• 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.

• 통합자연과학논문집
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• 제5권4호
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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 the Korean Statistical Society
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• 제14권2호
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• pp.76-86
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• 1985

Shewhart X-chart, which is most widely used in practice, is shown to be inappropriate for the cases where the process distribution is one-sided asymmetrical, and thus some nonparametric Shewhart type charts are developed instead. These schemes may be applied usefully when there is not enough information in determining the process distribution. The average run lengths are obtained to compare the efficiency of control charts for various shifts of the location parameter and for some typical one-sided asymmetrical distributions.

• 품질경영학회지
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• 제32권2호
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• pp.132-153
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• 2004

CUSUM control charts are widely used to monitor processes with small shifts. CUSUM control charts are, however, less effective in detecting for recurring cycles or frequent small shifts in the processes. With Shewhart control charts, we have applied the variety of run rules to check the stability of process in addition to the situations that some points fall outside the control limits. In this paper, we propose the Z -CUSUM control chart for monitoring the process with recurring cycles or frequent small shifts by use of the zone concept as like the Shewhart control charts.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 2004년도 품질경영모델을 통한 가치 창출
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• pp.57-63
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• 2004

CUSUM control charts are widely used to monitor processes with small shifts. CUSUM control charts, however, are less effective in detecting for recurring cycles or frequent small shifts in the process. With Shewhart control charts, we have applied the variety of run rules to check the stability of process in addition to the situations that some points fall outside the control limits. In this paper, we propose the Z-CUSUM control chart for monitoring the process with recurring cycles or frequent small shifts by use of the zone concept as like the Shewhart control charts.

• 대한안전경영과학회지
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• 제12권3호
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• pp.257-262
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• 2010

The study investigates the various Acceptance Control Charts (ACCs) based on the factors that include process independence, data weighting scheme, subgrouping, and use of control charts. USL - LSL > $6{\sigma}$ that used in the good condition processes in the ACCs are designed by considering user's perspective, producer's perspective and both perspectives. ACCs developed from the research is efficiently applied by using the simple control limit unified with APL (Acceptable Process Level), RLP (Rejectable Process Level), Type I Error $\alpha$, and Type II Error $\beta$. Sampling interval of subgroup examines i.i.d. (Identically and Independent Distributed) or auto-correlated processes. Three types of weight schemes according to the reliability of data include Shewhart, Moving Average(MA) and Exponentially Weighted Moving Average (EWMA) which are considered when designing ACCs. Two types of control charts by the purpose of improvement are also presented. Overall, $\alpha$, $\beta$ and APL for nonconforming proportion and RPL of claim proportion can be designed by practioners who emphasize productivity and claim defense cost.

• Industrial Engineering and Management Systems
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• 제11권4호
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• pp.385-389
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• 2012

With the development of computer storage and the rapidly growing ability to process large amounts of data, the multivariate control charts have received an increasing attention. The existing univariate and multivariate control charts are a single hypothesis testing approach to process mean or variance by using a single statistic plot. This paper proposes a multiple hypothesis approach to developing a new multivariate control scheme. Plotted Hotelling's $T^2$ statistics are used for computing the corresponding p-values and the procedure for controlling the false discovery rate in multiple hypothesis testing is applied to the proposed control scheme. Some numerical simulations were carried out to compare the performance of the proposed control scheme with the ordinary multivariate Shewhart chart in terms of the average run length. The results show that the proposed control scheme outperforms the existing multivariate Shewhart chart for all 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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• 제26권6호
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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.

• 산업경영시스템학회지
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• 제25권4호
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• pp.1-7
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• 2002

Statistical process control is used widely as an effective tool to solve the quality problems in practice fields. All the control charts used in statistical process control are parametric methods, suppose that the process distributes normal and observations are independent. But these assumptions, practically, are often violated if the test of normality of the observations is rejected and/or the serial correlation is existed within observed data. Thus, in this study, to screening process, the Combined Shewhart - CUSUM quality control chart is described and evaluated that used bootstrap method. In this scheme the CUSUM chart will quickly detect small shifts form the goal while the addition of Shewhart limits increases the speed of detecting large shifts. Therefor, the CSC control chart is detected both small and large shifts in process, and the simulation results for its performance are exhibited. The bootstrap CSC control chart proposed in this paper is superior to the standard method for both normal and skewed distribution, and brings in terms of ARL to the same result.