Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
권호 표지

Comparison for the Economic Performance of Control Charts with the VSI and VSS Features

VSI와 VSS 관리도의 경제적 효율 비교

  • 박창순 (중앙대학교 응용통계학과) ;
  • 이재헌 (광주대학교 산업정보공학과) ;
  • 김영일 (중앙대학교 정보시스템학과)
  • Published : 2002.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

Variable sampling interval(VSI) and variable sample size(VSS) control charts vary the sampling rate for the next sample depending on the current chart statistic. This paper develops EWMA charts with the VSI and VSS features, and investigates the effectiveness of these charts in context of an economic model. The economic properties of these charts are evaluated by using Markov chain methods. The model contains cost parameters which allow the specification of the costs associated with sampling, false alarms, and operating off target. This economic model can be used to quantify the cost saving that can be obtained by using control charts with the VSI and VSS features instead of with the fixed sampling rate(FSR) feature, and can also be used to gain insight into the way that control charts with the VSI and VSS features should be designed to achieve optimal economic performance. The economic performance of X charts with the VSI and VSS features is also considered.

Keywords

References

  1. Annadi, H. P., Keats, J. B., Runger, G. C., and Montgomery, D. C.(1995), 'An Adaptive Sample Size CUSUM Control Chart', International Journal of Production Research, Vol. 33, pp. 1605-1616 https://doi.org/10.1080/00207549508930231
  2. Arnold, J. C. and Reynolds, M. R., Jr.(1994), 'CUSUM Charts with Variable Sample Size and Variable Interval Size', Proceedings, Section on Quality and Productivity, ASA, pp. 87-92
  3. Arnold, J. C. and Reynolds, M. R., Jr.(2001), 'CUSUM Control Charts with Variable Sample Sizes and Sampling Intervals', Journal of Quality Technology, Vol. 33, pp. 66-81 https://doi.org/10.1080/00224065.2001.11980048
  4. Arnold, J. C., Reynolds, M. R., Jr., and Sawalapurkar-Powers, U.(1993), 'Control Charts with Variable Sample Size and Variable Interval Size', Proceedings, Section on Quality and Productivity, ASA, pp. 138-143
  5. Chengalur-Smith, I. N., Arnold, J. C., and Reynolds, M. R., Jr.(1989), 'Variable Sampling Intervals for Multiparameter Shewhart Charts', Communications in Statistics .' Theory and Methods, Vol. 18, pp. 1769-1792 https://doi.org/10.1080/03610928908830000
  6. Costa, A. F. B.(1994),' $\bar{X}$ Charts with Variable Sample Size', Journal of Quality Technology, Vol. 26, pp. 155-163 https://doi.org/10.1080/00224065.1994.11979523
  7. Costa, A. F. B.(1997), '$\bar{X}$ Charts withVariable Sample Sizes and SamplingIntervals', Journat of Quatity Technotogy, Vol. 29, pp. 197-204
  8. Costa, A. F. B.(1999), 'Joint $\bar{X}$ and R Charts with Variable Sample Sizes and Sampling Intervals', Journal of Quality Technology, Vol. 31, pp. 387-397
  9. Duncan, A. J.(1971), 'The Economic Design of $\bar{X}$ Chart When There Is a Multiplicity of Assignable Causes', Journal of the American Statistical Association, Vol. 66, pp. 39-53
  10. Lasdon, L. S., Waren, A. D., Jain, A., and Ranter, M.(1978), 'Design and Testing of Generalized Reduced Gradient Code for Nonlinear Programming', ACM Transactions on Mathematical Software, Vol. 4, pp34-50 https://doi.org/10.1145/355769.355773
  11. Lorenzen, T. J. and Vance, L. C.(1986), 'The Economic Design of Control Charts : A Unified Approach', Technometrics, Vol. 28, pp. 3-10 https://doi.org/10.2307/1269598
  12. Park, C. and Reynolds, M. R. Jr.(1994), 'Economic Design of a Variable Sample Size $\bar{X}$-Charts', Communications in Statistics Simulation and Computation, Vol. 23, pp. 467-483 https://doi.org/10.1080/03610919408813182
  13. Park, C. and Reynolds, M. R., Jr.(1999), 'Economic Design of a Variable Sampling Rate $\bar{X}$-Chart', Journal of Quality Technology, Vol. 31, pp. 427-443
  14. Prabhu, S. S., Montgomery, D. C., and Runger, G. C.(1994), 'A Combined Adaptive Sample Size and Sampling Interval $\bar{X}$ Control Scheme', Journal of Quality Technology, Vol. 26, pp. 164-176 https://doi.org/10.1080/00224065.1994.11979524
  15. Prabhu, S. S., Montgomery, D. C., and Runger, G. C.(1997), 'Economic-Statistical Design of an Adaptive $\bar{X}$ Chart' International Journal of Production Economics, Vol. 49, pp. 1-15
  16. Prabhu, S. S., Runger, G. C., and Keats, J. B.(1993), 'An Adaptive Sample Size X Chart', International Journal of Production Research, Vol. 31, pp. 2895-2909 https://doi.org/10.1080/00207549308956906
  17. Rendtel, U.(1990), 'CUSUM Schemes with Variable Sampling Intervals and Sample Sizes', Statistical Papers, Vol. 31, pp. 103-118 https://doi.org/10.1007/BF02924681
  18. Reynolds, M. R., Jr.(1989), 'Optimal Variable Sampling Interval Control Charts', Sequential Analysis, Vol. 8, pp. 361-379 https://doi.org/10.1080/07474948908836187
  19. Reynolds, M. R., Jr.(1995), 'Evaluating Properties of Variable Sampling Interval Control Charts', Sequential Analysis, Vol. 14, pp. pp. 59-97 https://doi.org/10.1080/07474949508836320
  20. Reynolds, M. R.,Jr.(1996a), 'Shewhart and EWMA Variable Sampling Interval Control Charts with Sampling at Fixed Times', Journal of Quality Technology, Vol. 28, pp. 199-212
  21. Reynolds, M. R., Jr.(1996b), 'Vahable Sampling Interval Control Charts with Sampling at Fixed Times', IIE Transactions, Vol. 28, pp. 497-510
  22. Reynolds, M. R., Jr., Amin, R. W., and Arnold, J. C.(1990), 'CUSUM Charts with Variable Sampling Interval', Technometrics, Vol. 32, pp. 371-384 https://doi.org/10.2307/1270114
  23. Reynolds, M. R., Jr., Amin, R. W., Arnold, J. C., and Nachlas, J. A.(1988) ' X Charts with Variable Sampling Interval', Technometrics, Vol. 30, pp. 181-192 https://doi.org/10.2307/1270164
  24. Reynolds, M. R., Jr. and Arnold, J. C.(1989), 'Optimal Shewhart Control Charts with Variable SamplingIntervals Between Samples' SequentialAnatysis, Vol. 8, pp. 51-77
  25. Reynolds, M. R., Jr. and Amold, J. C.(2001), 'EWMA Control Charts with Variable Sample Sizes and Variable Sampling Intervals', IIE Transactions, Vol. 33, pp. 511-530
  26. Reynolds, M. R., Jr., Arnold, J. C., and Baik, J. W.(1996), 'Variable Sampling Interval $\bar{X}$-Charts in the Presence of Correlation', Journal of Quality Technology, Vol. 28, pp. 12-30
  27. Runger, G. C. and Pignatiello, J. J., Jr.(1991), 'Adaptive Sampling for Process Control', Journal of Quality Technology, Vol. 23, pp. 135-155
  28. Saccucci, M. S., Amin, R. W., and Lucas, J. M.(1992), 'Exponentially Weighted Moving Average Control Schemes with Variable Sampling Intervals', Communications in Statistics : Simulation and Computation, Vol. 21, pp. 627- 657 https://doi.org/10.1080/03610919208813040
  29. Zimmer, L. S., Montgomery, D. C., and Runger, G. C.(1998), 'Evaluation of a Three-State Adaptive Sample Size $\bar{X}$ Control Chart', International Journal of Production Research, Vol. 36, pp. 733-743 https://doi.org/10.1080/002075498193660