Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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The Z-CUSUM Control Chart for the Process with Recurring Cycles or Frequent Small Shifts

순환주기나 빈번한 작은 이동이 발생하는 공정관리틀 위한 Z-CUSUM 관리도

  • Published : 2004.06.01
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Abstract

CUSUM control charts are widely used to monitor processes with small shifts. CUSUM control charts are, however, less effective in detecting for recurring cycles or frequent small shifts in the processes. With Shewhart control charts, we have applied the variety of run rules to check the stability of process in addition to the situations that some points fall outside the control limits. In this paper, we propose the Z -CUSUM control chart for monitoring the process with recurring cycles or frequent small shifts by use of the zone concept as like the Shewhart control charts.

Keywords

References

  1. Abdellatif M.A. and E.I. Shabrawy A.Z.(1996), 'The economic design of cumulative sum charts used to maintain current control of non normal process means', Computers & Industrial Engineering, Vol. 31, pp. 783-790 https://doi.org/10.1016/S0360-8352(96)00242-2
  2. Besterfield, D. H.(2001), Quality Control, Prentice Hall, pp. 179-206
  3. Bissell, A. F(1979), 'A Semi parabolic Mask for Cusum Charts', The Statistician, Vol. 28, pp. 1-7 https://doi.org/10.2307/2988027
  4. Champ, C. W. and Woodall, W. H. (1987), 'Exact Results for Shewhart Control Charts with Supplementary Run Rules', Technometrics, Vol. 29, pp. 393-399 https://doi.org/10.2307/1269449
  5. Chiu, W. K.(1974), 'The Economic Design of CUSUM Charts for Controlling Nomal Means', Applied Statistics, Vol. 23, pp. 420-433 https://doi.org/10.2307/2347134
  6. Deming, W. E.(1982), Quality, Productivity, and Competitive Position Massa chusetts Institute of Technology
  7. Ewan, W. D.(1963), 'When and How to Use CUSUM Charts', Technometrics, Vol. 5, pp. 1-22 https://doi.org/10.2307/1266488
  8. Gan, F. F.(1993), 'The Run Length Distribution of a Cumulative Sum Control Chart', Journal of Quality Technology, Vol. 25, pp. 205-215 https://doi.org/10.1080/00224065.1993.11979455
  9. Gibra, I. N.(1975), 'Recent Developments in Control Chart Techniques', Journal of Quality Technology, Vol. 7, pp. 183-192 https://doi.org/10.1080/00224065.1975.11980695
  10. Goel, A. L. and Wu, S. M. (1973), 'Economically Optimum Design of CUSUM Charts', Management Science, Vol. 19, pp. 1271-1282 https://doi.org/10.1287/mnsc.19.11.1271
  11. Hawkins, D. M.(1992), 'A Fast Accurate Approximation for Average Run Lengths of CUSUM Control Charts', Journal of Quality Technology, Vol.24. pp. 37-43 https://doi.org/10.1080/00224065.1992.11979372
  12. Hawkins, D. M.(1993), 'Cumulative Sum Control Charting: An Underutilized SPC Tool', Quality Engineering, Vol.25. pp. 463-477
  13. Johnson, N. L. and Leone, F. C.(1962), 'Cumulative Sum Control Charts: Mathema tical Principles Applied to Construction and Use', Industrial Quality Control, Vol. 18, pp. 15-21
  14. Lu, C. W. and Reynolds, M. R.(2001), 'CUSUM charts for monitoring an autocor related process', Journal of Quality Technology, Vol. 33, pp. 316-335 https://doi.org/10.1080/00224065.2001.11980082
  15. Lucas, J. M(1973), 'A Modified 'V' Mask Control Schemes', Technometrics, Vol. 15, pp. 833-847 https://doi.org/10.2307/1267393
  16. Lucas, J. M.(1982), 'Conbined Shewh art CUSUM Quality Control Schemes', Journal of Quality Technology, Vol. 14, pp. 51-59 https://doi.org/10.1080/00224065.1982.11978790
  17. Lucas, J. M. and Crosier, R. B. (1982), 'Fast Initial Response for CUSUM Quality Control Schemes', Technometrics, Vol. 24, pp. 199-205 https://doi.org/10.2307/1268679
  18. Luceno, A.(1999), 'Average Run Len gths and Run Legth Probability Distributions for Cuscore Charts to Control Normal Mean', Computational Statistics and Data Analysis, Vol. 32, pp. 177-195 https://doi.org/10.1016/S0167-9473(99)00025-0
  19. Luceno, A. and Puig-Pey, J.(2000), 'Evaluation of the Run Length Probability Distribution for CUSUM Charts: Assessing Chart Performance', Technometrics, Vol. 42, pp. 411-416 https://doi.org/10.2307/1270951
  20. Luceno, A. and Puig-Pey, J.(2000a), 'Computing the Run Length Probability Distribution for CUSUM Charts', Journal of Quality Technology, Vol. 34, pp. 209-214
  21. Montgomery, D. C.(2001), INTRO- DUCTION TO STATISTICAL QUALITY CONTROL, Wiley, pp. 166-177 & pp. 406-430
  22. Atienza, O. O., Tang, L.C. and Ang, B. W.(2002), 'A CUSUM scheme for auto correlated observations', Journal of Quality Technology, Vol. 34, pp. 187-200 https://doi.org/10.1080/00224065.2002.11980145
  23. Nelson, L S..(1984), 'The Shewhart Control Chart Tests for Special Causes', Journal of Quality Technology, Vol. 14, pp. 237-239
  24. Page, E. S.(1961), 'Cumulative Sum Charts', Technometrics, Vol. 3, pp. 1-10 https://doi.org/10.2307/1266472
  25. Page, E. S.(1962), 'Cumulative Sum Schemes Using Gauging', Technometrics, Vol. 4, pp. 97-109 https://doi.org/10.2307/1266175
  26. Rahim E. S. and Lashkari R. S. (1982), 'An Economic Design of cusum Charts to Control Non- Normal Process Means', Computers & Industrial Engineering, Vol. 6, pp. 1-18 https://doi.org/10.1016/0360-8352(82)90021-3
  27. Rowlands, R. J., Nix, A. B., Abdollian, M. A. and Kemp, K. W.(1982), 'Snub -nosed V-mask Control Schemes', The Statistician, Vol. 31, pp. 133-142 https://doi.org/10.2307/2987884
  28. Taylor, H. M.(1968), 'The Economic Design of Cumulative Sum Control Charts', Technometrics, Vol. 10, pp. 479-488 https://doi.org/10.2307/1267102
  29. Waldmann, K. H.(1996), 'Design of double CUSUM quality control schemes', European Journal of Operational Research, Vol. 95, pp. 641-648 https://doi.org/10.1016/0377-2217(95)00317-7
  30. Woodall, W. H.(1983), 'The Distribution of the Run Length of One-sided CUSUM Procedures for Continuous Random Variables', Technometrics, Vol. 25, pp. 295-301 https://doi.org/10.2307/1268615
  31. Woodall, W. H.(1984), 'One the Markov Chain Approach to the Two-sided CUSUM Procedure', Technometrics, Vol. 26, pp. 41-46 https://doi.org/10.2307/1268414
  32. Woodall, W. H.(1985), 'The Statistical Design of Quality Control Charts', The Statistician, Vol. 34, pp. 155-160 https://doi.org/10.2307/2988154
  33. Woodall, W. H.(1986), 'The Design of CUSUM Quality Control Charts', Journal of Quality Technology, Vol. 18, pp. 99-102 https://doi.org/10.1080/00224065.1986.11978994
  34. Yshchin, E.(1985), 'One the Markov Chain Approach to the Two-sided CUSUM Procedure', Technometrics, Vol. 26, pp. 41-46