of the Korean Data and Information Science Society
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• 제16권3호
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• pp.639-650
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• 2005

Theoretical and numerical comparison have shown that variable sampling interval (VSI) charts are substantially more efficient than fixed sampling interval(FSI) charts in term of ATS(average time to signal). But the frequency of switching between different sampling intervals is a complicating factor in VSI procedures. VSI EWMA charts for monitoring mean vector of related qualify characteristics are investigated. To compare the efficiencies of the proposed charts, the performances are evaluated for matched FSI and VSI charts in terms of average time to signal(ATS) and average number of samples to signal(ANSS). For the switching behavior of the proposed VSI charts, average number of switches(ANSW) are also investigated.

• Journal of the Korean Data and Information Science Society
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• 제20권3호
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• pp.593-599
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• 2009

We consider the problem of using control charts to monitor more than one parameter with emphasis on simultaneously monitoring the mean and variance. The fixed sampling interval (FSI) control charts are modified to use variable sampling interval (VSI) control charts depending on what is being observed from the data. In general, approaches of monitoring the mean and variance simultaneously is to use separate charts for each parameter and a combined chart. In this paper, we use three basic strategies which are separate Shewhart charts for each parameter, a combined Shewhart chart and a combined CUSUM chart. We showed that a combined VSI CUSUM chart is comparatively more efficient than any other chart if the shifts in both mean and variance are small.