Process capability analysis of non-normal process data using the Burr XII distribution


This paper proposes a novel modification of Clements’s method using the Burr XII distribution to improve the accuracy of estimates of indices associated with one-sided specification limits for non-normal process data. This work proposes a novel Burr-based method, and compares it with Clements’s method by simulation. Finally, an example application to semiconductor manufacturing is presented.

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  1. 1.

    Kotz S, Johnson NL (1993) Process capability indices. Chapman and Hall, London, UK

  2. 2.

    Montgomery D (1996) Introduction to statistical quality control. Wiley, New York

  3. 3.

    Johnson NL (1949) System of frequency curves generated by methods of translation. Biometrika 36:149–176

    Article  MATH  MathSciNet  Google Scholar 

  4. 4.

    Box GEP, Cox DR (1964) An analysis of transformation. J Roy Stat Soc B 26:211–243

    MATH  MathSciNet  Google Scholar 

  5. 5.

    Somerville S, Montgomery D (1996) Process capability indices and non-normal distributions. Qual Eng 19(2):305–316

    Google Scholar 

  6. 6.

    Clements JA (1989) Process capability calculations for non-normal distributions. Qual Prog 22:95–100

    Google Scholar 

  7. 7.

    Gruska GF, Mirkhani K, Lamberson LR (1989) Non-normal data analysis. Applied Computer Solutions, Inc, St.Clair Shores, Michigan

  8. 8.

    Kotz S, Lovelace CR (1998) Process capability indices in theory and practice. Arnold, London

  9. 9.

    Pern WL, Kotz S (1994) Application of Clements’ method for calculating second and third generation process capability indices for non-normal Pearsonian populations. Qual Eng 7(1):139–145

    Google Scholar 

  10. 10.

    Wu HH, Wang JS, Liu TL (1998) Discussions of the Clements-based process capability indices. In: Proceedings of the 1998 CIIE National Conference, pp 561–566

  11. 11.

    Burr IW (1942) Cumulative frequency distribution. Ann Math Stat 13:215–232

    MATH  MathSciNet  Google Scholar 

  12. 12.

    Burr IW (1973) Parameters for a general system of distributions to match a grid of α3 and α4. Commun Stat 2:1–21

    MATH  MathSciNet  Article  Google Scholar 

  13. 13.

    Zimmer WJ, Burr IW (1963) Variables sampling plans based on non-normal populations. Ind Qual Control July:18–36

    Google Scholar 

  14. 14.

    Rodriguez RN (1977) A guide to the Burr type XII distributions. Biometricka 64:129–134

    Article  MATH  Google Scholar 

  15. 15.

    Burr IW (1967) The effect of non-normality on constants for \(\bar{X}\) and R charts. Ind Qual Control May:563–569

    Google Scholar 

  16. 16.

    Castagliola P (1996) Evaluation of non-normal process capability indices using Burr’s distributions. Qual Eng 8(4):587–593

    Google Scholar 

  17. 17.

    Chou CY, Cheng PH (1997) Ranges control chart for non-normal data. J Chinese Inst Ind Eng 14(4):401–409

    Google Scholar 

  18. 18.

    Yourstone SA, Zimmer WJ (1992) Non-normality and the design of control charts for averages. Decis Sci 23:1099–1113

    Google Scholar 

  19. 19.

    Chou CY, Cheng PH, Liu HR (2000) Economic-statistical design of \(\bar{X}\) charts for non-normal data by considering quality loss. J Appl Stat 27(8):939–951

    Article  MATH  Google Scholar 

  20. 20.

    Wang FK, Kents JB, Zimmer WJ (1996) The maximum likelihood estimation of the Burr XII parameters with censored and uncensored data. Microelectron Reliab 36:359–362

    Article  Google Scholar 

  21. 21.

    Zimmer WJ, Keats JB, Wang FK (1998) The Burr XII distribution in reliability analysis. J Qual Technol 30(4):2–19

    Google Scholar 

  22. 22.

    Ali Mousa MAM, Jaheen ZF (2002) Statistical inference for the Burr model based on progressively censored data. Comput Math Appl 43:1441–1449

    Article  MathSciNet  MATH  Google Scholar 

  23. 23.

    Luo HJ, Shu WY (1999) A nonlinear regression model on the deviations of exposure in the photolithographic process. Dissertation, National Tsing-Hua University

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Correspondence to Fei-Long Chen.

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Liu, PH., Chen, FL. Process capability analysis of non-normal process data using the Burr XII distribution. Int J Adv Manuf Technol 27, 975–984 (2006).

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  • Burr-based method
  • Burr XII distribution
  • Clements’s method
  • Non-normal distributions
  • Process capability index