DOI QR코드

DOI QR Code

Heuristic Process Capability Indices Using Distribution-decomposition Methods

분포분할법을 이용한 휴리스틱 공정능력지수의 비교 분석

  • Received : 2013.03.15
  • Accepted : 2013.04.29
  • Published : 2013.06.30

Abstract

Purpose: This study develops heuristic process capability indices (PCIs) using distribution-decomposition methods and evaluates the performances. The heuristic methods decompose the variation of a quality characteristic into upper and lower deviations and adjust the value of the PCIs using decomposed deviations in accordance with the skewness. The weighted variance(WV), new WV(NWV), scaled WV(SWV), and weighted standard deviation(WSD) methods are considered. Methods: The performances of the heuristic PCIs are investigated under the varied situations such as various skewed distributions, sample sizes, and specifications. Results: WV PCI is the best under the normal populations, WSD and SWV PCIs are the best under the low skewed populations, NWV PCI is the best under the moderate and high skewed populations. Conclusion: Comprehensive analysis shows that the NWV method is most adequate for a practical use.

References

  1. Abbasi, B., and Niaki, S. T. A. 2010. "Estimating Process Capability Indices of Multivariate Nonnormal Processes." International Journal of Advanced Manufacturing Technology 50(5):823-830. https://doi.org/10.1007/s00170-010-2557-y
  2. Bai, D. S., and Choi, I. S. 1995. "$\bar{X}$ and R Charts for Skewed Populations." Journal of Quality Technology 25(2):120-131.
  3. Baik, J., and Jo, J. 1999. "Criticism and Guideline for the Use of Process Capability Index." Journal of the Korean Society for Quality Management 27(2):81-100.
  4. Bittanti S., Lovera, M., and Moiraghi, L. 1998. "Application of Non-normal Process Capability Indices to Semiconductor Quality Control." IEEE Transactions on Semiconductor Manufacturing 11(2):296-303. https://doi.org/10.1109/66.670179
  5. Castagliola, P. 2000. "$\bar{X}$ Control Chart for Skewed Populations Using a Scaled Weighted Variance Method." International Journal of Reliability, Quality and Safety Engineering 7(3):237-252. https://doi.org/10.1142/S0218539300000201
  6. Chang, Y. S., and Bai, D. S. 2001. "Control Charts for Positively-skewed Populations with Weighted Standard Deviations." Quality and Reliability Engineering International 17(5):397-406. https://doi.org/10.1002/qre.427
  7. Chang, Y. S., and Bai, D. S. 2007. Process Capability Indices, Skewed in Encyclopedia of Statistics in Quality and Reliability. Ruggeri, F., Kenett, R. S., and Faltin, F. W. Ed. England: John Wiley & Sons Ltd.
  8. Chang, Y. S., Choi, I. S., and Bai, D. S. 2002. "Process Capability Indices for Skewed Populations." Quality and Reliability Engineering International 18(5):383-393. https://doi.org/10.1002/qre.489
  9. Chen, J-P. 2000. "Re-evaluating the Process Capability Indices for Non-normal Distribution." International Journal of Production Research 38(6):1311-1324. https://doi.org/10.1080/002075400188861
  10. Cho, J-J, Park, B-S, and Park, H-i. 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.
  11. Choobineh, F., and Ballard, J. L. 1987. "Control-limits of QC Charts for Skewed Distributions Using Weighted-variance." IEEE Transactions on Reliability 36(4):473-477.
  12. English, J. R., and Taylor, G. D. 1993. "Process Capability Analysis - A Robustness Study." International Journal of Production Research 31(7):1621-1635. https://doi.org/10.1080/00207549308956813
  13. Gunter, W. H. 1989. "The Use and Abuse of $C_{pk}$, Part 2." Quality Progress 22(3):769-777.
  14. Im, T. J., and Pyun, S. S. "A Process Capability Index $C_{pd}$ Consistent with the Proportion of Nonconforming Items." Journal of the Korean Society for Quality Management 28(2):103-122.
  15. IMSL Library. 1990. Reference Manual. USA: Visual Numerics.
  16. Khoo, M. B. C., Abdu, M. A., Atta, M. A., and Wu, Z. 2009. "A Multivariate Synthetic Control Chart for Monitoring the Process Mean Vector of Skewed Populations Using Weighted Standard Deviations." Communications in Statistics - Simulation and Computation 38(7):1493-1518. https://doi.org/10.1080/03610910903019905
  17. Kotz, S., and Johnson, N. L. 2002. "Process Capability Indices - A Review, 1992-2000." Journal of Quality Technology 34(1):2-19.
  18. Pearn, W. L., and Kotz, S. 2006. Encyclopedia and Handbook of Process Capability Indices. Singapore: World Scientific Publishing Co. Pte. Ltd.
  19. Pyzdek, T. 1995. "Why Normal Distributors Aren't - All That Normal." Quality Engineering 7(4):769-777. https://doi.org/10.1080/08982119508918823
  20. Somerville, S. E., and Montgomery, D. C. 1996-97. "Process Capability Indices and Non-normal Distributions." Quality Engineering 9(2):305-316. https://doi.org/10.1080/08982119608919047
  21. Wu, C-W, Pearn, W. L., and Kotz, S. 2009. "An Overview of Theory and Practice on Process Capability Indices for Quality Assurance." International Journal of Production Economics 117: 338-359. https://doi.org/10.1016/j.ijpe.2008.11.008
  22. Wu, H-H, Swain, J. J., Farrington, P. A., and Messimer, S. L. 1999. "A Weighted Variance Capability Index for General Non-normal Processes." Quality and Reliability Engineering International 15(5):397-402. https://doi.org/10.1002/(SICI)1099-1638(199909/10)15:5<397::AID-QRE274>3.0.CO;2-N