• 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.

• Proceedings of the Society of Korea Industrial and System Engineering Conference
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• 2002.05a
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• pp.359-364
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• 2002

In case of pn control chart often used in mass production system of plant industry and so on, we could evaluate it's performance by the approximation to normal distribution. It has many differences according to sample sizes and defective fraction, and have disadvantage that needs much samples to use the normal distribution approximation. Existent control charts can not detect the cause of process something wrong because it is taking the sampling intervals of fixed length about all times from the process. Therefore, to overcome this shortcoming we use VSI(variable sampling intervals) techniques in this paper. This technique takes a long sampling interval to have the next sampling point if the sample point is in stable state, and if the sample point is near control lines, it takes short sampling interval because the probability to escape control limit is high. To analyze performance of pn control charts that have existent fixed sampling intervals(FSI) and that use VSI technique, we compare ATS of two charts, and analyze the performance of each control chart by the sample sizes, process fraction defective and control limits that Ryan and Schwertman had proposed.

• 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 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.36 no.1
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• pp.7-19
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• 2008

During the past two decades, a huge amount of research on adaptive control charts has been accomplished. Especially, variable sampling interval (VSI), variable sample size (VSS), and variable sample size and sampling interval (VSSI) charts have been focused by many researchers due to their simplicity and efficiency. On the other hand, the difference among notations, assumptions, methodologies may cause confusions in per forming further studies or practical implementations. This research analyses and compares diverse models so as to provide a unified view on statistical and economical characteristics. As a result, we perform comparative study on economical design models of VSI, VSS, and VSSI charts, respectively, We also present practical guidelines to utilize those adaptive control charts.

• 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.

• Journal of Korean Society for Quality Management
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• v.32 no.4
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• pp.156-168
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• 2004

This research investigates the statistical efficiency of variable sampling size & sampling interval(VSSI) $\bar{X}$ charts under two assignable causes. Algorithms for calculating the average run length(ARL) and average time to signal(ATS) of the VSSI $\bar{X}$ chart are proposed by employing Markov chain method. States of the process are defined according to the process characteristics after the occurrence of an assignable cause. Transition probabilities are carefully derived from the state definition. Statistical properties of the proposed chart are also investigated. A simple procedure for designing the proposed chart is presented based on the properties. Extensive sensitivity analyses show that the VSSI $\bar{X}$ chart is superior to the VSS or VSI $\bar{X}$ chart as well as to the Shewhart $\bar{X}$ chart in statistical sense, even tinder two assignable causes.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.723-729
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• 2005

Traditional statistical process control(SPC) applied to discrete part industry in the form of control charts can look for and eliminate assignable causes by process monitoring. On the other hand, engineering process control(EPC) applied to the process industry in the form of feedback control can maintain the process output on the target by continual adjustment of input variable. This study presents controlling and monitoring rules adopted variable sampling interval(VSI) to change sampling intervals in a predetermined fashion on the predicted process levels for integrated EPC and SPC systems. Twelve rules classified by EPC schemes(MMSE, constrained PI, bounded or deadband adjustment policy) and type of sampling interval combined with EWMA chart of SPC are proposed under IMA(1,1) disturbance model and zero-order (responsive) dynamic system. The properties of twelve control rules under three patterns of process change(sudden shift, drift and random shift) are evaluated and discussed through simulation and control rules for integrated VSI EPC and SPC systems are recommended.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1593-1600
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• 2015

A control chart is very useful in monitoring various production process. There are many situations in which the simultaneous control of two or more related quality variables is necessary. We construct bivariate Shewhart control charts based on the trace of the product of the estimated variance-covariance matrix and the inverse of the in-control matrix and investigate the properties of bivariate Shewart control charts with VSI procedure for monitoring covariance matrix in term of ATS (Average time to signal) and ANSW (Average number of switch) and probability of switch, ASI (Average sampling interval). Numerical results show that ATS is smaller than ARL. From examining the properties of switching in changing covariances and variances in ${\Sigma}$, ANSW values show that it does not switch frequently and does not matter to use VSI procedure.

• Journal of Integrative Natural Science
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• v.9 no.3
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• pp.215-222
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• 2016

When the linear correlation of the quality variables are considerably high, multivariate control charts may be a more effective way than univariate charts which operate quality variables and process parameters individually. Performances and efficiencies of the multivariate control charts under multivariate normal process has been considered. Some numerical results are presented under small scale of the shifts in the process to see the improvement of the efficiency of EWMA chart and CUSUM chart, which use past quality information, comparing to Shewart chart, which do not use quality information. We can know that the decision of the optimum value of the smoothing constant in EWMA structure or the reference value in CUSUM structure are very important whether we adopt combine-accumulate technique or accumulate-combine technique under the given condition of process.