Journal of Korean Society of Industrial and Systems Engineering (산업경영시스템학회지)

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
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Residual-based Robust CUSUM Control Charts for Autocorrelated Processes

자기상관 공정 적용을 위한 잔차 기반 강건 누적합 관리도

  • Lee, Hyun-Cheol (Department of Business Administration, Korea Aerospace University)
  • 이현철 (한국항공대학교 경영학과)
  • Received : 2012.05.24
  • Accepted : 2012.07.31
  • Published : 2012.09.30
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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.

Keywords

References

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