• 품질경영학회지
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• 제33권3호
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• pp.126-134
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• 2005

This paper proposes a selectively cumulative sum(S-CUSUM) control chart for detecting shifts in the process mean. The basic idea of the S-CUSUM chart is to accumulate previous samples selectively in order to increase the sensitivity. The S-CUSUM chart employs a threshold limit to determine whether to accumulate previous samples or not. Consecutive samples with control statistics out of the threshold limit are to be accumulated to calculate a standardized control statistic. If the control statistic falls within the threshold limit, only the next sample is to be used. During the whole sampling process, the S-CUSUM chart produces an 'out-of-control' signal either when any control statistic falls outside the control limit or when L -consecutive control statistics fall outside the threshold limit. The number L is a decision variable and is called a 'control length'. A Markov chain approach is employed to describe the S-CUSUM sampling process. Formulae for the steady state probabilities and the Average Run Length(ARL) during an in-control state are derived in closed forms. Some properties useful for designing statistical parameters are also derived and a statistical design procedure for the S-CUSUM chart is proposed. Comparative studies show that the proposed S-CUSUM chart is uniformly superior to the CUSUM chart or the Exponentially Weighted Moving Average(EWMA) chart with respect to the ARL performance.

• 산업경영시스템학회지
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• 제27권2호
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• pp.114-122
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• 2004

In statistical process control applications, variable sample size (VSS) $\bar{X}$ chart is often used to detect the assignable cause quickly. However, it is usually assumed that only one assignable cause results in the out-of-control in the process. In this paper, we propose the algorithm to minimize the function of cost per unit time and compare the economic design and the statistical design by use of the value of cost per unit time. We consider double assignable causes to occur with compound in the process and adopt the Markov chain approach to investigate the statistical properties of VSS $\bar{X}$ chart. A procedure that can calculate the control chart's parameters is proposed by the economic design.

• 경영과학
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• 제31권3호
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• pp.27-39
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• 2014

We derive a generalized statistic form of Q control chart, which is especially suitable for short run productions and start-up processes, for the detection of process mean shifts. The generalization means that the derived control chart statistic concurrently uses within lot variability and between lot variability to explain the process variability. The latter variability source is noticeably prevalent in lot type production processes including semiconductor wafer fabrications. We first obtain the generalized Q control chart statistic when both the process mean and process variance are unknown, which represents the case of implementing statistical process control charting for short run productions and start-up processes. Also, we provide the corresponding generalized Q control chart statistics for the rest of three cases of previous Q control chart statistics : (1) both the process mean and process variance are known (2) only the process mean is unknown and (3) only the process variance is unknown.

• 품질경영학회지
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• 제36권3호
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• pp.34-44
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• 2008

This research proposes a design method based on the statistical characteristics of the Shewhart control chart incorporated with 2 of 2 and 2 of 3 runs rules respectively. A Markov chain approach is employed in order to calculate the in-control and out-of-control average run lengths(ARL). Two different control limit coefficients for the Shewhart scheme and the runs rule scheme are derived simultaneously to minimize the out-of-control average run length subject to the reasonable in-control average run length. Numerical examples show that the statistical performance of the hybrid control scheme are superior to that of the original Shewhart control chart.

• 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.

• 품질경영학회지
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• 제40권3호
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• pp.337-346
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• 2012

Purpose: A Control chart is one of the important statistical process control tools that can improve processes by reducing variability and defects. Methods: In the present study, we propose the local $T^2$ multivariate control chart that can efficiently detect abnormal observations by considering the local pattern of the in-control observations. Results: A simulation study has been conducted to examine the property of the proposed control chart and compare it with existing multivariate control charts. Conclusion: The results demonstrate the usefulness and effectiveness of the proposed control chart.

• Communications for Statistical Applications and Methods
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• 제21권1호
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• pp.69-80
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• 2014

This paper considers the problem of monitoring the mean of a normally distributed process variable when the objective is to effectively detect both a sustained shift and a linear drift. The design and application of a generalized likelihood ratio (GLR) chart for simultaneously monitoring a sustained shift and a linear drift are evaluated. The GLR chart has the advantage that when we design this chart, we do not need to specify the size of the parameter change. The performance of the GLR chart is compared with that of other control charts, such as the standard cumulative sum (CUSUM) charts and the cumulative score (CUSCORE) charts. And we compare the proposed GLR chart with the GLR charts designed for monitoring only a sustained shift and for monitoring only a linear drift. Finally, we also compare the proposed GLR chart with the chart combinations. We show that the proposed GLR chart has better overall performance for a wide range of shift sizes and drift rates relative to other control charts, when a special cause produces a sustained shift and/or a linear drift in the process mean.

• 산업경영시스템학회지
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• 제39권3호
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• pp.10-17
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• 2016

Control Chart is a graph which dots the characteristic values of a process. It is the tool of statistical technique to keep a process in controlled condition. It is also used for investigating the state of a process. Therefore many companies have used Control Chart as the tool of statistical process control (SPC). Products from a production process represent accidental dispersion values around a certain reference value. Fluctuations cause of quality dispersion is classified as a chance cause and a assignable cause. Chance cause refers unmanageable practical cause such as operator proficiency differences, differences in work environment, etc. Assignable cause refers manageable cause which is possible to take actions to remove such as operator inattention, error of production equipment, etc. Traditionally ${\bar{x}}-R$ control chart or ${\bar{x}}-s$ control chart is used to find and remove the error cause. Traditional control chart is to determine whether the measured data are in control or not, and lets us to take action. On the other hand, RNELCC (Reflected Normal Expected Loss Control Chart) is a control chart which, even in controlled state, indicates the information of economic loss if a product is in inconsistent state with process target value. However, contaminated process can cause control line sensitive and cause problems with the detection capabilities of chart. Many studies on robust estimation using trimmed parameters have been conducted. We suggest robust RNELCC which used the idea of trimmed parameters with RNEL control chart. And we demonstrate effectiveness of new control chart by comparing with ARL value among traditional control chart, RNELCC and robust RNELCC.

• 품질경영학회지
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• 제35권2호
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• pp.37-44
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• 2007

Today, the statistical process control (SPC) in manufacture environment is an important role at the process by the productivity improvement of the manufacturing systems. The control chart in this statistical method is widely used as an important statistical tool to find the assignable cause that provoke the change of the process parameters such as the mean of interest or standard deviation. But the traditional SPC don't grasp the change of process according to the points fallen the near control limits because of monitoring the variance of process such as the fixed sampling interval and the sample size and handle the cost of the aspect of these sample point. The control chart can be divided into the statistical and economic design. Generally, the economic design considers the cost that maintains the quality level of process. But it is necessary to consider the cost of the process improvement by the learning effects. This study does the economic design in the VSI $\bar X$ control chart and added the concept of loss function of Taguchi in the cost model. Also, we preyed that the VSI $\bar X$ control chart is better than the FSI $\bar X$ in terms of the economic aspects and proposed the standard of the process improvement using the VSI $\bar X$ control chart.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 추계 학술발표회 논문집
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• pp.97-103
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• 2003

Shewhart-type control charts have historically been used for attribute data, though they have ARL biased property and even are unable to detect the improvement of a process with some process parameters. So far most efforts have been made to improve the performance of attribute control charts in terms of faster detection of special causes without increasing the rates of false alarm. In this paper, control limits are proposed that yield an ARL (nearly) unbiased chart for attributes. Optimal design is also proposed for attribute control charts under a natural sense of criterion.