• Journal of the Korean Data and Information Science Society
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• 제13권2호
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• pp.21-29
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• 2002

Several different control statistics to simultaneously monitor dispersion matrix of several quality variables are presented since different control statistics can be used to describe variability. Multivariare cumulative sum (CUSUM) control charts are proposed and the performances of the proposed CUSUM charts are evaluated in terms of average run length (ARL). Multivariate Shewhart charts are also proposed to compare the properties of the proposed CUSUM charts. The numerical results show that multivariate CUSUM charts are more efficient than multivariate Shewhart charts for small or moderate shifts. And we also found that small reference value of the CUSUM chart is more efficient for small shift.

• 품질경영학회지
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• 제22권2호
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• pp.20-32
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• 1994

This paper is concerned with the design of four control charts for real-time monitoring of the continuous flow processes. Control charts for both uncorrelated data and correlated data are designed using the Kalman filtering techinque. The relative performance between the designed control charts and traditional control charts is evaluated in terms of the Average Run Length(ARL). Results show that the Adaptive EWMA control charts designed for uncorrelated data has better performance when process mean is shifted, while the residual control charts for correlated data has better performance when process is in control.

• 산업경영시스템학회지
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• 제21권47호
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• pp.211-218
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• 1998

In start-up process control applications it may be necessary to limit the sample size to one measurement. A control chart for individual measurements is used whenever it is desirable to examine each individual value from the process immediately. A possible option would be to use an exponential weighted moving(EWM), using modifying statistics with individual measurement, chart for monitoring the process center, and using a moving range (MR) chart for monitoring process variability. In this paper it is shown that there is scheme in using the EWM procedure based on average run length. An expression for the ARL is given in terms of an integral equation, approximated using numerical quadrature. In this case, where it is reasonable to assume normality and negligible autocorrelation in the observations, provide graphs that simplify the design of EWM-MR chart and taking method of exponential smoothing constant(λ) and constant(K) are suggested. The charts suggested above evaluate using the conditional probability.

• 산업경영시스템학회지
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• 제39권2호
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• pp.37-45
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• 2016

Control chart is representative tools of statistical process control (SPC). It is a graph that plotting the characteristic values from the process. It has two steps (or Phase). First step is a procedure for finding a process parameters. It is called Phase I. This step is to find the process parameters by using data obtained from in-controlled process. It is a step that the standard value was not determined. Another step is monitoring process by already known process parameters from Phase I. It is called Phase II. These control chart is the process quality characteristic value for management, which is plotted dot whether the existence within the control limit or not. But, this is not given information about the economic loss that occurs when a product characteristic value does not match the target value. In order to meet the customer needs, company not only consider stability of the process variation but also produce the product that is meet the target value. Taguchi's quadratic loss function is include information about economic loss that occurred by the mismatch the target value. However, Taguchi's quadratic loss function is very simple quadratic curve. It is difficult to realistically reflect the increased amount of loss that due to a deviation from the target value. Also, it can be well explained by only on condition that the normal process. Spiring proposed an alternative loss function that called reflected normal loss function (RNLF). In this paper, we design a new control chart for overcome these disadvantage by using the Spiring's RNLF. And we demonstrate effectiveness of new control chart by comparing its average run length (ARL) with ${\bar{x}}-R$ control chart and expected loss control chart (ELCC).

• 응용통계연구
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• 제34권5호
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• pp.735-744
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• 2021

제품의 수명을 유지시키는 것은 품질관리의 주요 목표 중 하나이다. 실제 공정에서는 시간 및 비용의 문제로 인해 모든 표본의 수명을 측정할 수 없는 경우가 많이 발생하기 때문에, 대부분 중도절단된 자료를 포함시켜 표본을 구성한다. 이 논문에서는 제1형의 우측중도절단된 수명 자료가 로그정규분포를 따르는 경우, 제품 수명의 평균을 모니터링하는 두 가지 누적합 관리도 절차를 제안한다. 하나는 우도비에 기초한 누적합 관리도이고, 다른 하나는 이항분포에 기초한 누적합 관리도 절차이다. 모의실험을 통해 평균런길이를 비교하는 방법으로 제안된 두 관리도 절차의 성능을 비교하였다. 모의실험 결과, 중도절단율이 낮은 경우, 형상모수값이 작은 경우, 평균의 감소 변화량이 큰 경우에는 우도비 누적합 관리도가 더 효율적이며, 반대로 중도절단율이 높은 경우, 형상모수값이 큰 경우, 평균의 감소 변화량이 적은 경우에는 이항 누적합 관리도가 더 효율적인 것으로 나타났다.

• Industrial Engineering and Management Systems
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• 제4권1호
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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.

• 품질경영학회지
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• 제40권4호
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• pp.467-480
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• 2012

Purpose: This paper introduces new 2-of-3 main and supplementary runs rules to increase the performance of the classical $\bar{X}$ control chart for detecting small process shifts. Methods: The proposed runs rules are compared with other competitive runs rules by numerical experiments. Nonlinear optimization problem to minimize the out-of-control ARL at a specified shift of process mean for determining action and warning limits at a time is formulated and a procedure to find two limits is illustrated with a numerical example. Results: The proposed 2-of-3 main and supplementary runs rules demonstrate an improved performance over other runs rules in detecting a sudden shift of process mean by simultaneous changes of mean and standard deviation. Conclusion: To increase the performance in the detection of small to moderate shifts, the proposed runs rules will be used with $\bar{X}$ control charts.

• Journal of the Korean Data and Information Science Society
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• 제28권5호
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• pp.981-999
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• 2017

단순확률모형을 고려하는 표준관리도에서는 표본간 분산을 고려하지 않고 공정분산을 추정한다. 표본간 분산이 존재하는 경우에는, 공정분산이 과소추정된다. 공정분산이 과소추정되면 좁아진 관리한계로 인해 관리도의 민감도는 향상되지만 과도한 오경보율을 발생시킨다. 이 논문에서는 공정모형으로 분산성분모형, 즉 변동의 원인을 표본내 분산과 표본간 분산으로 구분하는 확률모형을 고려한다. 관리한계는 표본내 분산과 표본간 분산을 모두 사용하여 설정하고 그에 따른 평균런길이를 통하여 효율을 살펴 보았다. 관리형태는 가장 널리 사용되는 ${\bar{X}}$, EWMA, CUSUM 관리도를 고려하였다. 관리한계 설정에서 표본내 분산만을 사용한 경우 (Case I)와 표본간 분산도 함께 사용한 경우 (Case II)를 통해 관리도의 효율을 비교하였다. 또한, 공정 모수가 주어진 경우와 추정된 두 경우에 대해서도 관리도의 효율을 비교하였다. 그 결과, 표본간 분산이 증가할 때 Case I의 오경보율은 급격히 증가한 반면 Case II의 경우에는 동일하게 유지됨을 알 수 있었다.

• 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.

• 산업경영시스템학회지
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• 제39권1호
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• pp.116-122
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• 2016

Recently, the production cycle in manufacturing process has been getting shorter and different types of product have been produced in the same process line. In this case, the control chart using coefficient of variation would be applicable to the process. The theory that random variables are located in the three times distance of the deviation from mean value is applicable to the control chart that monitor the process in the manufacturing line, when the data of process are changed by the type of normal distribution. It is possible to apply to the control chart of coefficient of variation too. ${\bar{x}}$, s estimates that taken in the coefficient of variation have just used all of the data, but the upper control limit, center line and lower control limit have been settled by the effect of abnormal values, so this control chart could be in trouble of detection ability of the assignable value. The purpose of this study was to present the robust control chart than coefficient of variation control chart in the normal process. To perform this research, the location parameter, ${\bar{x_{\alpha}}}$, $s_{\alpha}$ were used. The robust control chart was named Tim-CV control chart. The result of simulation were summarized as follows; First, P values, the probability to get away from control limit, in Trim-CV control chart were larger than CV control chart in the normal process. Second, ARL values, average run length, in Trim-CV control chart were smaller than CV control chart in the normal process. Particularly, the difference of performance of two control charts was so sure when the change of the process was getting to bigger. Therefore, the Trim-CV control chart proposed in this paper would be more efficient tool than CV control chart in small quantity batch production.