The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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The in-control performance of the CCC-r chart with estimated parameters

추정된 모수를 사용한 CCC-r 관리도에서 관리상태의 성능

  • Kim, Jaeyeon (Department of Applied Statistics, Chung-Ang University) ;
  • Kim, Minji (Department of Applied Statistics, Chung-Ang University) ;
  • Lee, Jaeheon (Department of Applied Statistics, Chung-Ang University)
  • 김재연 (중앙대학교 응용통계학과) ;
  • 김민지 (중앙대학교 응용통계학과) ;
  • 이재헌 (중앙대학교 응용통계학과)
  • Received : 2018.05.11
  • Accepted : 2018.07.25
  • Published : 2018.08.31
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Abstract

The CCC-r chart is more effective than traditional attribute control charts for monitoring high-quality processes. In-control process parameters are typically unknown and should be estimated when implementing a CCC-r chart. Phase II control chart performance can deteriorate due to the effect of the estimation error. In this paper, we used the standard deviation of average run length (ARL) as well as the average of ARL to quantify the between-practitioner variability in the CCC-r chart performance. The results indicate that the CCC-r chart requires larger Phase I data than previously recommended in the literature in order to have consistent chart in-control performance among practitioners.

CCC-r 관리도는 고품질공정에서 공정불량률을 관리하는 경우 매우 효율적이라고 알려져 있다. 이 관리도를 사용할 때 관리상태의 공정모수는 일반적으로 알려져 있지 않기 때문에 제1국면의 표본을 추출하여 이를 추정해야 한다. 제2국면에서 관리도의 성능은 제1국면에서 추정한 모수와 관리한계에 영향을 받기 때문에, 추정 오차의 영향을 살펴보는 것은 중요하다. 이 논문에서는 일반적으로 많이 사용하는 평균런길이의 평균(average of average run length) 이외에 평균런길이의 표준편차(standard deviation of average run length)를 사용하여 CCC-r 관리도의 관리상태의 성능을 평가하였다. 그 결과 CCC-r 관리도에서 안정적인 관리상태의 성능을 유지하기 위해서는 이전에 권장하던 제1국면의 표본 크기보다 훨씬 더 큰 표본이 필요하다는 사실을 알 수 있었다.

Keywords

References

  1. Faraz, A., Heuchenne, C., and Saniga, E. (2017). The np chart with guaranteed in-control average run lengths, Quality and Reliability Engineering International, 33, 1057-1066. https://doi.org/10.1002/qre.2091
  2. Gandy, A. and Kvaloy, K. J. (2013) Guaranteed conditional performance of control charts via bootstrap methods, Scandinavian Journal of Statistics, 40, 647-668. https://doi.org/10.1002/sjos.12006
  3. Jones, M. A. and Steiner, S. H. (2012) Assessing the effect of estimation error on risk-adjusted CUSUM chart performance, International Journal for Quality in Health Care, 24, 176-181. https://doi.org/10.1093/intqhc/mzr082
  4. Lee, J., Wang, N., Xu, L., Schuh, A., and Woodall, W. H. (2013). The effect of parameter estimation on upper-sided Bernoulli cumulative sum charts, Quality and Reliability Engineering International, 29, 639-651. https://doi.org/10.1002/qre.1413
  5. Montgomery, D. C. (2013). Statistical Quality Control: A Modern Introduction (7th ed.), John Wiley & Sons, NJ.
  6. Quesenberry, C. P. (1993). The effect of sample size on estimated limits for X and X control charts, Journal of Quality Technology, 25, 237-247. https://doi.org/10.1080/00224065.1993.11979470
  7. Saleh, N. A., Mahmoud, M. A., Jones-Farmer, L. A., Zwetsloot, I. N. E. Z., and Woodall, W. H. (2015a). Another look at the EWMA control chart with estimated parameters, Journal of Quality Technology, 47, 363-382. https://doi.org/10.1080/00224065.2015.11918140
  8. Saleh, N. A., Mahmoud, M. A., Keefe, M. J., and Woodall, W. H. (2015b). The difficulty in designing Shewhart X and X control charts with estimated parameters, Journal of Quality Technology, 47, 127-138. https://doi.org/10.1080/00224065.2015.11918120
  9. Xie, M., Lu, X. S., Goh, T. N., and Chan, L. Y. (1999). A quality monitoring and decision-making scheme for automated production processes, International Journal of Quality & Reliability Management, 16, 148-157. https://doi.org/10.1108/02656719910218238
  10. Yang, Z., Xie, M., Kuralmani, V., and Tsui, K. L. (2002). On the performance of geometric charts with estimated control limits, Journal of Quality Technology, 34, 448-458. https://doi.org/10.1080/00224065.2002.11980176
  11. Zhang, M., Peng, Y., Schuh, A., Megahed, F. M., and Woodall, W. H. (2013). Geometric charts with estimated control limits, Quality and Reliability Engineering International, 29, 209-223. https://doi.org/10.1002/qre.1304
  12. Zhao, M. J. and Driscoll, A. R. (2016). The c-chart with bootstrap adjusted control limits to improve conditional performance, Quality and Reliability Engineering International, 32, 2871-2881. https://doi.org/10.1002/qre.1971