Robust Control Chart using Bootstrap Method

붓스트랩 방법을 이용한 로버스트 관리도

  • 송서일 (동아대학교 산업시스템공학과) ;
  • 조영찬 (동아대학교 산업시스템공학과) ;
  • 박현규 (동아대학교 산업시스템공학과)
  • Published : 2003.09.01

Abstract

Statistical process cintrol is intended to assist operators of a stable system in monitoring whether a change has occurred in the process, and it uses several control charts as main tools. In design and use of control chart, it is rational that probability of false alarm is minimized in stable process and probability of detecting shifts is maximized in out-of-control. In this study, we establish bootstrap control limits for robust M-estimator chart by applying the bootstrap method, called resampling, which could not demand assumptions about pre-distribution when the process is skewed and/or the normality assumption is doubt. The results obtained in this study are summarized as follows : bootstrap M-estimator control chart is developed for applying bootstrap method to M-estimator chart, which is more robust to keep ARL when process contain contaminate quality characteristic.

Keywords

References

  1. W. A. Shewhart, Statistical Methods from the viewpoint of Quality Control,Republished in 1986 by Dover Publications, New York, NY, (1939)
  2. C. E. Noble, 'Variations in Conventional Control Charts,' Industrial Quality Control, Vol. 8, No.3, pp. 17-22, (1951)
  3. N. R. Farnum and L. W. Stanton, 'Using Counts to Monitor a Process Mean,' Journal of quality Control, Vol. 9, No.5, pp. 30-34, (1953)
  4. B. F. Arnold, 'The Sign Test in Current Control,' Statistische Hefte, Vol. 26, pp. 253-262, (1985) https://doi.org/10.1007/BF02932537
  5. B. F. Arnold, 'Comparison of the Approximate and Exact Optimum Economic Design of Control Charts Basing on the Sign Test,' Statistische Hefte, Vol. 27,pp. 239-241, (1986) https://doi.org/10.1007/BF02932570
  6. H. Peter and L. Johannes, 'A Control Chart Based on Ranks,' Journal of Quality Technology, Vol. 23, No.2, pp. 117-124, (1991)
  7. James A. Alloway, Jr. and M. Raghavachari, 'Control Chart Based on the Hodges-Lehmann Estimator,' Journal of Quality Technology, Vol. 23, No.4, pp. 336-347, (1991)
  8. Edward A. Pappanastos and Benjamin M. Adams, 'Alternative Designs of the Hodges-Lehmann Control Chart,' Journal of Quality Technology, Vol. 28, No.2, pp. 213-223, (1996)
  9. Moustafa O. Abu-Shawiesh and Mokhtar B. Abdullah, 'New Robust Statistical Process Control Chart for Location,' Quality Engineering, Vol. 12, No.2, pp.149-159, (1999) https://doi.org/10.1080/08982119908962572
  10. 이 병근, 정 현석, 남 호수. 공정평균을 관리하기 위한 로버스트 관리도, 공업경영학회지, 21권, 48집, 65-71 (1998)
  11. S. M. Bajgier, 'The Use of Bootstrappping to Construct Limits on Control Charts,' Proceeding of the Decision Science Institute, San Diego, CA., pp. 1611-1613 (1992)
  12. T. Seppala, H. Moskowitz, R. Plante and 1. Tang, 'Statistical Process Control via the Subgroup,' Journal of Quality Technology, Vol. 27, No.2, pp. 139-153 (1995)
  13. R. Y. Liu and J. Tang, 'Control Charts for Dependent and Indepent Measurements Based on Bootstrap,' Journal of the American Statistical Association, Vol. 91, No. 436, pp. 1694-1700 (1996) https://doi.org/10.2307/2291598
  14. L. A. Jones and W. H. Woodall, 'The Performance of Bootstrap Control Charts,' Journal of Quality Technology, Vol. 30, No.4, pp. 362-375 (1998)