• Communications for Statistical Applications and Methods
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• 제12권2호
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• pp.265-273
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• 2005

In this paper, we proposed multivariate EWMA control charts for both combine-accumulate and accumulate-combine approaches to monitor dispersion matrix of multiple quality variables. Numerical performance of the proposed charts are evaluated in terms of average run length(ARL). The performances show that small smoothing constants with accumulate-combine approach is preferred for detecting small shifts of the production process.

• 산업경영시스템학회지
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• 제23권56호
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• pp.83-92
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• 2000

This paper presents a study on control schemes for gradual increases (drifts) in a process variance. A new control chart, the Drifting Variance Control Chart (DVCC) is designed using Likelihood Ratio Test (LRT), and the ARL performance of the chart is evaluated for different subgroup sizes. The performance of this chart is then compared to some of the popular control schemes for the process dispersion, like the Shewhart S$^2$chart, the CUSUM chart and the EWMA chart. Results are presented and discussed. Also included is a sensitivity analysis that investigates how the DVCC performs when applied to a stepped change in process variance.

• 응용통계연구
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• 제9권1호
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• pp.91-109
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• 1996

지수가중이동평균관리도는 최근 들어 공정검색과 공정수정에 널리 이용되고 있으나 모수의 설정에 관한 연구는 많지 않다. 관리도의 설계는 통계적 설계와 경제적 설계로 분류한다. 통계적 설계는 허용된 제1종 오류하에서 제2종 오류를 최소화하는데 반해 경제적 설계는 공정에서 발생하는 모든 가능한 비용을 고려한 비용함수를 최소화한다. 이 논문에서는 지수가중이동평균관리도의 통계적 설계와 함께 경제적 설계를 정의한 다음 각 설계에서의 최적모수를 선정하여 결과를 비교한다. 경제적 설계에서 설정된 최적모수는 통계적 설계와 다르게 나타남을 알 수 있고 특히 가중치의 값은 통계적 설계에서 보다 항상 큰 값으로 나타난다. 경제적 설계에서는 고려하는 이상원인의 수에 따라 단일이상원인과 다중이상원인 모형으로 구분하여 설계한다. 다중이상원인의 평균적 개념으로 적용되는 단일이상원인 모형에서는 실제 다중이상원인이 존재할 때에 잘못된 판단을 할 수 있음을 보이고 있다.

• 품질경영학회지
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• 제35권1호
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• pp.24-34
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• 2007

This paper investigates the average run length (ARL) of a selectively moving average (S-MA) control chart. The S-U chart is designed to detect shifts in the process mean. The basic idea of the S-MA chart is to accumulate previous samples selectively in order to increase the sensitivity. The ARL of the S-MA chart was shown to be monotone decreasing with respect to the decision length in a previous research [3]. This paper derives the steady-state ARL in a closed-form and shows that the monotone property is resulted from head-start assumption. The steady-state ARL is shown to be a sum of head-start ARL and an additional term. The statistical design procedure for the S-MA chart is revised according to this result. Sensitivity study shorts that the steady-state ARL performance is still better than the CUSUM chart or the Exponentially Weighted Moving Average (EWMA) chart.

• 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.

• 품질경영학회지
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• 제26권2호
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• pp.51-60
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• 1998

Exponetially weighted moving average(EWMA) control chart to simultaneously monitor correlation coefficients of several correlated quality variables under multivariate normal process are proposed. Performances of the proposed control charts are measured in terms of average run length(ARL) by simulation. Numerical results show that smaller values of smoothing constant are more efficient in terms of ARL.

• Management Science and Financial Engineering
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• 제6권1호
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• pp.1-19
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• 2000

This papeer proposes a general approach of the multivariate expontially weighted moving average(MEWMA) chart, in which the smoothing matrix has full elements instead of only diagonal elements. The average run length (ARL) properties of this scheme are examined for a diverse set of quality control environments and the information to design the chhart is provied. Performance of the scheme is measured by estmating ARL and compared to those of two group cumulative sum (CUSUM) chats. The comparison resullts show that the MEWMA chart can improve its ARL performance in detecting a small shifts out-of-control in the start-up stage, the general MEWMA chart of a full smoothing matrix appears to offer an exceptional protection aginst departures from control in the process mean.

• 품질경영학회지
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• 제38권2호
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• pp.190-201
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• 2010

This research proposes a method for designing VSI (Variable Sampling Interval) control charts with supplementary run rules. The basic idea is to apply various run rules and the VSI scheme to a control chart in order to increase the sensitivity. The sampling process of the VSI run rules chart is constructed by Markov chain approach. A procedure for designing the VSI run rules chart is proposed based on Lorenzen and Vance's model. Sensitivity study shows that the VSI run rules charts outperform the FSI (Fixed Sampling Interval) run rules charts for wide range of process mean shifts. A major advantage of the VSI run rules chart over other charts such as CUSUM, EWMA, and adaptive charts is it's simplicity in implementation. Some useful guidelines are proposed based on the sensitivity study.

• International Journal of Quality Innovation
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• 제7권2호
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• pp.141-156
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• 2006

This study describes a novel algorithm for optimizing the quality yield of silicon wafer slicing. 12 inch wafer slicing is the most difficult in terms of semiconductor manufacturing yield. As silicon wafer slicing directly impacts production costs, semiconductor manufacturers are especially concerned with increasing and maintaining the yield, as well as identifying why yields decline. The criteria for establishing the proposed algorithm are derived from a literature review and interviews with a group of experts in semiconductor manufacturing. The modified Delphi method is then adopted to analyze those results. The proposed algorithm also incorporates the analytic hierarchy process (AHP) to determine the weights of evaluation. Additionally, the proposed algorithm can select the evaluation outcomes to identify the worst machine of precision. Finally, results of the exponential weighted moving average (EWMA) control chart demonstrate the feasibility of the proposed AHP-based algorithm in effectively selecting the evaluation outcomes and evaluating the precision of the worst performing machines. So, through collect data (the quality and quantity) to judge the result by AHP, it is the key to help the engineer can find out the manufacturing process yield quickly effectively.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2006년도 추계학술대회
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• pp.560-570
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• 2006

This paper proposes a selectively cumulative sum (S-CUSUM) control chart with variable sampling intervals (VSI) for detecting shifts in the process mean. The basic idea of the VSI S-CUSUM chart is to adjust sampling intervals and to accumulate previous samples selectively in order to increase the sensitivity. The VSI S-CUSUM chart employs a threshold limit to determine whether to increase sampling rate as well as to accumulate previous samples or not. If a standardized control statistic falls outside the threshold limit, the next sample is taken with higher sampling rate and is accumulated to calculate the next control statistic. If the control statistic falls within the threshold limit, the next sample is taken with lower sampling rate and only the sample is used to get the control statistic. The VSI 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 model is employed to describe the VSI S-CUSUM sampling process. Some useful formulae related to the steady state average time-to signal (ATS) for an in-control state and out-of-control state are derived in closed forms. A statistical design procedure for the VSI S-CUSUM chart is proposed. Comparative studies show that the proposed VSI S-CUSUM chart is uniformly superior to the VSI CUSUM chart or to the Exponentially Weighted Moving Average (EWMA) chart with respect to the ATS performance.