Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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Bootstrap Confidence Intervals of the Process Capability Index Based on the EDF Expected Loss

EDF 기대손실에 기초한 공정능력지수의 붓스트랩 신뢰구간

  • 임태진 (숭실대학교 산업·정보시스템공학과) ;
  • 송현석 (숭실대학교 산업·정보시스템공학과)
  • Published : 2003.12.01
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Abstract

This paper investigates bootstrap confidence intervals of the process capability index(PCI) based on the expected loss derived from the empirical distribution function(EDF). The PCI based on the expected loss is too complex to derive its confidence interval analytically, so the bootstrap method is a good alternative. We propose three types of the bootstrap confidence interval; the standard bootstrap(SB), the percentile bootstrap(PB), and the acceleration biased­corrected percentile bootstrap(ABC). We also perform a comprehensive simulation study under various process distributions, in order to compare the accuracy of the coverage probability of the bootstrap confidence intervals. In most cases, the coverage probabilities of the bootstrap confidence intervals from the EDF PCI turned out to be more accurate than those from the PCI based on the normal distribution. It is expected that the bootstrap confidence intervals from the EDF PCI can be utilized in real processes where the true distribution family may not be known.

Keywords

References

  1. 임태진, 송현석(2003), 'EDF 기대손실에기초한 로버스트 공정능력지수", 「품질경영학회지」, 31귄, 1호, pp.109-122
  2. 정영배, 문혜진(2002), "역정규 손실함수를 이용한 공정능련지수에 관한 연구", '품질경영학회지' pp.66-78
  3. 조중재, 김주성, 박병선(1999), '공정능력지수 C$C_p_k$에 대한 보다 나은 비모수적 붓스트랩 신뢰구간에 관한 연구',「응용통계연구」 , 12권, 1호, pp.45-65
  4. Boyles, R. A.(1991), 'The TaguchiCapability Index', Journal of uatity Technology, Vol. 23, No. 1, pp.17-26 https://doi.org/10.1080/00224065.1991.11979279
  5. Chan, L. K., Cheng, S. W., and Sprine, F. A.(1988), 'A NewMeasure of Process Capability :$C_p_m$', JournaI of the QualityTechnoIogy, Vol. 20, No.3,pp.162-175
  6. Chan, L. K., Xiong, Z., and Zang,D.(1990), 'On The AsymptoticDistributions of Some ProcessCapability Indices', Communications in Statistics- Theory and Methods,Vol. 19, pp.11-18 https://doi.org/10.1080/03610929008830183
  7. Choi, K. C., Nam, K. H., and Park,D. H.(1996), 'Estimation of CapabilityIndex Based on Bootstrap Method',Microelect. & ReIiab., Vol. 36, No.9,pp.1141-1153 https://doi.org/10.1016/0026-2714(95)00211-1
  8. Franklin, L. A. and Wasserman, G.S.(1992), 'Bootstrap Lower ConfidenceLimits For Capability Indices',Journal of Quality Technology, Vol.24, No 4, pp.196-210 https://doi.org/10.1080/00224065.1992.11979401
  9. Efron, B. (1979), 'Bootstrap Methods:Another Look at the Jackknife', Ann.Statist., Vol. 7, No. 1, pp.1-26 https://doi.org/10.1214/aos/1176344552
  10. Efron, B. (1993), An Introduction tothe Bootstrap, Chapman & Hall,New York London
  11. Hall, P. (1988), 'TheoreticalComparison of Bootstrap ConfidenceIntervals', Ann. Statist., Vol. 16,pp.927-953 https://doi.org/10.1214/aos/1176350933
  12. Pearn, W. L., Kotz, S., and Johnson,N. L.(1992), 'Disthbutional andInferential Properties of ProcessCapability Indices', JournaI of Quatity Technology, Vol. 24, No. 4,pp.216-231
  13. Spiring, F. A.(1993), 'The ReflectedNormal Loss Function', The Canadian JournaI of Statistics, Vol.21, No. 3, pp.321-330 https://doi.org/10.2307/3315758
  14. Spiring, F. A. and Yeung, A.S.(1998), 'A General Class of LossFunctions with IndustrialApplications' Journat of QuatityTechnotogy, Vol. 30, No. 2,pp.152-162