Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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A note on CUSUM design for autocorrelated processes

자기상관 공정에 대한 누적합관리도에서 설계모수 값의 결정

  • 이재준 (인하대학교 자연과학대학 통계학과) ;
  • 이종선 (인하대학교 자연과학대학 통계학과)
  • Published : 2008.12.31
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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.

Keywords

References

  1. Alwan, L. C. and Roberts, H. V.(1988), "Time- Series Modeling for Statistical Process Control", Journal of Business & Economic Statistics, Vol. 6, pp. 87-95 https://doi.org/10.2307/1391421
  2. Douglas C. Montgomery and Christina M. Mastrangelo (1991), "Some Statistical Process Control Methods for Autocorrelated Data", Journal of Quality Technology, Vol. 23, No. 3, 179-197 https://doi.org/10.1080/00224065.1991.11979321
  3. Douglas M. Hawkins and David H. Owell (1997), "Cumulative Sum Charts and Changing for Quality Improvement", Sringer, New York
  4. Jae Jun Lee, Sinsup Cho (2004), "Problems of Special Causes in Feedback Adjustment", Journal of the Korean Society for Quality management, Vol. 32, No. 2, pp. 201-211
  5. George C Runger, Thomas R. Willemain and Sharad Prabhu (1995), "Average Run Length for CUSUM Control Charts Applied to Residuals", Communications Statistics-Theory and Method, Vol.24,No.1, pp.273-282 https://doi.org/10.1080/03610929508831487
  6. Runger G. C. and T. R. Willemain (1996), "Batch Mean Control Charts for Autocorrelated Data", IIE Transaction, Vol. 28(6), pp. 483-487 https://doi.org/10.1080/07408179608966295
  7. S. Jack Hu and Chinmo Roan (1996), "Change Patterns of Time Series Based Control Charts", Journal of Quality Technology, Vol. 28, No. 3, pp. 302-312 https://doi.org/10.1080/00224065.1996.11979680