자기상관 공정 적용을 위한 잔차 기반 강건 누적합 관리도
Residual-based Robust CUSUM Control Charts for Autocorrelated Processes
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초록
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.
Abstract
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.
참고문헌 (19)
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