자기상관 공정에 대한 누적합관리도에서 설계모수 값의 결정
A note on CUSUM design for autocorrelated processes
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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.
Abstract
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.
참고문헌 (7)
- Alwan, L.C., "Time- Series Modeling for Statistical Process Control", Journal of Business & Economic Statistics, 6, pp.87~95 (1988)
- Douglas C. Montgomery, "Some Statistical Process Control Methods for Autocorrelated Data", Journal of Quality Technology, 23(3), pp.179~197 (1991)
- Douglas M. Hawkins, "Cumulative Sum Charts and Changing for Quality Improvement" (1997), Sringer
- 이재준, "Problems of Special Causes in Feedback Adjustment", 품질경영학회지, 32(2), pp.201~211 (2004), 한국품질경영학회
- George C Runger, "Average Run Length for CUSUM Control Charts Applied to Residuals", Communications Statistics-Theory and Method, 24(1), pp.273~282 (1995)
- Runger G. C., "Batch Mean Control Charts for Autocorrelated Data", IIE Transaction, 28(6), pp.483~487 (1996)
- S.Jack Hu, "Change Patterns of Time Series Based Control Charts", Journal of Quality Technology, 28(3), pp.302~312 (1996)