Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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Statistical design of Shewhart control chart with runs rules

런 규칙이 혼합된 슈와르트 관리도의 통계적 설계

  • Kim, Young-Bok (Dept. of Industrial Engineering, Seoul National University) ;
  • Hong, Jung-Sik (Dept. of Industrial & Information Systems Engineering, Seoul National University of Technology) ;
  • Lie, Chang-Hoon (Dept. of Industrial Engineering, Seoul National University)
  • 김영복 (서울대학교 산업공학과) ;
  • 홍정식 (서울산업대학교 산업정보시스템공학과) ;
  • 이창훈 (서울대학교 산업공학과)
  • Published : 2008.09.30
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Abstract

This research proposes a design method based on the statistical characteristics of the Shewhart control chart incorporated with 2 of 2 and 2 of 3 runs rules respectively. A Markov chain approach is employed in order to calculate the in-control and out-of-control average run lengths(ARL). Two different control limit coefficients for the Shewhart scheme and the runs rule scheme are derived simultaneously to minimize the out-of-control average run length subject to the reasonable in-control average run length. Numerical examples show that the statistical performance of the hybrid control scheme are superior to that of the original Shewhart control chart.

Keywords

References

  1. 박창순, 이재헌, 김영일(2002), 'VSI와 VSS 관리도의 경제적 효율 비교',품질경영학회지, 30권, 2호, pp. 99-117
  2. 송서일, 박현규, 정혜진(2004), 'VSI EWMA 관리도의 경제적 통계적 설계',품질경영학회지, 32권, 1호, pp. 92-101
  3. 이호중, 임태진(2005), '두 개의 이상원인을 고려한 VSSI X 관리도의 경제적-통계적 설계',대한산업공학회지, 31권, 1호, pp. 87-98
  4. 임태진(2005), '선택적 누적합(S-CUSUM) 관리도', 품질경영학회지, 33권, 3호, pp. 126-134
  5. Acosta-Mejia, C. A.(2007), 'Two Sets to Runs Rules for the X Chart', Quality Engineering, Vol.19, pp.129-136 https://doi.org/10.1080/17513470701263641
  6. Bai, D. S. and Lee, K. T.(1998), 'An Economic Design of Variable Sampling Interval X Control Charts', International Journal of Production Economics, Vol.54, pp.57-64 https://doi.org/10.1016/S0925-5273(97)00125-4
  7. Brook, D. and Evans D. A.(1972), 'An approach to the Probability Distribution of CUSUM Run Lengths', Biometrika, Vol.59, pp.539-549 https://doi.org/10.1093/biomet/59.3.539
  8. Champ, C. W. and Woodall, W. H.(1987), 'Exact Results for Shewhart Control Charts With Supplementary Runs Rules', Technometrics, Vol.29, No.4, pp.393-399 https://doi.org/10.2307/1269449
  9. Chen, Y. K., Hsieh, K. L. and Chang, C. C.(2007), 'Economic Design of the VSSI X Control Charts for Correlated Data', International Journal of Production Economics, Vol.107, No.2, pp.528-539 https://doi.org/10.1016/j.ijpe.2006.10.008
  10. Chung, K. J.(1992), 'Determination of Optimal Design Parameters of an X Control Chart', Journal of Operational Research Society, Vol.43, No.12, pp.1151-1157 https://doi.org/10.2307/2584271
  11. Costa, A. F. B. and Magalhaes M. S. De. (2005), 'Economic design of two-stage charts: The Markov chain approach', International Journal of Production Economics, Vol.95, No.1, pp.9-20 https://doi.org/10.1016/j.ijpe.2003.10.024
  12. Fu, J. C., Spiring, F. A. and Xie, H. (2002), 'On the average run lengths of quality control schemes using a Markov chain approach', Statistics & Probability Letters, Vol.56, pp.369-380 https://doi.org/10.1016/S0167-7152(01)00183-3
  13. Fu, J. C., Shmueli, G. and Chang, Y. M. (2003), 'A unified Markov chain approach for computing the run length distribution in control charts with simple or compound rules', Statistics & Probability Letters, Vol.65, pp.457-466 https://doi.org/10.1016/j.spl.2003.10.004
  14. Hurwitz A. and Mathur M.(1992), 'A very Simple Set of Process Control Rules', Quality Engineering, Vol. 5, No. 1, pp. 21-29 https://doi.org/10.1080/08982119208918947
  15. Khoo, M. B. C. and Ariffin, K. N. bt. (2006), 'Two Improved Runs rules for the Shewhart X Control Chart', Quality Engineering, Vol.18, pp.173-178 https://doi.org/10.1080/08982110600567517
  16. Klein, M. (2000), 'Two Alternatives to the Shewhart X Control Chart', Journal of Quality Technology, Vol.32, pp.427-431 https://doi.org/10.1080/00224065.2000.11980028
  17. Prabhu, S. S., Montgomery, D. C. and Runger, G. C.(1997), 'Economic-Statistical Design of an Adaptive X Chart', International Journal of Production Economics, Vol.49, pp.1-15 https://doi.org/10.1016/S0925-5273(96)00100-4
  18. Taylor, H. M. (1968), 'The Economic Design of Cumulative Sum Control Charts, Technometrics', 10(3), 479-488 https://doi.org/10.2307/1267102
  19. Woodall, W. H.(1985), 'The statistical design of quality control charts', The Statistician, Vol.34, pp.155-160 https://doi.org/10.2307/2988154