• Journal of the Korean Data and Information Science Society
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• v.20 no.3
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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.

• 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.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.28 no.4
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• pp.85-93
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• 2005

This paper is designed a VSI ${\overline{X}}$-CRL synthetic control chart in aspect of economy. We found the optimal sampling interval and various control limit factors under various cost parameters using cost function, proposed Lorenzen and Vance. Optimal design parameters include the sample size, control limit width, sampling interval, CRL/S chart control limit; L. Comparison and analysis of cost parameters are applied between synthetic VSI ${\overline{X}}$-CRL chart and FSI ${\overline{X}}$-CRL chart. The result of this paper shows that VSI ${\overline{X}}$-CRL chart brings cost-cutting effect of 3.04% control expense less than FSI control chart. It may not be difficult to establish the optimal economic control parameters to apply the practical cost parameters in the field.

• Journal of Integrative Natural Science
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• v.5 no.3
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• pp.151-156
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• 2012

Because of the equivalence between control chart procedures and hypothesis testing, we propose to use likelihood ratio test (LRT) statistic $Z_i^2$ as the multivariate control statistic for simultaneous monitoring means of the multivariate normal process. Properties and comparisons of the proposed control charts are explored and conducted for matched fixed sampling interval (FSI) and variable sampling interval (VSI) with two sampling interval charts. The result of numerical comparisons shows that EWMA chart with two sampling interval procedure is more efficient than the corresponding FSI chart for small or moderate changes. When large shift of the process has occurred, we also found that Shewhart chart is more efficient than EWMA chart.

• Journal of Korean Society for Quality Management
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• v.30 no.4
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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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• v.14 no.4
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• pp.1045-1053
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• 2003

Markovian EWMA control chart for simultaneously monitoring mean vector of the several correlated quality characteristics is investigated. Properties of multivariate Shewhart chart and EWMA chart are evaluated for matched FSI (fixed sampling interval) and VSI(variable sampling interval) scheme. We obtained VSI EWMA chart is more efficient than Shewhart chart for small or moderate shifts. And, we obtained stablized numerical results with Markov chain method when the number of transient state is greater than 100.

• Journal of the Korean Data and Information Science Society
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• v.26 no.4
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• pp.997-1006
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• 2015

In industrial quality control, when engineers use VSI control procedure they should consider both required time to signal and switching behaviors together in the case of production process changed. Up to the present, many researchers have studied fixed sampling interval (FSI) chart and variable sampling interval (VSI) chart in the points of average number of samples to signal (ANSS) and average time to signal (ATS). However, ANSS and ATS do not provide any switching information between different sampling intervals of VSI schemes. In this study, performances of two sampling intervals VSI chart and three sampling intervals VSI chart are evaluated and compared. The numerical results show that ANSS and ATS values of two sampling intervals VSI chart and three sampling interval VSI chart are similar regardless the amount of shifts. However, the values of switching behaviors including ANSW are less efficient in three sampling intervals VSI charts than in two sampling intervals VSI chart.

• Journal of the Korean Data and Information Science Society
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• v.17 no.3
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• pp.973-982
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• 2006

Performances of variable sampling interval(VSI) multivariate control charts with accumulate-combine approach for monitoring mean vector of p related quality variables were investigated. Shewhart control chart is also proposed to compare the performances of CUSUM and EWMA charts. Numerical comparisons show that performances of CUSUM and EWMA charts are more efficient than Shewhart chart for small or moderate shifts, and VSI chart is more efficient than fixed sampling interval(FSI) chart. We also found that performances of the CUSUM or EWMA chart with accumulate-combine approach are substantially efficient than those of Shewhart chart.

• Journal of Korean Society for Quality Management
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• v.25 no.3
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• pp.62-73
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• 1997

Previous VSI control chart works have been done on quality variable whose distribution is normal. But there are many situations in which hte assumption of not a, pp.opriate. Also, in many industrial processes, the interest is to monitor the number of defectives. In this paper, we will take the existing properties of VSI control chart developed for the normal distribution and a, pp.y them to the np-chart based on the discrete binomial distribution. We will consider the CUSUM chart for the number of defectives. Here, the interesting object is to compute the VSI ATS for CUSUM control chart using Markov chain a, pp.oach and to compare FSI ATS and VSI ATS.

• Journal of Integrative Natural Science
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• v.5 no.4
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• pp.246-252
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• 2012

Multivariate cumulative sum (CUSUM) control charts for simultaneously monitoring both means and variances under multivariate normal process are investigated. Performances of multivariate CUSUM schemes are evaluated for matched fixed sampling interval (FSI) and variable sampling interval (VSI) features in terms of average time to signal (ATS), average number of samples to signal (ANSS). Multivariate Shewhart charts are also considered to compare the properties of multivariate CUSUM charts. Numerical results show that presented CUSUM charts are more efficient than the corresponding Shewhart chart for small or moderate shifts and VSI feature with two sampling intervals is more efficient than FSI feature. When small changes in the production process have occurred, CUSUM chart with small reference values will be recommended in terms of the time to signal.