• Industrial Engineering and Management Systems
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• v.4 no.1
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• pp.75-81
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• 2005

Borror et al. discussed the EWMA(Exponentially Weighted Moving Average) chart to monitor the count of defects which follows the Poisson distribution, referred to the $EWMA_c$ chart, as an alternative Shewhart c chart. In the $EWMA_c$ chart, the Markov chain approach is used to calculate the ARL (Average Run Length). On the other hand, in order to monitor the process fraction defectives P in high-yield processes, Xie et al. presented the CCC(Cumulative Count of Conforming)-r chart of which quality characteristic is the cumulative count of conforming item inspected until observing $r({\geq}2)$ nonconforming items. Furthermore, Ohta and Kusukawa presented the $CS(Confirmation Sample)_{CCC-r}$ chart as an alternative of the CCC-r chart. As a more superior chart in high-yield processes, in this paper we present an $EWMA_{CCC-r}$ chart to detect more sensitively small or moderate shifts in P than the $CS_{CCC-r}$ chart. The proposed $EWMA_{CCC-r}$ chart can be constructed by applying the designing method of the $EWMA_C$ chart to the CCC-r chart. ANOS(Average Number of Observations to Signal) of the proposed chart is compared with that of the $CS_{CCC-r}$ chart through computer simulation. It is demonstrated from numerical examples that the performance of proposed chart is more superior to the $CS_{CCC-r}$ chart.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.451-459
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• 2017

There are many researches showing that when a process change has occurred, variable sampling intervals (VSI) control chart is better than the fixed sampling interval (FSI) control chart in terms of reducing the required time to signal. When the process engineers use VSI control procedure, frequent switching between different sampling intervals can be a complicating factor. However, average number of samples to signal (ANSS), which is the amount of required samples to signal, and average time to signal (ATS) do not provide any control statistics about switching performances of VSI charts. In this study, we evaluate numerical switching performances of multivariate VSI EWMA chart including average number of switches to signal (ANSW) and average switching rate (ASWR). In addition, numerical study has been carried out to examine how to improve the performance of considered chart with accumulate-combine approach under several different smoothing constant and sample size. In conclusion, process engineers, who want to manage the correlation coefficients of related quality variables, are recommended to make sample size as large and smoothing constant as small as possible under permission of process conditions.

• Journal of the Korea Safety Management & Science
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• v.13 no.4
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• pp.225-235
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• 2011

Autoregressed Controller, which have trend algorithm, seeks to minimize variability by transferring the output variable to the related process input variable, while multivariate process control techniques seek to reduce variability by detecting and eliminating assignable causes of variation. In the case of process control, a very reasonable objective is to try to minimize the variance of the output deviations from the target or set point. We also investigate algorithm with relevant Shewhart chart, Theoretical control charts, precontrol and process capability. To help the people who want to make the theoretical system, we compare the main techniques in "a study on the relation between multivariate process control techniques and trend algorithms".

• 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 Korean Society for Quality Management
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• v.25 no.1
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• pp.100-115
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• 1997

Shewhart control chart is a basic technique to monitor the state of a process. We observe samples of size four or five and plot some statistic(e.g., mean or range) of each sample on the chart. When setting up the chart, we need to obtain u, pp.r and lower control limits. It is common practice that those limits are calculated from the preliminary 20-40 samples presumed to be homogeneous. However, it may ha, pp.n in practice that the samples are contaminated by outlying observations caused by various reasons. The presence of outlying observations make the control limits wider and hence decrease the sensitivity of the charts. In this paper, we introduce robust control charts with tighter control limits when outlying observations are present in the preliminary samples. Examples will be given via simulation study.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.3
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• pp.123-146
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• 1995

Several quality control schemes have been extensively compared using multivariate normal data sets simulated with various correlation structures. They include multiple univariate CUSUM charts, multivariate EWMA charts, multivariate CUSUM charts and Shewhart T$^{3}$ chart. This paper considers a new approach of the multivariate EWMA chart, in which the smoothing matrix has full elements instead of only diagonal elements. Performance of the schemes is measured by avaerage run length (ARL), coefficient of variation of run length (CVRL) and rank in order of signaling of off-target shifts in the process mean vector. The schemes are also compared by noncentrality parameter. The multiple univariate CUSUM charts are generally affected by the correlation structure. The multivariate EWMA charts provide better ARL performance. Especially, the new EWMA chart shows remarkable results in small shifts.

• The Korean Journal of Applied Statistics
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• v.30 no.3
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• pp.487-501
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• 2017

A machine vision system (MVS) is a computer system that utilizes one or more image-capturing devices to provide image data for analysis and interpretation. Recently there have been a number of industrial- and medical-device applications where control charts have been proposed for use with image data. The use of image-based control charting is somewhat different from traditional control charting applications, and these differences can be attributed to several factors, such as the type of data monitored and how the control charts are applied. In this paper, we investigate the adjustment effect of image size and region of interest (ROI) size, when we use control charts to monitor grayscale image data in industry.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1353-1366
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• 2015

These days Shewhart control chart for evaluating stability of the process is widely used in various field. But it must follow strict assumption of distribution. In real-life problems, this assumption is often violated when many quality characteristics follow non-normal distribution. Moreover, it is more serious in multivariate quality characteristics. To overcome this problem, many researchers have studied the non-parametric control charts. Recently, SVDD (Support Vector Data Description) control chart based on RBF (Radial Basis Function) Kernel, which is called K-chart, determines description of data region on in-control process and is used in various field. But it is important to select kernel parameter or etc. in order to apply the K-chart and they must be predetermined. For this, many researchers use grid search for optimizing parameters. But it has some problems such as selecting search range, calculating cost and time, etc. In this paper, we research the efficiency of selecting parameter regions as data structure vary via simulation study and propose a new method for determining parameters so that it can be easily used and discuss a robust choice of parameters for various data structures. In addition, we apply it on the real example and evaluate its performance.

• The Korean Journal of Applied Statistics
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• v.19 no.1
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• pp.81-96
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• 2006

This paper proposes a simple control chart method which can be practically used for asymmetric process data where the distribution is unknown. If we use the Shewhart type control charts which are based on normality assumption for the asymmetric process data, the type I error could increase as the asymmetry increases and the effectiveness of control chart to control variation decreases. To solve such problems, this paper suggests to calculate the control limits based on the quartiles. If we obtain the control limits by such quartile method, the type I error could decrease and it looks much more practical for asymmetric distributed process data.

• Communications for Statistical Applications and Methods
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• v.22 no.5
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• pp.519-530
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• 2015

The geometric chart has proven more effective than Shewhart p or np charts to monitor the proportion nonconforming in high-quality processes. Implementing a geometric chart commonly requires the assumption that the in-control proportion nonconforming is known or accurately estimated. However, accurate parameter estimation is very difficult and may require a larger sample size than that available in practice in high-quality process where the proportion of nonconforming items is very small. Thus, the error in the parameter estimation increases and may lead to deterioration in the performance of the control chart if a sample size is inadequate. We suggest adjusting the control limits in order to improve the performance when a sample size is insufficient to estimate the parameter. We propose a linear function for the adjustment constant, which is a function of the sample size, the number of nonconforming items in a sample, and the false alarm rate. We also compare the performance of the geometric charts without and with adjustment using the expected value of the average run length (ARL) and the standard deviation of the ARL (SDARL).