Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
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Statistical Tests for Process Capability Index Cp Based on Mixture Normal Process

혼합 정규공정 하에서의 공정능력지수 Cp에 대한 가설검정

  • Cho, Joong Jae (Department of Information and Statistics, Chungbuk National University) ;
  • Heo, Tae-Young (Department of Information and Statistics, Chungbuk National University) ;
  • Jeong, Jun Chel (Department of Information and Statistics, Chungbuk National University)
  • 조중재 (충북대학교 정보통계학과) ;
  • 허태영 (충북대학교 정보통계학과) ;
  • 정준철 (충북대학교 정보통계학과)
  • Received : 2014.04.30
  • Accepted : 2014.06.11
  • Published : 2014.06.30
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Abstract

Purpose: The purpose of this study is to develop the statistical test for process capability index $C_p$ based on mixture normal process. Methods: This study uses Bootstrap method to calculate the approximate P-value for various simulation conditions under mixture normal process. Results: This study indicates that our proposed method is effective way to test for process capability index $C_p$ based on mixture normal process. Conclusion: This study finds out that statistical test for process capability index $C_p$ based on mixture normal process is useful for real application.

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References

  1. Beran, Rudolf. 1984. "Bootstrap Methods in Statistics." Jahresberichtr der Deutschen Mathematiker Vereiningung 86:14-30.
  2. Cho, Joong Jae, Park, Byoung Sun, and Jo, See Heyon. 1996. "Bootstrapping a Unified Process Capability Index." Journal of the Korean Statistical Society 26(4):543-554.
  3. Cho, Joong Jae, Park, Byoung Sun, and Kim, Ju Sung. 1999. "Better Nonparametric Bootstrap Confidence Intervals for Capability Index $C_{pk}$." The Korean Journal of Applied Statistics 12(1):45-65.
  4. Cho, Joong Jae, Park, Byoung Sun, and Park, Hyo-il. 2004. "Better Confidence Limits for Process Capability Index $C_{pmk}$ under the assumption of Normal Process." Journal of the Korean Society for Quality Management 32(4):229-241.
  5. Diciccio, Thomas, and Tibshirani, Robert. 1987. "Bootstrap Confidence Intervals and Bootstrap Approximations." Journal of the American Statistical Association 82:163-170. https://doi.org/10.1080/01621459.1987.10478409
  6. Efron, Bradley. 1979. "Bootstrap Methods: Another look at the Jackknife." Annals of Statistics 7(1):1-26. https://doi.org/10.1214/aos/1176344552
  7. Efron, Bradley, and Tibshirani, Robert. 1993. An Introduction to the Bootstrap. Chapman & Hall.
  8. Franklin, LeRoy, and Wasserman, Gray. 1991. "Bootstrap Confidence Interval Estimate of $C_{pk}$: An Introduction." Communications in Statistics-Simulation and Computation 20(1):231-242 https://doi.org/10.1080/03610919108812950
  9. Franklin, LeRoy, and Wasserman, Gray. 1992. "Bootstrap Lower Confidence Interval Limits for Capability Indices." Journal of Quality Technology 24:196-210. https://doi.org/10.1080/00224065.1992.11979401
  10. Hall, Peter. 1988. "Theoretical Comparison of Bootstrap Confidence Intervals." Annals of Statistics 16:927-953. https://doi.org/10.1214/aos/1176350933
  11. Jeong, Jun Chel. 2011. "Statistical Inference for Process Capability Index $C_{p}$ under a Mixed Normal Distribution." A thesis for the degree of Master, Chungbuk National University.
  12. Kim, Pyong-Koo, and Cho, Joong Jae. 1998. "Some Process Capability Indices using Loss Function under Contaminated Normal Process." Journal of the Korean Society for Quality Management 26(4):65-78.
  13. Lin, P. C., and Pearn, Wen Lea. 2002. "Testing Process Capabiblity for one-sided specification limit with Application to the voltage level translator." Microelectronics Reliability 42:1975-1983. https://doi.org/10.1016/S0026-2714(02)00103-8
  14. Pearn, Wen Lea, Yang, S. L., and Chen, Kuen-Suan. 2001. "Testing Process Capability $C_{pmk}$ with an Application," International Journal of Reliability Quality and Safety Engineering 8(1):15-34. https://doi.org/10.1142/S0218539301000360
  15. Shin, Kyung-Seok, Kim, Seong Jip, and Kang, Chang Wook. 1996. "An Improved Process Incapability Index for the Evaluation of Process Capability." Journal of the Korean Society for Quality Management 24(4):90-102.