• 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 Korean Society of Industrial and Systems Engineering
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• v.34 no.2
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• pp.1-8
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• 2011

This paper proposes a variable sampling interval multivariate $T^2$ control chart with sampling at fixed times, where samples are taken at specified equally spaced fixed time points and additional samples are allowed between these fixed times when indicated by the preceding $T^2$ statistics. At fixed sampling points, the $T^2$ statistics are composed of all quality characteristics and a part of quality characteristics are selected to obtain $T^2$ statistics at additional sampling points. A Markov chain approach is used to evaluate the performance of the proposed chart. Numerical studies for the performance of the proposed chart show that the proposed chart reduces the observations obtained from a process and detects the assignable cause of a process with low correlated quality characteristics quickly.

• 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 the Korean Data and Information Science Society
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• v.23 no.4
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• pp.859-866
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• 2012

Some switching properties of multivariate control charts are investigated when the interval between two consecutive sample selections is not fixed but changes according to the result of the previous sample observation. Many articles showed that the performances of variable sampling interval control charts are more efficient than those of fixed sampling interval control charts in terms of average run length (ARL) and average time to signal (ATS). Unfortunately, the ARL and the ATS do not provide any information on how frequent a switch is being made. We evaluate several switching properties of two sampling interval Shewhart and CUSUM procedures for controlling mean vector of correlated quality variables.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.767-771
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• 2002

This paper proposes a multivariate $T^2$ variable interval control chart with sampling at fixed times, where samples are taken at specified equally spared fixed time points, and additional samples are allowed between these fixed times when indicated by the preceding $T^2$ statistics. At fixed sampling tunes, the $T^2$ statistics are composed of all quality characteristics, and a part of qualify characteristics are selected to obtain $T^2$ statistics at additional sampling times. A Markov chain approach is used to evaluate the performance of the proposed chart.

• Journal of Korean Institute of Industrial Engineers
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• v.39 no.5
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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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• v.20 no.4
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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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• 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 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 the Korean Data and Information Science Society
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• v.4
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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.