• 산업경영시스템학회지
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• 제34권4호
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• pp.57-65
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• 2011

Monitoring auto correlated processes is prevalent in recent manufacturing environments. As a proactive control for manufacturing processes is emphasized especially in the semiconductor industry, it is natural to monitor real-time status of equipment through sensor rather than resultant output status of the processes. Equipment's sensor data show various forms of correlation features. Among them, considerable amount of sensor data, statistically autocorrelated, is well represented by Box-Jenkins autoregressive moving average (ARMA) model. In this paper, we present a design method of statistical process control (SPC) used for monitoring processes represented by the ARMA model. The proposed method shows benefits in the power of detecting process changes, and considers robustness to ARMA modeling errors simultaneously. We prove benefits through Monte carlo simulation-based investigations.

• 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.

• 응용통계연구
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• 제37권2호
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• pp.191-207
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• 2024

자기상관 공정에서 이상상태를 빠르게 탐지하는 절차에 대해 많은 연구가 진행되어 왔다. 가장 전통적인 절차는 관측된 데이터에 대해 적합한 시계열 모형에서 계산된 잔차를 이용하는 잔차 관리도이다. 그러나 최근에는 통계적 학습 방법을 이용하여 자기상관 공정을 모니터링하는 절차가 많이 제안되었다. 이 논문에서는 딥러닝에 기반한 비지도 학습 방법인 LSTM Autoencoder의 잠재 벡터를 이용한 모니터링 절차를 제안하고, 이를 모의실험을 통해 LSTM Autoencoder의 복원 오차를 이용한 절차, RNN 분류 모니터링 절차, 그리고 잔차 관리도 절차의 성능과 비교하였다. 모의실험 결과, 제안된 절차와 RNN 분류 모니터링 절차의 성능은 유사하지만, 제안된 절차는 학습에 이상상태의 데이터가 필요하지 않기 때문에 이상상태의 데이터를 충분하게 확보할 수 없는 공정에 유용하게 적용할 수 있다는 장점이 있다.

• 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.

• 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 Data and Information Science Society
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• 제25권6호
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• pp.1539-1547
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• 2014

In this paper we apply the autoregressive process to the nonlinear quantile regression in order to infer nonlinear quantile regression models for the autocorrelated data. We propose a kernel method for the autoregressive data which estimates the nonlinear quantile regression function by kernel machines. Artificial and real examples are provided to indicate the usefulness of the proposed method for the estimation of quantile regression function in the presence of autocorrelation between data.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 2006년도 춘계학술대회
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• pp.313-318
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• 2006

Many control charting methods for both i.i.d and autocorrelated data can be viewed as charting the output of a linear filter applied to the process data. We propose a generalization of this concept, in which the filter parameters are optimally selected to minimize the out-of-control ARL while constraining the in-control ARL to some desired value. A number of interesting characteristics of the optimal fitters are discussed.

• 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.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 2007년도 춘계학술대회
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• pp.302-309
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• 2007

To conduct statistical process control needs the assumption that the process data are independent. However, most of chemical processes, like a semi-conduct processes do not satisfy the assumption because of autocorrelation. It causes abnormal out of control signal in the process control and misleading process capability. In this study, we introduce that Shore's method to solve the problem and to find the optimal subgroup size to estimate variance for AR(l) model. Especially, we focus on finding an actual subgroup size for small samples using simulation. It may be very useful for statistical process control to analyze process capability and to make a Shewhart chart properly.

• 품질경영학회지
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• 제35권2호
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• pp.106-112
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• 2007

In statistical process control, it is assumed that the process data are independent. However, most of chemical processes such as semi-conduct processes do not satisfy the assumption because of presence of autocorrelation between process data. It causes abnormal out of control signal in the process control and misleading estimation in process capability. In this study, we adopted Shore's method to solve the problem and propose an optimal subgroup size to estimate the variance correctly for AR(1) processes. Especially, we focus on finding an actual subgroup size for small samples based on simulation study.