Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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Economic-Statistical Design of VSI Run Rules Charts

VSI 런-규칙 관리도의 경제적-통계적 설계

  • Kang, Bun-Kyu (Dept. of Industrial & Information Systems Engineering, Soongsil University) ;
  • Lim, Tae-Jin (Dept. of Industrial & Information Systems Engineering, Soongsil University)
  • 강분규 (숭실대학교 산업.정보시스템공학과) ;
  • 임태진 (숭실대학교 산업.정보시스템공학과)
  • Received : 2010.06.09
  • Accepted : 2010.06.23
  • Published : 2010.06.30
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Abstract

This research proposes a method for designing VSI (Variable Sampling Interval) control charts with supplementary run rules. The basic idea is to apply various run rules and the VSI scheme to a control chart in order to increase the sensitivity. The sampling process of the VSI run rules chart is constructed by Markov chain approach. A procedure for designing the VSI run rules chart is proposed based on Lorenzen and Vance's model. Sensitivity study shows that the VSI run rules charts outperform the FSI (Fixed Sampling Interval) run rules charts for wide range of process mean shifts. A major advantage of the VSI run rules chart over other charts such as CUSUM, EWMA, and adaptive charts is it's simplicity in implementation. Some useful guidelines are proposed based on the sensitivity study.

Keywords

References

  1. Acosta-Mejia, C. A.(2007), "Two Sets to Runs Rules for the Chart", Quality Engineering, Vol.19, pp. 129-136. https://doi.org/10.1080/17513470701263641
  2. Amin, R. W. and Letsinger W. C.(1991), "Improved switching rules in control procedures using variable sampling intervals", Commun Stat Simul Comput, Vol. 20, pp. 205-230. https://doi.org/10.1080/03610919108812949
  3. 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
  4. Costa, A. F. B.(1994), "X Charts with Variable Sample Size", Journal of Quality Technology, Vol. 26, No.3, pp.155-163.
  5. Costa, A. F. B.(1997), "X Charts with Variable Sample Size and Sampling Intervals", Journal of Quality Technology, Vol. 29, No. 2, pp. 197-204.
  6. Das T. K., Jain, V., and Gosavi, A.(1997), "Economic Design of Dual-Sampling-Interval Policies for X Charts with and without Run Rules", IIE. Transactions, Vol. 29, pp. 497-506.
  7. Duncan, A. J.(1956), "The Economic Design of X Charts Used to Maintain Current Control of a Process", Journal of the American Statistical Association, 51(274), pp. 228-242. https://doi.org/10.2307/2281343
  8. Khoo, M. B. C. and Ariffin, K. N. (2006), "Two Improved Runs rules for the Shewhart Control Chart", Jounal of Quality Technology, Vol.32, pp. 427-431.
  9. Kim, Y. B., Hong, J. S., and Lie, C. H.(2009), "Economic statistical design of 2-of-2 and 2-of-3 runs rule scheme", Quality and Reliability Engineering International, Vol. 25, pp. 215-228. https://doi.org/10.1002/qre.963
  10. Klein, M.(2000), "Two alternatives to the Shewhart X control chart", Journal of Quality Technology, Vol. 32, pp. 427-431.
  11. Lorenzen, T. J. and Vance, L. C.(1986), "The Economic Design of Control Charts: A Unified Approach", Technometrics, Vol. 28, No. 3, pp. 3-10. https://doi.org/10.1080/00401706.1986.10488092
  12. Montgomery, D. C.(2001), Introduction to Statistical Quality Control(4th ed.), New York, NY: Wiley.
  13. Page, E. S.(1962) "A modified control chart with warning lines", Biometrika, Vol. 49, pp. 171-176. https://doi.org/10.1093/biomet/49.1-2.171
  14. Parkhideh, S. and Parkhideh, B.(1996), "The economic design of a flexible zone chart with AT&T rules", IIE Trans. Vol. 28, Np. 3, pp. 261-266. https://doi.org/10.1080/07408179608966272
  15. Parkhideh, S. and Parkhideh, B.(1998), "Design of a flexible zone individuals control chart.", Jour. Prod, Econ, Vol. 36, No. 8, pp. 2259-2267.
  16. Prabhu, S. S., Runger, G. C., and Keats, J. B.(1993), "X Chart with Adaptive Sample Sizes", International Journal of Production Research, Vol. 31, pp. 2895-2909. https://doi.org/10.1080/00207549308956906
  17. Prabhu, S. S., Montgomery, D. C., and Runger, G. C.(1994), "A Combined Adaptive Sample Size and Sampling Interval X Control Chart Scheme", Journal of Quality Technology, Vol. 26, No. 3, pp.164-176.
  18. Prabhu, S. S., Montgomery, D. C., and Runger, G. C.(1997), "Economic- Statistical Design of Adaptive X Chart", International Journal of Production Economics, Vol. 49, No. 1, pp. 1-15. https://doi.org/10.1016/S0925-5273(96)00100-4
  19. Reynolds, M. R., Amin, R. W., Arnold, J. C., and Nachlas, J. A.(1988), "X Charts with Variable Sampling Intervals", Technometrics, Vol. 30, No. 2, pp. 181-192. https://doi.org/10.2307/1270164
  20. Tagaras, G.(1998), "A Survey of Recent Developments in the Design of Adaptive Control Charts" ournal of Quality Technology, Vol. 30, No. 3, pp. 212-231.