• Asia Marketing Journal
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• 제11권1호
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• pp.29-38
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• 2009

시계열 확산 데이터를 활용하여 Bass 확산모형을 최소자승법(OLS)으로 추정하면, 초기에는 과다 추정하고 변곡점을 지나서는 수요를 낮게 추정하는 경향이 있다. 또한 확산모형에서 필요한 변수가 모형에서 빠짐으로 인해 발생하는 설정오류는 잔차의 자기상관을 발생시킬 수 있다. 자기상관이 오차항에 있을 경우, 추정된 모형의 모수들은 불편추정치이나 비효율적 추정치가 된다. 따라서 이러한 문제를 해결하는 확산모형의 개발이 요구된다. 본 연구에서는 자기상관 오차항을 고려한 수정된 확산모형을 제안하였다. 모형의 검증을 위해 미국의 CT-스캐너와 우리나라의 FPD TV 판매량를 제안된 모형에 응용하였다. 분석결과, 제안된 모형이 기존 모형에 비해 적합도와 모형의 주요 추정 통계량에서 우수함을 보였다.

• 품질경영학회지
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• 제27권4호
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• pp.123-142
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• 1999

Conventional SPC assumes that observations are independent. Often in industrial practice, however, observations are not independent. A common approach to building control charts for autocorrelated data is to apply conventional SPC to the residuals from a time series model of the process or is to apply conventional SPC to the weighted or unweighted subgroup means. In this paper, we propose a robust CUSUM control scheme for the detection of level change, without model identification or subgrouping of autocorrelated data. The proposed CUSUM chart and other conventional control charts are compared by a Monte Carlo simulation. It is shown that the proposed CUSUM chart is more effective than conventional CUSUM chart when the process is autocorrelated.

• 응용통계연구
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• 제28권5호
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• pp.1025-1034
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• 2015

1920년대에 소개되었던 Shewhart 관리도는 관측치가 서로 독립임을 가정했다. 오늘날은 데이터 측정과 자료수집 기술이 발전하면서 자기상관 공정 데이터가 많이 발생하고 있으며, 이것은 통계적 공정 관리의 성능에 부정적인 영향을 끼치게 된다. 자기상관이 존재하는 데이터에 대하여 가장 쉽게 접근할 수 있는 관리도는 먼저 자기상관구조를 모형화할 수 있는 적절한 시계열 모형을 가정한 다음 잔차를 구하여, 그 잔차에 기반한 Shewhart 관리도를 적용하는 것이다. 실제 문제에서 시계열 모형의 참 모수값은 알려져 있지 않으므로, 이 값은 일단계 표본(과거의 관리상태 표본)으로부터 추정된다. 본 논문에서는 이러한 모수추정이 이단계 표본을 모니터링하는데 어떠한 영향이 있는지 살펴보았다.

• 산업경영시스템학회지
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• 제35권3호
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• pp.52-61
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• 2012

The design method for cumulative sum (CUSUM) control charts, which can be robust to autoregressive moving average (ARMA) modeling errors, has not been frequently proposed so far. This is because the CUSUM statistic involves a maximum function, which is intractable in mathematical derivations, and thus any modification on the statistic can not be favorably made. We propose residual-based robust CUSUM control charts for monitoring autocorrelated processes. In order to incorporate the effects of ARMA modeling errors into the design method, we modify parameters (reference value and decision interval) of CUSUM control charts using the approximate expected variance of residuals generated in model uncertainty, rather than directly modify the form of the CUSUM statistic. The expected variance of residuals is derived using a second-order Taylor approximation and the general form is represented using the order of ARMA models with the sample size for ARMA modeling. Based on the Monte carlo simulation, we demonstrate that the proposed method can be effectively used for statistical process control (SPC) charts, which are robust to ARMA modeling errors.

• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.155-167
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• 2007

Knowing the time of the process change could lead to quicker identification of the responsible special cause and less process down time, and it could help to reduce the probability of incorrectly identifying the special cause. In this paper, we propose the maximum likelihood estimator (MLE) for the process change point when a control chart is used in monitoring the mean of a process in which the observations can be modeled as an AR(1) process plus an additional random error. The performance of the proposed MLE is compared to the performance of the built-in estimator when they are used in EWMA charts based on the residuals. The results show that the proposed MLE provides good performance in terms of both accuracy and precision of the estimator.

• 품질경영학회지
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• 제36권4호
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• pp.87-92
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• 2008

It is common to use CUSUM charts for detecting small level shifts in processes control, in which reference value(k) and decision interval(h) are the design parameters to be determined. To control process with autocorrelation, CUSUM charts could be applied to residuals obtained from fitting ARIMA models. However, constant level shifts in processes lead to varying mean shifts in residual processes and thus standard CUSUM charts may need to be modified. In this paper, we study the performance of CUSUM charts with various design parameters applied to autocorrelated processes, especially focussing on ARMA(1,1) models, and propose how they can be determined to get better performance in terms of the average run length.

• 산업경영시스템학회지
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• 제22권51호
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• pp.1-10
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• 1999

In recent industry society, it is revealed that, as an increase in the use of automated manufacturing and process inspection technology, the data from mass production system exhibits some degrees of autocorrelation. The operation characteristics of traditional control charts developed under the independence assumption are adversely affected by the presence of serial correlation. Therefore, when autocorrelated construction contacted with time-series models explain, the time-series models are the Box-Jenkins forecast models which have been proposed as the best forecasting tool which allows for partitioning of variation into result from the autocorrelation structure and variation due to unusual but assignable causes. In this paper, for the AR(1) process of Box-Jenkins forecast models, when the constant term ξ are zero and different from zero, I want to analyze the sensitivity of (equation omitted), CUSUM and EWMA control chart for forecast residuals.

• Communications for Statistical Applications and Methods
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• 제5권2호
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• pp.373-381
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• 1998

In this paper a new control chart which accounts for correlation between process subgroups will be proposed. We consider the case where the process fluctuations are autocorrelated by a stationary AR(1) time series and where n($\geq1$) items are sampled from the process at each sampling time. A simulation study is presented and shows that for correlated subgroups, the proposed control chart makes a significant improvement over the traditionally employed X-bar chart which ignores subgroup correlations. Finally, we illustrate the proposed chart by comparing the standardized residuals and X-bar chart on a data set of motor shaft diameters.

• Journal of the Korean Statistical Society
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• 제4권1호
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• pp.39-56
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• 1975

Ever since Gauss discussed the least-squares method in 1812 and Bertrand translated Gauss's work in French, the least-squares method has been used for various economic analysis. The justification of the least-squares method was given by Markov in 1912 in connection with the previous discussion by Gauss and Bertrand. The main argument concerned the problem of obtaining the best linear unbiased estimates. In some modern language, the argument can be explained as follow.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2006년도 춘계공동학술대회 논문집
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• pp.92-100
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• 2006

In many common control charting situations, the statistic to be charted can be viewed as the output of a linear filter applied to the sequence of process measurement data. In recent work that has generalized this concept, the charted statistic is the output of a general linear filter in impulse response form, and the filter is designed by selecting its impulse response coefficients in order to optimize its average run length performance. In this work, we restrict attention to the class of all second-order linear filters applied to the residuals of a time series model of the process data. We present an algorithm for optimizing the design of the second-order filter that is more computationally efficient and robust than the algorithm for optimizing the general linear filter. We demonstrate that the optimal second-order filter performs almost as well as the optimal general linear filter in many situations. Both methods share a number of interesting characteristics and are tuned to detect any distinct features of the process mean shift, as it manifests itself in the residuals.